P.D. Ledger

Imaging cerebral haemorrhage with magnetic induction tomography: numerical modelling

Magnetic induction tomography (MIT) is a new electromagnetic imaging modality which has the potential to image changes in the electrical conductivity of the brain due to different pathologies. In this study the feasibility of detecting haemorrhagic cerebral stroke with a 16-channel MIT system operating at 10 MHz was investigated. The finite-element method combined with a realistic, multi-layer, head model comprising 12 different tissues, was used for the simulations in the commercial FE package, Comsol Multiphysics. The eddy-current problem was solved and the MIT signals computed for strokes of different volumes occurring at different locations in the brain. The results revealed that a large, peripheral stroke (volume 49 cm(3)) produced phase changes that would be detectable with our currently achievable instrumentation phase noise level (17 m degrees ) in 70 (27%) of the 256 exciter/sensor channel combinations. However, reconstructed images showed that a lower noise level than this, of 1 m degrees , was necessary to obtain good visualization of the strokes. The simulated MIT measurements were compared with those from an independent transmission-line-matrix model in order to give confidence in the results.

Frequency-difference MIT imaging of cerebral haemorrhage with a hemispherical coil array: numerical modelling

The feasibility of detecting a cerebral haemorrhage with a hemispherical MIT coil array consisting of 56 exciter/sensor coils of 10 mm radius and operating at 1 and 10 MHz was investigated. A finite difference method combined with an anatomically realistic head model comprising 12 tissue types was used to simulate the strokes. Frequency-difference images were reconstructed from the modelled data with different levels of the added phase noise and two types of a priori boundary errors: a displacement of the head and a size scaling error. The results revealed that a noise level of 3 m degrees (standard deviation) was adequate for obtaining good visualization of a peripheral stroke (volume approximately 49 ml). The simulations further showed that the displacement error had to be within 3-4 mm and the scaling error within 3-4% so as not to cause unacceptably large artefacts on the images.

Fast Magnetic Flux Leakage Signal Inversion for the Reconstruction of Arbitrary Defect Profiles in Steel Using Finite Elements

This paper proposes a fast and effective method for reconstructing arbitrary defect profiles in steel plates from magnetic flux leakage (MFL) measurements widely used in nondestructive testing (NDT) of oil storage tanks and pipelines. The inverse reconstruction problem is formulated based on a nonlinear forward model using the finite element method (FEM) and is implemented in 2-D. A Gauss-Newton optimization is applied to reconstruct the defect geometry, using efficiently calculated Jacobian information directly derived from the FEM system matrix.

An Adjoint Enhanced Reduced-Order Model for Monostatic RCS Computation

Abstract This article considers the numerical simulation of three-dimensional electromagnetic wave scattering problems and describes the construction of a reduced-order approximation that enables the rapid prediction of the monostatic radar cross section (RCS). Associated certainty bounds ensure confidence in the results of the computed approximation. Numerical examples are included to demonstrate the performance of the proposed procedure.

Computing Maxwell eigenvalues by using higher order edge elements in three dimensions

We use recently proposed hierarchic basis functions and a tetrahedral partitioning to compute Maxwell eigenvalues on a bounded polygonal domain in /spl Ropf//sup 3/, using a p-version finite-element procedure based on edge elements. The problem formulation requires a set of basis functions that are H(curl)-conforming and another compatible set that is H/sup 1/-conforming. In this preliminary study, we employ a uniform order of approximation throughout the domain.

The development of an hp -adaptive finite element procedure for electromagnetic scattering problems

The development of an hp-adaptive edge element procedure for the simulation of two-dimensional electromagnetic scattering problems on hybrid meshes of triangles and quadrilaterals is described. The interest in this paper is the accurate prediction of the scattering width for simulations involving a single frequency incident wave. Sharp, constant free, error bounds on the scattering width output are obtained by employing an a posteriori procedure. The elemental contributions to the bound gap are used to drive an adaptive solution process, with the aim of improving the accuracy of the computed output. A novel extension to previous work, is the proposed reduced-order model for the economical calculation of the bound gap for all viewing angles of the scattering width. The theory is supported by numerical examples. This paper constitutes the full length version of the paper that was originally submitted in an extended abstract form for the 2002 Robert J. Melosh medal competition for the best student paper on finite element analysis.

The cardiff Mk2b MIT head array: Optimising the coil configuration

A hemispherical MIT helmet coil array for imaging cerebral haemorrhage has been designed using a realistic 12-tissue finite-difference model of the head including a large peripheral haemorrhage (volume 49 ml). The coil array was first optimised by reaching a compromise between the quality of the reconstructed images and the financial cost of the digital detection system. The practical implementation of the helmet is partially complete.

Understanding the Magnetic Polarizability Tensor

The aim of this paper is to provide new insights into the properties of the rank 2 polarizability tensor M̆ proposed by Ledger and Lionheart for describing the perturbation in the magnetic field caused by the presence of a conducting object in the eddy-current regime. In particular, we explore its connection with the magnetic polarizability tensor and the Pólya-Szegö tensor and how, by introducing new splittings of M̆, they form a family of rank 2 tensors for describing the response from different categories of conducting (permeable) objects. We include new bounds on the invariants of the Pólya-Szegö tensor and expressions for the low-frequency and high-conductivity limiting coefficients of M̆. We show, for the high-conductivity case (and for frequencies at the limit of the quasi-static approximation), that it is important to consider whether the object is simply or multiply connected but, for the low-frequency case, the coefficients are independent of the connectedness of the object. Furthermore, we explore the frequency response of the coefficients of M̆ for a range of simply and multiply connected objects.

An Explicit Formula for the Magnetic Polarizability Tensor for Object Characterization

The magnetic polarizability tensor (MPT) has attracted considerable interest due to the possibility it offers for characterizing conducting objects and assisting with the identification and location of hidden targets in metal detection. An explicit formula for its calculation for arbitrary-shaped objects is missing in the electrical engineering literature. Furthermore, the circumstances for the validity of the magnetic dipole approximation of the perturbed field, induced by the presence of the object, are not fully understood. On the other hand, in the applied mathematics community, an asymptotic expansion of the perturbed magnetic field has been derived for small objects and a rigorous formula for the calculation of the MPT has been obtained. The purpose of this paper is to relate the results of the two communities, to provide a rigorous justification for the MPT, and to explain the situations in which the approximation is valid.

An Investigation of a Preconditioner for High-Frequency Maxwell Problems

Abstract This article describes a preconditioner for the indefinite linear equation system that is obtained when the vector wave equation is discretized by hp edge finite elements. A theoretical investigation of the eigenspectrum of the preconditioned system for p = 1 quadrilateral elements illustrates that the preconditioner will perform well, once the mesh spacing is sufficiently fine. Numerical experiments are included, which demonstrate the effectiveness of the preconditioner for h and p refinements in both two and three dimensions.