Problem Of Magnetic Induction Tomography Research Articles

Solution of 2D MIT Forward Problem by Considering Skin and Proximity Effects in Coils

Previous studies on the forward problem of magnetic induction tomography (MIT) have used simplified Maxwell's equations which assume a constant and position-independent total current density (TCD) inside the coils (ignoring skin effect). Moreover, they assume that TCD is independent of relative position of the coils (ignoring proximity effect). This article presents an improved finite element (FE) modeling for the two-dimensional (2D) forward problem of MIT by incorporating skin and proximity effects in the exciter and sensor coils. Consideration of skin and proximity effects requires the use of a position-dependent TCD in Maxwell's equations inside the coil domain. The FE method implementation of the improved forward method is validated with a simple analytical test problem. To evaluate the performance of the improved method in possible medical and industrial applications with low conductivity regions, a 16 coils 2D MIT system is modeled and the FE method is employed to solve the forward problem using a synthetic phantom. Results show the difference between the real parts of induced voltages obtained from the early and improved method falls into the range which is meaningful in terms of achievable conductivity contrast from the improved one. This discrepancy can generate considerable errors in image reconstruction. By considering skin and proximity effects, the improved method generates lower voltages in the coils suggesting the use of more precise hardware to detect inclusion. Findings show the importance and necessity of using improved method for modeling 2D MIT coils especially at low conductivity applications where measured signals are inherently weak.

Solution of the inverse problem of magnetic induction tomography based on Helmholtz coil

Magnetic induction tomography is a contactless technique that can measure conductivity distribution in biological tissues. This study proposed that Helmholtz coils as the excitation coils will generate a set of uniform excitation fields. The system model consists of a circular background area, a circular disturbance object, a set of Helmholtz coils, and eight magnetic detection coils. The diameter of the Helmholtz coil is 200 mm. The detection coil is a square, and its side length is 12 mm. The excitation current of the system is 30 mA, and the frequency is 10 MHz. This study discusses the reconstructed images of different locations, different volumes, different distances, and different electrical conductivities of perturbation bodies. The anti-noise ability of different noise signals is also analysed. Finally, the image differences are evaluated through structural similarity index (SSIM). The results show that the algorithm can distinguish the position and volume characteristics of the target object. However, when the volume of the target object is low, the position will be deviated. This algorithm can distinguish the position of the two, which is far away from each other.

Shape sensitivities for an inverse problem in magnetic induction tomography based on the eddy current model

In this paper the shape derivative of an objective depending on the solution of an eddy current approximation of Maxwell’s equations is obtained. Using a Lagrangian approach in the spirit of Delfour and Zolésio, the computation of the shape derivative of the solution of the state equation is bypassed. This theoretical result is applied to magnetic impedance tomography, which is an imaging modality aiming at the contactless mapping (identification) of the unknown electrical conductivities inside an object given measurements recorded by receiver coils.

Analysis and Imaging in Magnetic Induction Tomography using the Impedance Method

This article discusses the utilization of the impedance method in computation of the forward problem in magnetic induction tomography (MIT). The algorithms for the inverse problem were also developed. The new approach for solving the resulting ill-conditioned linear system of the inverse problem is proposed and the quality of images obtained is discussed based on a quality index proposed in the literature. The results show the prevalence of TAS in relation to linear correlation between the real image and obtained image. With respect to contrast TRT prevalece in relation TAS. The indices of average luminance presents similarity for the both methods. TAS prevails for smaller objects and TRT for larger objects, showing the greater robustness of TAS.

A New Hybrid Image Reconstruction Algorithm for Magnetic Induction Tomography

A new hybrid algorithm is presented in this paper, which solves the ill-posed inverse problem of magnetic induction tomography (MIT) and improves the quality of reconstructed image. The hybrid algorithm firstly produces the preliminary image region using Tikhonov regularization algorithm, and then it obtains the final reconstructed image using variation regularization algorithm. The hybrid algorithm, compared with the Tikhonov regularization algorithm and the variation regularization algorithm, overcomes the numerical instability of MIT image reconstruction and accelerates the convergence speed of image reconstruction, and it also improves the resolving power of targets conductor and the quality of the reconstructed image. Simulation results show that the quality of the reconstructed image obtained using the hybrid algorithm is enhanced, so an effective algorithm for magnetic induction tomography (MIT) is introduced.

Boundary integral formulations for the forward problem in magnetic induction tomography

In this paper we present two models for the forward problem of magnetic induction tomography. In particular, we describe the eddy current model, and a reduced simplified model. The error between the reduced and the full model is analyzed in dependence of parameters such as the frequency and the conductivity. In the case of a piecewise constant conductivity we derive a boundary integral formulation for the reduced model. Finally, we comment on numerical results for the forward problem and give a comparison of both models. Copyrightcopyright 2011 John Wiley & Sons, Ltd.

Numerical calculation of the eddy current problem in magnetic induction tomography for brain edema

Magnetic induction tomography is considered to be valuable in medical application of testing brain edema. In this paper, we use the edge finite element method with electric fiel d intensity E as the vector variable to simulate a multi-channel measuring system based on a real human brain finite element mo del. In simulation, we change the conductivity of brain edema and the frequency of exciting current to research the performance of the multi-channel measuring system in testing the brain edema.

A Method to Solve the Forward Problem in Magnetic Induction Tomography Based on the Weakly Coupled Field Approximation

Magnetic induction tomography (MIT) is a noninvasive modality for imaging the complex conductivity (kappa = sigma + jomegaepsilon) or the magnetic permeability (mu) of a target under investigation. Because MIT employs noncontact coils for excitation and detection, MIT may be suitable for imaging biological tissues. In medical applications where high resolutions are sought, image reconstruction is a time and memory consuming task because the associated inverse problem is nonlinear and ill-posed. The time and memory constraints are mainly imposed by the solution of the forward problem within the iterative image reconstruction procedure. This paper investigates the application of a weakly coupled approximation to the solution of the forward problem and examines the accuracy against the computation time and memory gained in adopting this approximation. Initially, an analytical solution for mutual impedance change of a coil pair due to a large planar conductive object is presented based on a full wave theory and used to demonstrate a 10 MHz frequency excitation as an acceptable upper frequency limit under which the approximation is valid. Subsequently, a numerical impedance method adopting the approximation is presented. Here the impedance method is used to solve the forward problem, which employs electrical circuit analogues to mesh the target into a network that can be solved using circuit analysis and sparse matrix technique. The error due to the approximation is further estimated numerically with the impedance method against a commercial finite-element package (commercial FE solver, COMSOL) and results show at 10 MHz excitation a 0.4% of tolerance is achieved for conductivities in the range <0.5 S/m. The results also show the method can be applied for low conductivity medical applications and is computationally efficient compared to equivalent finite-element methods.

Solution of three dimensional inverse problem of magnetic induction tomography using Tikhonov regularization method

Magnetic induction tomography, highly promising imaging technique for medical purposes, applies a magnetic field from an exciter to induce eddy currents in the object of low conductivity, and the magnetic field from these is then detected by a sensor. The induced eddy currents are proportional to the conductivity distribution. This paper deals with the solution of the fundamental inverse problem existing in magnetic induction tomography, which consists in the reconstruction of the eddy currents distribution basing on the magnetic field measurements. The problem has been solved by the Tikhonov regularization method. The choice of the regularization parameter and the accuracy of the proposed method have also been discussed.

A Model for the Forward Problem in Magnetic Induction Tomography Using Boundary Integral Equations

We propose a new formulation for the forward problem in magnetic induction tomography (MIT). We formulate the problem in terms of interior and exterior boundary integral equations (BIEs), subject to appropriate boundary conditions. We then transform a standard exterior BIE involving the magnetic vector potential to a BIE involving the electric fields. This transformation eliminates two boundary conditions involving the magnetic vector potential and its normal derivative. This greatly reduces the computational complexity of the model. Here, we compare numerical solutions of the model to analytical solutions.

Solution of the inverse problem of magnetic induction tomography (MIT) with multiple objects: analysis of detectability and statistical properties with respect to the reconstructed conducting region

Magnetic induction tomography (MIT) is a technique to image the passive electrical properties (i.e. conductivity, permittivity, permeability) of biological tissues. The inverse eddy current problem is nonlinear and ill-posed, thus a Gauss–Newton one-step method in combination with four different regularization schemes is used to obtain stable solutions. Simulations with 16 excitation coils, 32 receiving coils and different spherical perturbations inside a homogeneous cylinder were computed. In order to compare the statistical properties of the reconstructed results a Monte Carlo study with a SNR of 40 dB and 20 dB was carried out. Simulated conductivity perturbations inside a homogeneous cylinder can be localized and resolved and the results prove the feasibility of difference imaging with MIT.

Solution of the inverse problem of magnetic induction tomography (MIT)

Magnetic induction tomography (MIT) of biological tissue is used to reconstruct the changes in the complex conductivity distribution inside an object under investigation. The measurement principle is based on determining the perturbation ΔB of a primary alternating magnetic field B0, which is coupled from an array of excitation coils to the object under investigation. The corresponding voltages ΔV and V0 induced in a receiver coil carry the information about the passive electrical properties (i.e. conductivity, permittivity and permeability). The reconstruction of the conductivity distribution requires the solution of a 3D inverse eddy current problem. As in EIT the inverse problem is ill-posed and on this account some regularization scheme has to be applied. We developed an inverse solver based on the Gauss–Newton-one-step method for differential imaging, and we implemented and tested four different regularization schemes: the first and second approaches employ a classical smoothness criterion using the unit matrix and a differential matrix of first order as the regularization matrix. The third method is based on variance uniformization, and the fourth method is based on the truncated singular value decomposition. Reconstructions were carried out with synthetic measurement data generated with a spherical perturbation at different locations within a conducting cylinder. Data were generated on a different mesh and 1% random noise was added. The model contained 16 excitation coils and 32 receiver coils which could be combined pairwise to give 16 planar gradiometers. With 32 receiver coils all regularization methods yield fairly good 3D-images of the modelled changes of the conductivity distribution, and prove the feasibility of difference imaging with MIT. The reconstructed perturbations appear at the right location, and their size is in the expected range. With 16 planar gradiometers an additional spurious feature appears mirrored with respect to the median plane with negative sign. This demonstrates that a symmetrical arrangement with one ring of planar gradiometers cannot distinguish between a positive conductivity change at the true location and a negative conductivity change at the mirrored location.

Numerical Simulation of the Eddy Current Problem in Magnetic Induction Tomography for Biomedical Applications by Edge Elements

Magnetic induction tomography of biological tissue is used for reconstructing the conductivity distribution /spl kappa/=/spl sigma/+j/spl omega//spl epsiv/ or changes /spl Delta//spl kappa/ in a human body by measuring the perturbation /spl Delta/B of an alternating magnetic field B/sub 0/. The aim is to simulate the eddy current problem in magnetic induction tomography for biomedical applications by symmetric tetrahedral edge finite elements of second order. The method is validated by measurement data from a representative experiment, and numerical results of an edema in a human head are presented.