ELECTRO-MAGNETIC TISSUE PROPERTIES MRI P914_9781783263394_tp.indd 1 7/1/14 5:29 pm Modelling and Simulation in Medical Imaging ISSN: 2045-0362 Series Editor: Habib Ammari (Ecole Polytechnique, France) Vol. 1: Electro-Magnetic Tissue Properties MRI by Jin Keun Seo, Eung Je Woo, Ulrich Katscher and Yi Wang Modelling and Simulation in Medical Imaging - Vol. 1 ELECTRO-MAGNETIC TISSUE PROPERTIES MRI Jin Keun Seo Yonsei University, Korea Eung Je Woo Kyung Hee University, Korea Ulrich Katscher Philips Technologie GmbH, Germany Yi Wang Cornell University, USA Imperial College Press ICP P914_9781783263394_tp.indd 2 7/1/14 5:29 pm Published by Imperial College Press 57 Shelton Street Covent Garden London WC2H 9HE Distributed by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Modelling and Simulation in Medical Imaging — Vol. 1 ELECTRO-MAGNETIC TISSUE PROPERTIES MRI Copyright © 2014 by Imperial College Press All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 978-1-78326-339-4 Typeset by Stallion Press Email: [email protected] Printed in Singapore January 16, 2014 16:28 9in x 6in Electro-Magnetic Tissue Properties b1693-fm Preface Recently, imaging techniques in science, engineering, and medicine have evolved to expand our ability to visualize internal information of an object such as the human body. In particular, there has been marked progress in magnetic resonance (MR)-based electro- magnetic propertyimaging techniques which usemagnetic resonance imaging (MRI) to provide cross-sectional images of conductivity, permittivity, and susceptibility distributions inside the human body. These electromagnetic material properties of biological tissues are important biomarkers since they reveal physiological and pathologi- cal conditions of body tissues and organs. Magnetic resonance electrical impedance tomography (MREIT) is an MR-based conductivity imaging technique at low frequencies. In MREIT, we inject currents into an imaging object and measure induced magnetic flux density data from MR phase images. Qua- sistatic Maxwell equations provide a relation between the measured magnetic flux density and the conductivity from which we can reconstruct cross-sectional conductivity images. Magnetic resonance electrical properties tomography (MREPT) aims to reconstruct images of both conductivity and permittivity distributions inside the human body at MR frequency. In contrast to MREIT, MREPT does not require current injection since it is based on standard radio frequency (RF) field mapping techniques to measure the active magnetic RF field component. While MREIT and MREPT deal with electrical properties of conductivity and permittivity, quantitative susceptibility mapping (QSM) provides images of the magnetic susceptibility distribution inside the human body. Unlike susceptibility weighted imaging (SWI) methods, QSM utilizes MR v January 16, 2014 16:28 9in x 6in Electro-Magnetic Tissue Properties b1693-fm vi Electro-Magnetic Tissue Properties MRI phase images to produce absolute tissue susceptibility images by solving an inversion problem of magnetic sources. In recent literature, theories, image reconstruction algorithms and experimental techniques of these MR-based electro-magnetic propertyimagingmodalitieshavebeendevelopedtoadvancethemto the stage of in vivo animal or human experiments. These modalities belong to interdisciplinary research areas incorporating mathemat- ical theories and analyses of bioelectromagnetism, MR physics and imaging methods, inverse problems and image reconstruction algorithms,numericalanalysesandexperimentaltechniques.Inorder to facilitate clinical application studies as well as further technical refinements, we realized that an unmet need exists for a technical book dealing with MREIT, MREPT, and QSM. In this book, we present their mathematical formulations to describefundamental concepts and image reconstruction algorithms. We first introduce basics of bioelectromagnetism and MRI in the context of MREIT, MREPT, and QSM. We deal with each modality in a separate chapter where we explain associated measurement methods, interrelations between obtained MR data and image contrasts, image reconstruction algorithms, experimental techniques and potential biomedical applications. For researchers in applied mathematics, we also discuss mathematical theories including error estimates, uniqueness, and challenging open problems. To facilitate technical progress, we will follow a kind of unified approach, as summarized below: (cid:127) Understanding underlying physical phenomena. (cid:127) Mathematical formulation of forward problems in such a way that we can deal with them systematically and quantitatively. (cid:127) Data collection method: practical limitations associated with measurement sensitivity and specificity, noise, artifacts, interface between target object and instrument, data acquisition time. (cid:127) Mathematical analysisexplainingrelationsbetweenthosequalities and measurable data. (cid:127) Image reconstruction formulas and sensitivity analysis. (cid:127) Numerical implementation and in vivo experiments. (cid:127) Challenging problems and future research directions. January 16, 2014 16:28 9in x 6in Electro-Magnetic Tissue Properties b1693-fm Preface vii Expected readers of this book are graduate students and researchers in MR-based imaging science. Most of them will study or work in the areas of applied mathematics, biomedical engineering, and electrical engineering. The secondary audience will include sci- entist and engineers in universities and industry, who are interested in inverse problems in general. January 16, 2014 16:28 9in x 6in Electro-Magnetic Tissue Properties b1693-fm TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk January 16, 2014 16:28 9in x 6in Electro-Magnetic Tissue Properties b1693-fm Foreword This is the first volume in the Imperial College Press series entitled Modelling and Simulation in Medical Imaging. Thepurposeoftheseriesistopublishhigh-levelworksdescribing advanced technologies in biomedical imaging and related math- ematical problems and techniques. Its ultimate goal is to make mathematicalmodellingamoreeffectivetoolforbiomedicalimaging, leading to an enhancement of technological innovations. This first volume is co-authored by a prominent mathematician and leading scientists from biomedical imaging. It covers recent advances on magnetic resonance electrical impedance tomography (MREIT). The mathematical problems that appear in this area are important and pose significant challenges to pure and applied mathematicians. They have also recently attracted a lot of attention from researchers. The volume illustrates the interplay among many branches of mathematics and their applications in biomedical imaging. It high- lights the benefits of sharing ideas among the fields of mathematics andmedicalimaging,andleadstoveryoriginalmathematicallybased solutions to the most challenging problems in MREIT. This impressive and timely volume is of interest not only to mathematicians workinginthefieldofimaging,butalsotophysicists and engineers. We envision that it will stimulate much-needed progress in mathematical modelling for biomedical imaging. Habib Ammari Series Editor, Paris ix