Bachir Dekdouk

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 ( ¿ = ¿+ j¿¿) or the magnetic permeability (¿) 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.

Estimating magnetic polarizability tensor of buried metallic targets for land mine clearance

This paper addresses the problem of identifying metallic objects in buried landmines and discriminating them from clutter using low frequency electromagnetic induction (EMI) techniques. From dipolar fields, the magnetic polarizability tensor extracted from the target response can be used as a basis for identification. Here, a deterministic nonlinear optimization method is presented to estimate target polarizability matrix and location by fitting a dipole model to EMI data collected above target in a least squares sense. Using finite element simulated data with added synthetic low frequency noise (10 dB SNR), results show initial guess misestimating target position with few centimeters in the transversal (x, y) plane can be corrected very close to the true location. The method is also able to estimate the polarizability tensor to within 12 % error of the true tensor. Keywords-component; Electromagnetic Induction, landmines, UXO, Magnetic polarizability, nonlinear inverse problems.

Assessing the feasibility of detecting a Hemorrhagic type stroke using a 16 channel Magnetic Induction System

Magnetic induction tomography (MIT) has been proposed as a possible method for imaging stroke in the human brain. Hemorrhagic stroke is characterized by local blood accumulation in the brain and exhibits a greater change in conductivity with frequency compared to other tissues which is observed in the frequency range of interest [1-10] MHz. In this study, we investigate the feasibility of detecting hemorrhagic stroke using absolute and frequency difference imaging. For this purpose, a model of the head originally obtained from MRI and X-ray data was used, to which a large stroke (50 ml) was added. In addition, a model of a 16 channel circular array MIT system was employed. The received coil induced voltages were computed using a custom eddy current solver, based on the finite difference method. For absolute imaging, the induced voltages at the receiver coils were calculated from various coil combinations at 10 MHz frequency together with anticipated systematic errors and biases (orientation and displacement of the coils, movement of the head). The induced voltage noise due to these systematic inaccuracies was compared with the voltage change due to the stroke. In order to decrease the impact of this noise, frequency difference was also considered, whereby measurements were performed at another frequency (1MHz) and subtracted. Comparison results are presented and a realistic picture is delivered with to regard the required mechanical stability and electronics accuracy for this particular medical application

Contactless Inductive Bubble Detection in a Liquid Metal Flow

The detection of bubbles in liquid metals is important for many technical applications. The opaqueness and the high temperature of liquid metals set high demands on the measurement system. The high electrical conductivity of the liquid metal can be exploited for contactless methods based on electromagnetic induction. We will present a measurement system which consists of one excitation coil and a pickup coil system on the opposite sides of the pipe. With this sensor we were able to detect bubbles in a sodium flow inside a stainless steel pipe and bubbles in a column filled with a liquid Gallium alloy.

Evaluation of the effects of the screen based on an analytical solution of a simplified MIT system

Magnetic induction tomography (MIT) is a technology that reconstructs cross sectional conductivity distribution of an object from mutual impedance measurements of coils distributed around the object. In high frequency and low conductivity applications, an outer screen is generally used to confine the magnetic fields and to prevent electromagnetic interference from outside. However, the screen will alter the sensing and excitation field, hence the sensitivity distribution of the coil array. Therefore, the design parameters of the screen (thickness, distance to coil, materials) are important to the performance of the sensor system. This paper presents a simple method based on an analytical solution for the evaluation of the effects of the screen. The advantage of the approach includes efficient modelling of thin screens and physical insights into the effects of the screen.

A feasibility study on the delectability of Edema using Magnetic Induction Tomography using an Analytical Model

Magnetic induction tomography (MIT) is a low frequency electromagnetic modality, which aims to reconstruct the conductivity changes from coupled field measurements taken by inductive sensors. MIT is a subject of research for medical clinical applications where several reports have shown low conductivity tissue structures can be detected.

Towards metal detection and identification for humanitarian demining using magnetic polarizability tensor spectroscopy

This paper presents an inversion procedure to estimate the location and magnetic polarizability tensor of metal targets from broadband electromagnetic induction (EMI) data. The solution of this inversion produces a spectral target signature, which may be used in identifying metal targets in landmines from harmless clutter. In this process, the response of the metal target is modelled with dipole moment and fitted to planar EMI data by solving a minimization least squares problem. A computer simulation platform has been developed using a modelled EMI sensor to produce synthetic data for inversion. The reconstructed tensor is compared with an assumed true solution estimated using a modelled tri-axial Helmholtz coil array. Using some test examples including a sphere which has a known analytical solution, results show the inversion routine produces accurate tensors to within 12% error of the true tensor. A good convergence rate is also demonstrated even when the target location is mis-estimated by a few centimeters. Having verified the inversion routine using finite element modelling, a swept frequency EMI experimental setup is used to compute tensors for a set of test samples representing examples of metallic landmine components and clutter for a broadband range of frequencies (kHz to tens of kHz). Results show the reconstructed spectral target signatures are very distinctive and hence potentially offer an efficient physical approach for landmine identification. The accuracy of the evaluated spectra is similarly verified using a uniform field forming sensor.

The application of a priori structural information based regularization in image reconstruction in magnetic induction tomography

Magnetic induction tomography (MIT) is a non-invasive contactless modality that could be capable of imaging the conductivity distribution of biological tissues. In this paper we consider the possibility of using absolute MIT voltage measurements for monitoring the progress of a peripheral hemorrhagic stroke in a human brain. The pathology is modelled as a local blood accumulation in the white matter. The solution of the MIT inverse problem is nonlinear and ill-posed and hence requires the use of a regularisation method. In this paper, we describe the construction and present the performance of a regularisation matrix based on a priori structural information of the head tissues obtained from a very recent MRI scan. The method takes the MRI scan as an initial state of the stroke and constructs a learning set containing the possible conductivity distributions of the current state of the stroke. This data is used to calculate an approximation of the covariance matrix and then a subspace is constructed using principal component analysis (PCA). It is shown by simulations the method is capable of producing a representative reconstruction of a stroke compared to smoothing Tikhonov regularization in a simplified model of the head.

Absolute Imaging of Low Conductivity Material Distributions Using Nonlinear Reconstruction Methods in Magnetic Induction Tomography

Magnetic Induction Tomography (MIT) is a newly developing technique of electrical tomography that in principle is able to map the electrical conductivity distribution in the volume of objects. The image reconstruction problem in MIT is similar to electrical impedance tomography (EIT) in the sense that both seek to recover the conductivity map, but differ remarkably in the fact that data being inverted in MIT is derived from induction theory and related sources of noise are different. Progress in MIT image reconstruction is still limited, and so far mainly linear algorithms have been implemented. In difference imaging, step inversion was demonstrated for recovering perturbations within conductive media, but at the cost of producing qualitative images, whilst in absolute imaging, linear iterative algorithms have mostly been employed but mainly offering encouraging results for imaging isolated high conductive targets. In this paper, we investigate the possibility of absolute imaging in 3D MIT of a target within conductive medium for low conductivity application ( σ< 5S m −1 ). For this class of problems, the MIT image reconstruction exhibits non-linearity and ill-posedness that cannot be treated with linear algorithms. We propose to implement for the first time in MIT two effective inversion methods known in non-linear optimization as Levenberg Marquardt (LMM) and Powells Dog Leg (PDLM) methods. These methods employ damping and trust region techniques for controlling convergence and improving minimization of the objective function. An adaptive version of Gauss Newton is also presented (AGNM), which implements a damping mechanism to the regularization parameter. Here, the level of penalty is varied during the iterative process. As a comparison between the methods, different criteria are examined from image reconstructions using the LMM, PDLM and AGNM. For test examples, volumetric image reconstruction of a perturbation within homogeneous cylindrical background is considered. For inversion, an independent finite element FEM software package Maxwell by Ansys is employed to generate simulated data using a model of a 16 channel MIT system. Numerical results are employed to show different performance characteristics between the methods based on convergence, stability and sensitivity to the choice of the regularization parameter. To demonstrate the effect of scalability of absolute imaging in MIT for more realistic problems, a human head model with an internal anomaly is used to produce reconstructions for different finer resolutions. AGNM is adopted here and employs the Krylov subspace method to replace the computationally demanding direct inversion of the regularized Hessian.

Inductive detection of gas bubbles in a liquid metal flow: A contactless and non invasive methode

The detection of bubbles in liquid metals flow is important for many technical applications. The opaqueness and the high temperature of liquid metals set high demands on the measurement system. The electrical conductivity of the liquid metal is relatively high, which can be exploited with contactless methods based on electromagnetic induction. We will present a measurement system which consists of one transmitting coil and a planar gradiometric coil on opposite sides of the pipe. With this sensor we were able to detect bubbles in a Sodium flow inside a stainless steel pipe.