Optimising the Inverse Solution for Electrical Impedance Tomography of Acute Stroke and Brain Injury
Electrical Impedance Tomography (EIT) is novel medical imaging method which can be used to produce images of the internal electrical properties of a subject using rings of external ECG type electrodes. It is small, portable and safe, and has unique potential to provide images in acute stroke or head injury in ambulances, or at the bedside which would allow intervention much earlier than conventional imaging methods such as MRI or CT. This could transform the management of stroke by enabling early use of clot-dissolving agents, or give early warning of intracranial haemorrhage.
Production of EIT images in these conditions is challenging, as the inverse solution is ill-posed, underdetermined and non-linear. A new reconstruction algorithm has been developed in our group, where images are made of data recorded about a minute at multiple frequencies. This is computationally expensive, as it requires a solution using a large numerical Finite Element Mesh of the head of c.10M elements with multiple iterations. The aim of this project is to reduce the time to produce images from many hours at present to a few minutes and improve image quality. The current method requires solution of a set of differential equations with different right hand sides and frequencies. Approaches will include 1) Formulation as a large matrix equation, with solution by customized methods, such as the flexible generalized minimal residual method, 2) Use of spectral methods as the frequency dependence of the solution is very smooth and 3) Efficient solution for neighbouring frequencies with recycling Krylov subspace methods, as the linear systems are similar.
This will provide training in advanced inverse mathematical methods but also the opportunity to work in collection and interpretation of images in subjects with acute stroke or head injury in an interdisciplinary bioengineering/neurophysiology research group.
Related Methodological Themes