Table Of ContentELECTRO-MAGNETIC
TISSUE PROPERTIES MRI
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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
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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
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ISBN 978-1-78326-339-4
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Printed in Singapore
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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
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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.
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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.
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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
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