Выбор математической модели объекта исследования в электроимпедансной томографии

Зроблено огляд наукових праць, що стосуються питань моделювання досліджуваних об’єктів у разі електроімпедансної томографії. Спираючись на тривимірність процесів, які відбуваються в об’єктах дослідження при застосуванні електроімпедансних томографів, показано, що для адекватного моделювання об’єктів дослідження необхідно застосовувати квазістатичний або повнопольовий електродинамічні підходи.Introduction. A brief review of scientific publications relating to questions of the object for study modeling that implements the EIT methods is given. Formulation of the problem. EIT features associated with three-dimensionality of processes taking place in the study objects during the measurement and the complexity of the reconstruction process are shown. A comparative analysis of the quasi-static and full-wave model of the object for study is presented. Conclusion. Based on three-dimensional processes that take place in the study objects using EIT has shown that adequate models of study objects should be based on quasi-static or full-wave electrodynamics approaches.Выполнен обзор научных работ, касающихся вопросов моделирования исследуемых объектов в электроипедансной томографии. С учетом трехмерности процессов, происходящих в исследуемых объектах при использовании электроимпедансных томографов, показано, что для адекватного моделирования объектов исследования необходимо применять квазистатический или полнополевой электродинамические подходы

Direct EIT Reconstructions of Complex Admittivities on a Chest-Shaped Domain in 2-D

Electrical impedance tomography (EIT) is a medical imaging technique in which current is applied on electrodes on the surface of the body, the resulting voltage is measured, and an inverse problem is solved to recover the conductivity and/or permittivity in the interior. Images are then formed from the reconstructed conductivity and permittivity distributions. In the 2-D geometry, EIT is clinically useful for chest imaging. In this work, an implementation of a D-bar method for complex admittivities on a general 2-D domain is presented. In particular, reconstructions are computed on a chest-shaped domain for several realistic phantoms including a simulated pneumothorax, hyperinflation, and pleural effusion. The method demonstrates robustness in the presence of noise. Reconstructions from trigonometric and pairwise current injection patterns are included

Electrical impedance imaging in two-phase, gas-liquid flows: 1. Initial investigation

The determination of interfacial area density in two-phase, gas-liquid flows is one of the major elements impeding significant development of predictive tools based on the two-fluid model. Currently, these models require coupling of liquid and vapor at interfaces using constitutive equations which do not exist in any but the most rudimentary form. Work described herein represents the first step towards the development of Electrical Impedance Computed Tomography (EICT) for nonintrusive determination of interfacial structure and evolution in such flows

Imaging and inverse problems of electromagnetic nondestructive evaluation

Electromagnetic nondestructive evaluation (NDE) is used widely in industry to assess the character of structures and materials noninvasively. A major aspect of any NDE system is solving the associated inverse problem to characterize the material under study. The solution of the inverse problem is directly related to the physics of a particular electromagnetic NDE system which can be either fully dynamic, quasistatic, or static depending on the operating frequency and material parameters. In a general electromagnetic NDE system, indirect inversion techniques which utilize large amounts of a priori knowledge and some type of calibration scheme are employed to characterize materials. However, in certain test situations the governing physics of an electromagnetic NDE system allow direct inversion techniques to be employed which can be used to image flaws in a material. There has, however, been research which attempts to utilize direct inversion methods which do not rely on the underlying physics of the electromagnetic NDE system;This dissertation first describes the importance of the underlying physics to the solution of the electromagnetic NDE inverse problem. In this context, the inverse problem of fully dynamic electromagnetic NDE and magnetoquasistatic (MQS) NDE are developed to elucidate their underlying mathematical and physical properties. It is shown that the inverse problem for MQS phenomena is generally much more difficult than that of fully dynamic electromagnetic phenomena. Experiments are conducted which utilize fully dynamic millimeter wave NDE and MQS eddy current NDE to compare and contrast the physics and inverse problem of each technique. Two methods are then examined as a possible means of inverting MQS data with direct techniques. A transformation from diffusion to waves is examined as a method of inverting MQS data as a pseudo-wave field. An analytic inversion of the transformation is developed and used to gain insight into robustness issues associated with the method. Also, an averaging scheme is developed to increase the robustness of the transformation. Next, a technique is developed which utilizes phase shifts of steady state eddy current impedance measurements to directly image subsurface flaws in electrically conducting materials. A 1-D analytic study and a 2-D finite element simulation are used to gain insight into the underlying physics associated with the method. A modification to the technique is developed which utilizes the finite element model to account for phase distortions associated with the induced eddy currents in a test sample. An experiment is then carried out to demonstrate this direct inversion technique on actual eddy current data;The results of this study show that the use of direct inversion methods for imaging electromagnetic NDE must be carried out with a clear understanding of the underlying physical phenomena. There are many instances where direct inversion schemes can be applied to fully dynamic electromagnetic fields. Due to physical limitations associated with MQS phenomena, direct inversion methods are not generally applicable to MQS data. However, a transformation technique is shown to be a potential means for utilizing direct inversion techniques on MQS. A second direct inversion technique introduced for MQS data has potential for imaging subsurface flaws in electrically conducting materials. There are, however, severe limitations to both inversion methods which reduce their usefulness

Advanced electrode models and numerical modelling for high frequency Electrical Impedance Tomography systems

The thesis discusses various electrode models and finite element analysis methods for Electrical Impedance Tomography (EIT) systems. EIT is a technique for determining the distribution of the conductivity or admittivity in a volume by injecting electrical currents into the volume and measuring the corresponding potentials on the surface of the volume. Various electrode models were investigated for operating EIT systems at higher frequencies in the beta-dispersion band. Research has shown that EIT is potentially capable to distinguish malignant and benign tumours in this frequency band. My study concludes that instrumental effects of the electrodes and full Maxwell effects of EIT systems are the major issues, and they have to be addressed when the operating frequency increases. In the thesis, I proposed 1) an Instrumental Electrode Model (IEM) for the quasi-static EIT formula, based on the analysis of the hardware structures attached to electrodes; 2) a Complete Electrode Model based on Impedance Boundary Conditions (CEM-IBC) that introduces the contact impedances into the full Maxwell EIT formula; 3) a Transmission line Port Model (TPM) for electrode pairs with the instrumental effects, the contact impedance, and the full Maxwell effects considered for EIT systems. Circuit analysis, Partial Differential Equations (PDE) analysis, numerical analysis and finite element methods were used to develop the models. The results obtained by the proposed models are compared with widely used Commercial PDE solvers. This thesis addresses the two major problems (instrumental effects of the electrodes and full Maxwell effects of EIT systems) with the proposed advanced electrode models. Numerical experiments show that the proposed models are more accurate in the high frequency range of EIT systems. The proposed electrode models can be also applicable to inverse problems, and the results show promising. Simple hardware circuits for verifying the results experimentally have been also designed

Evaluation of 3D current injection patterns for human lung monitoring in electrical impedance tomography

Electrical impedance tomography (EIT) is a non-invasive imaging technique for monitoring the lungs continuously. During EIT Measurements, currents propagate intrinsically in 3D, since electrical current propagates diffusely in the human tissues, so a 2D EIT remains not sufficient to study the out-of-electrodes plane effects on the images. Until now, not enough effort has been made to evaluate the performance of 3D measurement patterns for lung monitoring. In this paper, to investigate 3D current injection patterns for 3D EIT, a 3D model mimicking the geometrical and electrical characteristics of the human thorax has been developed based on Finite Element Method (FEM) along with the Complete Electrode Model (CEM). Simulations have been performed with aligned (“planar,” “zigzag”, “square”, “zigzag opposite”, and “planar opposite”), and offset (“planar offset”, and “zigzag offset”) current injection patterns. Analysis shows the greatest current density diffusion results using the “zigzag opposite” current injection pattern

Forward and Inverse Modelling of Magnetic Induction Tomography (MIT) for Biomedical Application

Cette thèse développe un outil de simulation destiné au design d'instruments de tomographie par induction magnétique (MIT pour Magnetic Induction Tomography). Ce simulateur permet d'investiguer la possibilité d'utiliser la méthode d'imagerie par tomographie par induction magnétique afin de faire la conception d'un dispositif sans-contact capable de détecter une hémorragie à l'intérieur du crâne humain. La méthode spécifique de calcul numérique utilisée pour la simulation du dispositif de même que le calcul de la sensibilité avec la méthode directe (introduite dans cette thèse) et la résolution du problème inverse, qui construit une carte de la conductivité à partir des résultats de simulation, sont optimisés afin de simuler un dispositif opérant à 50 kHz. Ce dispositif est capable de détecter le changement de la conductivité dans une gamme se rapprochant de celle des tissus biologiques. Le fonctionnement de base de la tomographie par induction magnétique repose sur les mesures des propriétés électromagnétiques dites passives telles que la conductivité. L'utilisation d'une telle méthode pour détecter les hémorragies cérébrales se justifie par le fait que la conductivité du sang est plus élevée que la conductivité des autres tissus constituant le cerveau. Une autre application potentielle de cette méthode est le suivi en temps réel, de manière non invasive,de l'altération des tissus qui peut s'observer à partir d'un changement de conductivité, par exemple les problèmes respiratoires, la guérison de plaies ainsi que les processus ischémiques. Les bobines d'induction dans le dispositif de tomographie par induction magnétique produisent un champ magnétique primaire dans la région d'intérêt (ROI pour Region of Interest)et ce champ alternatif induit des courants alternatifs (courants de Foucault) dans les régions conductrices. Ces courants induits produisent à leur tour un champ magnétique secondaire dans la région d'intérêt. Ce champ magnétique secondaire produit un champ aux bobines de réception qui est utilisé pour reconstruire la distribution de la conductivité dans la région d'intérêt. Un défi important concernant l'état de l'art de ces dispositifs est la détection du signal secondaire en présence du signal primaire, qui est plusieurs ordres de grandeur plus fort. Le dispositif présente utilise une géométrie pour l'induction et la détection spécialement conçue pour opérer dans les basses fréquences avec un ratio signal sur bruit acceptable de même qu'une configuration du détecteur qui est moins sensible au champ primaire. La méthode directe du calcul de la matrice de sensibilité introduite dans cette thèse nous fournit une méthode numérique robuste pour la reconstruction d'images, ce qui résulte en une qualité d'image supérieure par rapport aux autres méthodes proposées dans la littérature.----------Abstract This thesis develops a simulation package for the design of Magnetic Induction Tomography (MIT) instruments and exploit the simulator to investigate the possibility of using the magnetic induction tomography imaging method to design a non-contact device capable of detecting a blood hemorrhage inside the skull. The specific numerical method (full Maxwell's equation) used for simulation of the device, followed by calculation of the sensitivity with the direct method (introduced in this dissertation) and a regularized inverse solver which reconstruct the conductivity map from the simulation outputs (magnetic field), are optimized to simulate a device operating at 50 kHz. This device is capable of detecting the change in conductivity in ranges close to biological tissues. MIT operates based on the measurement of passive electromagnetic properties such as conductivity. The rationale behind using this method for detecting cerebral stroke is based on the fact that the conductivity of the blood is larger than that of the other tissues in the head. Other potential medical applications for this device are real-time, non-invasive monitoring of tissue alterations which are refected in the change of the conductivity, e.g. ventilation disorders, wound healing and ischemic processes. The inductive coils in the MIT device produce a primary magnetic field in the region of interest (ROI) and this alternating magnetic field induces alternating (eddy) currents in the conductive regions. These eddy currents, in turn, generate a secondary magnetic field in the ROI. This secondary magnetic field generates a field at the receivers, which is used to reconstruct the conductivity distribution of the ROI. An important challenge in the state of art devices is the detection of the secondary signal in the presence of the primary signal, which is orders of magnitude stronger. The device uses a geometry in induction and detection designed to operate in low frequencies with acceptable SNR and detector configuration that is least sensitive to the primary field. The direct method of calculating the sensitivity matrix introduced in this thesis provides us with a robust numerical method for image reconstruction which results in superior image quality compared to other proposed methods in the state of the art. The proposed configurations involves a cylindrical shape device with 6 concentric excitation coils which are located at different heights on the outer surface of the cylinder. These coils produce a primary magnetic �eld with majority of the field lines parallel to the main axis of the cylinder, where we position the object of interest. This primary field induces eddy currents (conduction and displacement current) in the conductive regions of the ROI, which generate a secondary magnetic field

An Investigation of Microwave Tomography Technique to Image Brain Tumour Through Cross-Section Imaging with Different Number of Electrode

Brain tumours resulted from the irregular growth and cell division within the skull, indicating a high risk for malignancies to develop and can lead to brain injury or even death. The brain tumour can affect nervous system’s function based on the tumour’s growth rate and location. Early detection of brain tumour is essential to improve patients’ survival rates through appropriate medical care. As the current clinical imaging has a few impediments e.g.  radiation-based and expensive, tomography technique is seen possible to provide safe and inexpensive technology. The aim of this research is to investigate the feasibility of brain tumour detection using microwave tomography technique with different numbers of electrodes. The 2D finite element modelling approach is applied, and the images are reconstructed using a linear back projection (LBP) algorithm in MATLAB. A different number of rectangular sensing electrodes are arranged around the head phantom in an elliptical array, working in pairs as transmitters and receivers. The simulation shows that the system is able to detect the permittivity difference, thus detecting the existence of the tumour in the head phantom.Theimage reconstruction presented promising tumour images with an 8-antenna microwave tomography system at all locations, i.e. left, right, top, centre, and bottom, in comparison to 4-antenna and 12-antenna systems. &nbsp

An Investigation of Microwave Tomography Technique to Image Brain Tumour Through Cross-Section Imaging with Different Number of Electrode

Brain tumours resulted from the irregular growth and cell division within the skull, indicating a high risk for malignancies to develop and can lead to brain injury or even death. The brain tumour can affect nervous system’s function based on the tumour’s growth rate and location. Early detection of brain tumour is essential to improve patients’ survival rates through appropriate medical care. As the current clinical imaging has a few impediments e.g.  radiation-based and expensive, tomography technique is seen possible to provide safe and inexpensive technology. The aim of this research is to investigate the feasibility of brain tumour detection using microwave tomography technique with different numbers of electrodes. The 2D finite element modelling approach is applied, and the images are reconstructed using a linear back projection (LBP) algorithm in MATLAB. A different number of rectangular sensing electrodes are arranged around the head phantom in an elliptical array, working in pairs as transmitters and receivers. The simulation shows that the system is able to detect the permittivity difference, thus detecting the existence of the tumour in the head phantom.Theimage reconstruction presented promising tumour images with an 8-antenna microwave tomography system at all locations, i.e. left, right, top, centre, and bottom, in comparison to 4-antenna and 12-antenna systems. &nbsp