Christos Ktistis

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.

On the Low-Frequency Electromagnetic Responses of In-Line Metal Detectors to Metal Contaminants

This paper considers a dipole solution to the low-frequency electromagnetic responses of a typical in-line metal detector to metal contaminants. This solution is determined by the characteristics of metal targets and incident magnetic fields, which are treated separately as two independent factors. For the metal targets, the responses of sphere and wire samples are determined. The electromagnetic polarizability matrix of a metal sphere is directly computed from a spherical response function. The electromagnetic polarizability tensor of metal wire is derived from a measured eigenvalue matrix and a rotation matrix. The approximated responses of sphere and wire samples from the proposed solutions agree well with the measured responses from in-line metal detectors. In theory, the approximation method on metal wire samples is also applicable to the metal contaminants of other shapes.

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

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.

A Very-Low-Frequency Electromagnetic Inductive Sensor System for Workpiece Recognition Using the Magnetic Polarizability Tensor

The automatic recognition of a metal component or workpiece currently relies on optical techniques and image matching. It is not possible to distinguish workpieces with different materials. In this paper, a novel electromagnetic inductive sensor array similar to those used in the electromagnetic tomography has been designed to address this problem. Furthermore, instead of reconstructing the full magnetic polarizability tensor, we have proposed a partial tensor approach, which shows that a 2-D tensor is capable of distinguishing the material difference and recognising the geometric dominance of workpieces with experimental data. In addition, it has been found that the phase of the tensor is strongly linked to the materials properties while the magnitude of the tensor eigenvalues implies the basic geometry of workpiece.

Sparse electromagnetic tomography based on matching pursuit algorithms

A sparse Electromagnetic Tomography (EMT) system based on Matching Pursuit (MP) algorithms is introduced in this paper. The sparse EMT problem with a linear model is essentially a pursuit for the sparse representation of the spatial conductivity. The framework of sparse representation theory is adopted for the EMT problem. Such notations as spark and mutual-coherence are introduced as tools in the analysis of the recovery results. MP algorithms are considered as effective and efficient solvers towards sparse representation. Some variations of MP are compared in this paper for a random dictionary and the EMT dictionary. The result of conductivity reconstruction proves the effectiveness of MP algorithms for the proposed EMT system.

Determining the Electromagnetic Polarizability Tensors of Metal Objects During In-Line Scanning

In metal detection systems, the response of a detector to a metal object may be approximated from the electromagnetic polarizability tensor of the object. Conversely, the tensors may be determined from multiposition measurements as the detector and object are moved relative to each other. This paper introduces and sets out the general approach to determining the tensor during in-line scanning. Two common application scenarios are considered, which share a similar consideration in the calculation of the tensor components. The first is the case for detectors of landmines or explosive remnants of war, where the detector is scanned on a surface above the object. The condition of this inverse problem depends on the geometry of the coil(s) and the measurement protocol, which at present is not fully understood. Our results consider two cases, namely, a single line scan over the object as two extreme cases. The results suggest that tensor inversion is possible for the 2-D raster scan, but not for a single line scan. The second application is a conveyor-type metal detector, which is used with a typical detector for industrial process lines. Here, a new rotation measurement method is proposed and examined for the case of simple coaxial sensor coils and in-line scanning. Finally, different inverse methods are analyzed for the new rotation measurement method.

Determining the electromagnetic polarizability tensors of metal objects from rotation measurements

The electromagnetic responses of metal objects can be determined by their electromagnetic polarizability tensors. In landmine detection and geophysics, the electromagnetic tensors of metal objects are usually determined from multi-position measurements or simulations. In this paper, the electromagnetic tensors of metal objects are obtained from rotation measurements. This rotation measurement method can be applied to magnetic sensors with magnetic fields from one direction, e.g. in-line metal detectors.

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.