Inverse Problems for Magnetic Induction Tomography

Magnetic Induction Tomography (MIT) is a relatively new, non-invasive imaging technique which has applications in both industrial and clinical settings. In essence, it is capable of reconstructing the electromagnetic parameters (permittivity, permeability and conductivity) of an object from measurements made on its surface. An MIT device consists of two sets of coils placed around the boundary of the object to be imaged. The first set of coils is used for the purpose of excitation, and by passing a current through each coil in turn, a primary magnetic field is created. The second set of coils is then used for measurement. This procedure causes an eddy current when each of the primary magnetic fields interacts with a conducting body inducing secondary magnetic fields, and hence voltages, that are measured in the second set of coils.

Enabling MIT to take the step from being an experimental technique, which has already received some clinical interest, to become a viable imaging technique for the detection and monitoring of conditions, such as cerebral stroke, requires a step change in the quality of the reconstruction of the electromagnetic parameters and, therefore, an improvement of the computational approach used for the solution of the inverse problem. To achieve this we propose to solve the inverse Maxwell problem with a variational algorithm. Although a proof of concept of this work exists, in order to make this algorithm effective in a clinical environment, and hence applicable to the MIT problem, an implementation using high performance computing is needed, this research proposal aims to address this issue.

The proposed work will bring benefits across a broad spectrum of beneficiaries based both in the UK and beyond.

Our work will bring immediate benefits to interdisciplinary international academic researchers in the fields of Computer Science, Engineering, Mathematics and Medical Physics. Specifically, groups with interests in high performance computing, applied linear algebra, optimisation and parallel algorithms will benefit from new technological developments in the form algorithmic developments. Applied mathematicians and engineers working in academia in computational electromagnetism, error estimation and adaptivity as well as inverse problems will also benefit from the technological developments in this proposal in terms of the new computational procedures and implementations that will be developed. In addition, medical physicists working in academia on Magnetic Induction Tomography (MIT) devices will also benefit from a new imaging toolkit that will be developed as part of this proposal.

The work we will undertake will also bring immediate benefits to industry. Specifically, companies developing computational electromagnetics modelling software, medical device modelling software and companies developing imaging software for medical and industrial applications will benefit from the new technological developments in terms of new algorithms and implementations that will be developed as part of this project. Specific examples include improved linear algebra solution techniques on GPU processors and uncertainty quantification through error estimation. It will also bring benefits to companies developing imaging devices for medical and industrial processes, whereby, through the technological developments proposed, improved imaging resolution for MIT and other similar imaging devices will be accomplished. To ensure these benefits are realised, we will organise two one-day dissemination and impact events to disseminate our findings to the participants of the Welsh Electromagnetics Network and other interested groups during the lifecycle of our project.

In the medium term, the project will help to inform members of the public sector such as national heath care decision makers and regional managers for health care providers considering the investment in new medical technologies for improving the quality of patient diagnosis. This will lead to operational changes whereby low cost MIT can be used to supplement existing high cost imaging modalities (MRI, CT) in the initial stages of diagnosis and for patient monitoring.

In the longer term, the project will also benefit the general public by improving the health and well being of the nation through better imaging techniques to assist with medical diagnosis and monitoring of patients.