Karamehmedović, Mirza

Knudsen, Kim

Wriedt, Thomas

Electrical Impedance Tomography (EIT) aims to reconstruct inhomogeneities or inclusions in the interior of a medium based on current and voltage measurements at the boundary of the medium. In many practical applications of EIT, the e±ciency of the employed numerical inversion scheme is an essential parameter. The inversion methods typically evaluate an indicator function in order to estimate whether or not a given point is in the interior of the sought inclusion. The so-called sampling methods donot assume any µa priori knowledge about the boundary condition valid at the inclusion boundary, but the evaluation of their indicator functions can be numerically expensive. On the other hand, decomposition methods express the solution of the Laplace equation in the medium in terms of layer potentials and estimate the inclusion using boundary value error minimisation. However,matching the sources in the potentials with the measured current or voltage at the medium boundary can be numerically costly.We describe a novel method for the reconstruction of perfectly electrically conducting inclusions in arbitrary homogeneous, simply connected media of ¯nite conductivity and with su±ciently smooth boundary. Similarly to the decomposition methods, our approach is based on a boundary layer representation of a solution of the Laplace equation in the medium, and it uses µa prioriknowledge of the boundary condition satisfied at the interface between the inclusion and the medium. However, both of these developments occur at the analytic stage only, and the actual numerical computation involves neither forward-model sources nor boundary-error minimisation. The method requires inclusions to be placed relatively close to the boundary of the medium, andit is well-suited for detection of small inclusions and for detection and partial shape estimation of large inclusions. We give a mathematical justi¯cation for the indicator function used in the inversion method.Also, we illustrate the performance of the method using several numerical examples involving different medium geometries, as well as single and multiple inclusions of different shapes and positions within the medium. Finally, we compare the e±ciency and accuracy of the method to a decomposition scheme based on the Method of Auxiliary Sources

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Downloaded from orbit.dtu.dk on: Dec 20, 2017Numerical Reconstruction of Perfectly Conducting Inclusions from One ElectrostaticBoundary MeasurementKaramehmedovic, Mirza; Knudsen, Kim; Wriedt, ThomasPublication date:2012Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Karamehmedovic, M., Knudsen, K., & Wriedt, T. (2012). Numerical Reconstruction of Perfectly ConductingInclusions from One Electrostatic Boundary Measurement. Abstract from 31st Progress In ElectromagneticsResearch Symposium, Kuala Lumpur, Malaysia.Session 3P3aElectromagnetic Inverse Problems in Medicine andBiologyImage Reconstruction in Electric Field Tomography (EFT)Alexander V. Korjenevsky, T. S. Tuykin, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630Overview of Electric Field Tomography Experiments in RussiaVladimir Alekseevich Cherepenin, Alexander V. Korjenevsky, T. S. Tuykin, . . . . . . . . . . . . . . . . . . . . . . . . . 631Using Memristive Elements for Modeling Electrical Properties of Biological TissueOrjan G. Martinsen, Sverre Grimnes, Carsten A. Lu¨tken, Gorm Krogh Johnsen, . . . . . . . . . . . . . . . . . . 632Numerical Reconstruction of Perfectly Conducting Inclusions from One Electrostatic Boundary Measure-mentMirza Karamehmedovic, Kim Knudsen, Thomas Wriedt, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633The Impact of Model Mismatch Errors on Magnetic Induction Tomography Inverse ProblemDoga Gu¨rsoy, H. Scharfetter, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634A Software Based Framework for Estimating Patient Displacement in Magnetic Induction TomographyMamatjan Yasin, M. Ali Roula, Doga Gursoy, Andy Adler, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635629630 Progress In Electromagnetics Research Symposium Abstracts, KL, MALAYSIA, March 27–30, 2012Image Reconstruction in Electric Field Tomography (EFT)A. Korjenevsky and T. TuykinKotel’nikov Institute of Radioengineering & Electronics of the RAS, RussiaAbstract— The electric field tomography is relatively new imaging method applicable forbiomedical applications. It uses interaction of alternating electric field with the conducting me-dia to obtain information about the spatial distribution of its conductivity without electricalcontact with the object. The method is based on the Maxwell-Wagner relaxation phenomenon,i.e., finite relaxation time of the nonequilibrium free charges in the conductor. This phenomenonleads to the phase shift of the alternating electric field outside the object depending on its inter-nal electrical properties and geometry. Measuring such phase shifts using multiple transmittingand receiving electrodes enables to reconstruct internal structure of the object. Mathematicallysuch reconstruction procedure consists of solving the inverse problem for Laplace equation withinhomogeneous complex permittivity. While this inverse problem is ill-posed and nonlinear ingeneral, fast and robust linearized algorithms are most interesting for the practical system imple-mentation. Forming of the appropriate reconstruction matrix converting measured phase shiftsinto image is possible in various ways. One of them is single step regularized Gauss-Newtonmethod. Another is least squares optimization using extensive training data sets comprised ofdifferent distributions of properties and corresponding simulated results of measurement withappropriate noise added. Such approach is known as linear artificial neural network also. Oneof the popular heuristic algorithms is back projection. It is based on known spatial localizationof the most sensitive areas for each transmitter-receiver pair. We have implemented successfullythe back projection method for EFT taking into account that sensitivity is localized near the lineof electric field connecting the active and sensing electrodes. Corresponding results of numericalsimulation and applying the algorithm to the experimental data are demonstrated. The linearneural networks are considered also as very promising for EFT image reconstruction.Progress In Electromagnetics Research Symposium Abstracts, KL, MALAYSIA, March 27–30, 2012 631Overview of Electric Field Tomography Experiments in RussiaVladimir A. Cherepenin, Alexander V. Korjenevsky, and Timur S. TuykinThe Institute of Radioengineering and Electronics of Russian Academy of SciencesStreet Mokhovaya 11-7, Moscow 125009, RussiaAbstract— The paper introduces EFT operational principal briefly and overviews EFT exper-iments in Russia.EFT based on the Maxwell-Wagner relaxation phenomenon accompanying redistribution of nonequi-librium free charges carriers inside the inhomogeneous conductive object. It is a new kind ofquasistatic electro-magnetic tomography suitable for contactless imaging of biological objects.The first single-channel measuring EFT system and set of experiments are discussed. Singlechannel experiments proved EFT theory and shown possibility to obtain data required for EFTrealization.The first multi-channel measuring system for EFT is described. Experiments on imaging of a testobjects with different geometry and electrical properties are presented. The first EFT imagesobtained experimentally are given and discussed.632 Progress In Electromagnetics Research Symposium Abstracts, KL, MALAYSIA, March 27–30, 2012Using Memristive Elements for Modeling Electrical Properties ofBiological TissueØrjan G. Martinsen1, 2, Sverre Grimnes1, 2, Carsten A. Lu¨tken1, and Gorm Krogh Johnsen11Department of Physics, University of Oslo, N-0316 Oslo, Norway2Department of Clinical and Biomedical EngineeringOslo University Hospital, Rikshospitalet, N-0372 Oslo, NorwayAbstract— The memristor was predicted by Leon O. Chua to exist on purely theoreticalgrounds many years ago [1], but was not realized in the laboratory as a physical, electronic nano-component until 2009 [2]. The memristor is treated as an elementary passive circuit element,complementing resistors, coils, and capacitors (RLC), whose memristance M(q) = dφ/dq = v/iis defined by how the magnetic flux φ =∫v(t)dt responds to the charge dq = idt transported bythe electrical current i(t).Later the concept was expanded to memristive systems [3], which are generalizations of thememristor concept where the memristance is controlled by a number of state variables. Fur-thermore, in 2009 the theory was further expanded by Di Ventra et al. to memcapacitance andmeminductance [4].We show that electro-osmosis in human sweat ducts is of memristive nature and that memristorstherefore will be important when modeling electrical properties of human skin. We also show thatdielectric dispersion in biological tissue is of memcapacitive nature and that nonlinear phenomenaprobably play a significant role in the overall electrical properties of biomaterials.Progress In Electromagnetics Research Symposium Abstracts, KL, MALAYSIA, March 27–30, 2012 633Numerical Reconstruction of Perfectly Conducting Inclusions fromOne Electrostatic Boundary MeasurementMirza Karamehmedovic´1, Kim Knudsen2, and Thomas Wriedt11Department of Process and Chemical Engineering, University of Bremen, Germany2Department of Mathematics, Technical University of Denmark, DenmarkAbstract— Electrical Impedance Tomography (EIT) aims to reconstruct inhomogeneities orinclusions in the interior of a medium based on current and voltage measurements at the boundaryof the medium. In many practical applications of EIT, the efficiency of the employed numericalinversion scheme is an essential parameter.The inversion methods typically evaluate an indicator function in order to estimate whether ornot a given point is in the interior of the sought inclusion. The so-called sampling methods donot assume any a` priori knowledge about the boundary condition valid at the inclusion boundary,but the evaluation of their indicator functions can be numerically expensive. On the other hand,decomposition methods express the solution of the Laplace equation in the medium in terms oflayer potentials and estimate the inclusion using boundary value error minimisation. However,matching the sources in the potentials with the measured current or voltage at the mediumboundary can be numerically costly.We describe a novel method for the reconstruction of perfectly electrically conducting inclusionsin arbitrary homogeneous, simply connected media of finite conductivity and with sufficientlysmooth boundary. Similarly to the decomposition methods, our approach is based on a boundarylayer representation of a solution of the Laplace equation in the medium, and it uses a` prioriknowledge of the boundary condition satisfied at the interface between the inclusion and themedium. However, both of these developments occur at the analytic stage only, and the actualnumerical computation involves neither forward-model sources nor boundary-error minimisation.The method requires inclusions to be placed relatively close to the boundary of the medium, andit is well-suited for detection of small inclusions and for detection and partial shape estimationof large inclusions.We give a mathematical justification for the indicator function used in the inversion method.Also, we illustrate the performance of the method using several numerical examples involvingdifferent medium geometries, as well as single and multiple inclusions of different shapes andpositions within the medium. Finally, we compare the efficiency and accuracy of the method toa decomposition scheme based on the Method of Auxiliary Sources.634 Progress In Electromagnetics Research Symposium Abstracts, KL, MALAYSIA, March 27–30, 2012The Impact of Model Mismatch Errors on Magnetic InductionTomography Inverse ProblemD. Gu¨rsoy and H. ScharfetterGraz University of Technology, AustriaAbstract— Magnetic induction tomography (MIT) is a non-invasive and non-contact imagingmodality that attempts to reconstruct the internal conductivity distribution of the human body.It promises to facilitate diagnosis of several physiological disorders such as edema or internalhemorrhage and has the potential to be used for continuous monitoring of physiological uids.Several features of the device such as high-speed data acquisition, portability and comparablyinexpensiveness make the proposed modality attractive.In MIT, an array of coils is used to induce eddy-currents inside the body and the magnetic fieldsare recorded outside using an array of magnetic sensors. The corresponding inverse problemis defined as the reconstruction of conductivity distribution from the measured magnetic fieldsand is generally stated based on the minimization of the Euclidean norm of the data misfit term.Therefore, small differences between the modeled and true coil geometry induce errors in the datamisfit and generate artifacts in images. In this study, we performed a simulation study to analyzethe impact of modeling errors on measured data and corresponding conductivity reconstructions.For the analysis, we considered two different cases of coil geometry distortions: the displacementof coils from ideal positions and rotation of coils. We generated synthetic data by using a typical16-channel MIT system coil arrangement. We indexed the worst receiver channels in terms ofsusceptibility to distortion errors in data and in the corresponding reconstructed images. Itwas found that slight geometrical distortions of the coils may cause significant deviations in thedata considering local and small perturbations in conductivity. It was showed that the imagingartifacts appear on the proximity of the boundary of the conducting object.Progress In Electromagnetics Research Symposium Abstracts, KL, MALAYSIA, March 27–30, 2012 635A Software Based Framework for Estimating Patient Displacementin Magnetic Induction TomographyMamatjan Yasin1, Ali Roula2, Doga Gu¨rsoy3, and Andy Adler11Carleton University, Ottawa, K2E7E8, Canada2University of Glamorgan, Pontypridd, CF371DL, UK3Graz University of Technology, Graz, A-8010, AustriaAbstract— Magnetic Induction Tomography (MIT) is a contactless, inexpensive and non-invasive technique for imaging the conductivity distribution inside volume conductors. Time-difference imaging can be used for the monitoring of patients in critical care. This includesmonitoring of cerebral strokes and breathing (aeration and ventilation of the lung), as well as con-tinuous screening of oedema. However, MIT signals are much more sensitive to body movementsthan to the conductivity changes inside of the body. This is because small movements duringMIT measurements can overwhelm the signals of interest and cause significant image artefacts.Thus, it is crucial to accurately estimate and factor body movements into image reconstruction.Movement estimation is nonetheless a challenging problem due to 3 possible translations (alongx, y and z axis) and rotations which can cause significant signal magnitude changes as well asphase shifts.Methods: We proposed algorithmic methods for identifying and estimating object movementsfrom simulated MIT data prior to the image reconstruction step. A simulation was performedbased on a 16 channel MIT system where a finite-difference based MIT software package wasused to (i) generate reference data without a target and movement, and (ii) simulate whole tankmovement with a target placed close to edge of the tank. The homogenous tank (radius of13.5 cm and height of 20 cm) has the conductivity of 1 Sm−1, and the small cubic target has theconductivity of 3 Sm−1. The movement was estimated using frequency domain analysis (FFTand Wavelet), and statistical approaches (Independent Component Analysis (ICA)) that usedtraining data on various displacements. Once movements are identified, images are reconstructedby (i) minimizing movement artefacts for small movements; (ii) compensating for the movementsif these are accurately estimated, or (iii) taking a new MIT measurement if movements are toosevere.Results: Results show that movements of 1% of the radius of the tank cause image blurringbut the artifacts can be minimized by regularization. Higher movements totally distorted imageswhich require artifact compensation or acquisition of new measurements.The percentage errorsfor FFT based movement estimation were 35%, 0.3% and 6% for a displacement of 1% (1.3mm),5% (6.7mm) and 10% (13.5mm) respectively where the displacement was chosen relative to theradius of the tank. ICA and wavelet approaches also produced similar results to the FFT basedapproach. It was also found that the accuracy of movement estimation was found to be relatedto the size of the background in real measurements.636 Progress In Electromagnetics Research Symposium Abstracts, KL, MALAYSIA, March 27–30, 2012

Numerical Reconstruction of Perfectly Conducting Inclusions from One Electrostatic Boundary Measurement

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Numerical Reconstruction of Perfectly Conducting Inclusions from One Electrostatic Boundary Measurement

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