Magnetic resonance electrical impedance tomography (MREIT) for high-resolution conductivity imaging.

Abstract

Cross-sectional imaging of an electrical conductivity distribution inside the human body has been an active research goal in impedance imaging. By injecting current into an electrically conducting object through surface electrodes, we induce current density and voltage distributions. Based on the fact that these are determined by the conductivity distribution as well as the geometry of the object and the adopted electrode configuration, electrical impedance tomography (EIT) reconstructs cross-sectional conductivity images using measured current-voltage data on the surface. Unfortunately, there exist inherent technical difficulties in EIT. First, the relationship between the boundary current-voltage data and the internal conductivity distribution bears a nonlinearity and low sensitivity, and hence the inverse problem of recovering the conductivity distribution is ill posed. Second, it is difficult to obtain accurate information on the boundary geometry and electrode positions in practice, and the inverse problem is sensitive to these modeling errors as well as measurement artifacts and noise. These result in EIT images with a poor spatial resolution. In order to produce high-resolution conductivity images, magnetic resonance electrical impedance tomography (MREIT) has been lately developed. Noting that injection current produces a magnetic as well as electric field inside the imaging object, we can measure the induced internal magnetic flux density data using an MRI scanner. Utilization of the internal magnetic flux density is the key idea of MREIT to overcome the technical difficulties in EIT. Following original ideas on MREIT in early 1990s, there has been a rapid progress in its theory, algorithm and experimental techniques. The technique has now advanced to the stage of human experiments. Though it is still a few steps away from routine clinical use, its potential is high as a new impedance imaging modality providing conductivity images with a spatial resolution of a few millimeters or less. This paper reviews MREIT from the basics to the most recent research outcomes. Focusing on measurement techniques and experimental methods rather than mathematical issues, we summarize what has been done and what needs to be done. Suggestions for future research directions, possible applications in biomedicine, biology, chemistry and material science are discussed.

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IOP PUBLISHING
PHYSIOLOGICAL MEASUREMENT
Physiol. Meas. 29 (2008) R1–R26
doi:10.1088/0967-3334/29/10/R01
TOPICAL REVIEW
Magnetic resonance electrical impedance tomography
(MREIT) for high-resolution conductivity imaging
Eung Je Woo1and Jin Keun Seo2
1Department of Biomedical Engineering, Kyung Hee University, Korea
2Department of Mathematics, Yonsei University, Korea
E-mail: ejwoo@khu.ac.kr
Received 21 May 2008, accepted for publication 15 August 2008
Published 17 September 2008
Online at stacks.iop.org/PM/29/R1
Abstract
Cross-sectional imaging of an electrical conductivity distribution inside
the human body has been an active research goal in impedance imaging.
By injecting current into an electrically conducting object through surface
electrodes, we induce current density and voltage distributions. Based on
the fact that these are determined by the conductivity distribution as well as
the geometry of the object and the adopted electrode configuration, electrical
impedance tomography (EIT) reconstructs cross-sectional conductivity images
using measured current–voltage data on the surface.
exist inherent technical difficulties in EIT. First, the relationship between the
boundary current–voltage data and the internal conductivity distribution bears
a nonlinearity and low sensitivity, and hence the inverse problem of recovering
theconductivitydistributionisillposed. Second,itisdifficulttoobtainaccurate
information on the boundary geometry and electrode positions in practice, and
theinverseproblemissensitivetothesemodelingerrorsaswellasmeasurement
artifacts and noise. These result in EIT images with a poor spatial resolution.
In order to produce high-resolution conductivity images, magnetic resonance
electrical impedance tomography (MREIT) has been lately developed. Noting
that injection current produces a magnetic as well as electric field inside the
imagingobject, wecanmeasuretheinducedinternalmagneticfluxdensitydata
usinganMRIscanner. Utilizationoftheinternalmagneticfluxdensityisthekey
ideaofMREITtoovercomethetechnicaldifficultiesinEIT.Followingoriginal
ideas on MREIT in early 1990s, there has been a rapid progress in its theory,
algorithm and experimental techniques. The technique has now advanced to
thestageofhumanexperiments. Thoughitisstillafewstepsawayfromroutine
clinicaluse,itspotentialishighasanewimpedanceimagingmodalityproviding
conductivity images with a spatial resolution of a few millimeters or less. This
paper reviews MREIT from the basics to the most recent research outcomes.
Focusing on measurement techniques and experimental methods rather than
mathematical issues, we summarize what has been done and what needs to
Unfortunately, there
0967-3334/08/100001+26$30.00© 2008 Institute of Physics and Engineering in MedicinePrinted in the UKR1

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R2 Topical Review
be done. Suggestions for future research directions, possible applications in
biomedicine, biology, chemistry and material science are discussed.
Keywords: MRI, EIT, MREIT, conductivity, injection current, magnetic flux
density
(Some figures in this article are in colour only in the electronic version)
1. Introduction
1.1. Motivation
The electrical conductivity of a biological tissue is determined by its molecular composition,
cellularstructure,amountsofintra-andextra-cellularfluids,concentrationandmobilityofions
in those fluids, temperature and other factors (Geddes and Baker 1967, Gabriel et al 1996a,
1996b, Grimnes and Martinsen 2000). Conductivity values of tissues and organs change
with their physiological and pathological conditions to provide useful diagnostic information.
Some biological tissues such as muscle and white matter show anisotropy in their conductivity
values especially at low frequency. We will mainly deal with isotropic or equivalent isotropic
conductivity in this review. Assuming a low frequency of less than a few kHz, we will ignore
effects of permittivity and consider only conductivity.
Noticing the abundance of information related to conductivity, there have been numerous
studies to visualize a conductivity distribution inside the human body (Webster 1990, Holder
2005). In order to visualize a conductivity distribution inside an imaging object, we should
probe it in such a way that we can obtain a measurable physical quantity that provides
information on the conductivity. When we inject current into an electrically conducting object
through a pair of electrodes, it produces distributions of current density, voltage and magnetic
flux density inside the object. Assuming that boundary geometry and electrode configuration
are fixed, the induced internal current density distribution is dictated by the conductivity
distribution to be imaged. Local change of an internal conductivity value results in a distortion
of the current pathway whose effect is conveyed to boundary voltage and internal magnetic
flux density.
Electricalimpedancetomography(EIT)reconstructsconductivityandpermittivityimages
from measured boundary current–voltage data (Barber and Brown 1984, Webster 1990,
Metherall et al 1996, Cheney et al 1999, Holder 2005). Surface electrodes, as many as
256 (usually 8 to 32), are attached on or around a body segment in a two- or three-dimensional
configuration. Sinusoidalcurrentswithafrequencyfromalmostdctoabout1MHzareinjected
through chosen or all electrodes. An EIT system measures induced voltages on chosen or
all electrodes, of which amplitudes and phases are determined by internal conductivity and
permittivitydistributions. Thisboundarycurrent–voltagedatasetisusedtoreconstructimages
of conductivity and permittivity distributions. Permittivity effects are often ignored especially
at frequencies below 10 kHz.
The relation between the boundary current–voltage data and the internal conductivity
and permittivity distributions bears a nonlinearity and low sensitivity, and hence the inverse
problem in EIT is ill posed. The measured data are affected by boundary geometry and
electrode positions and it is in practice difficult to accurately quantify them. The amount of
information in the measured data set is limited by the finite number of electrodes. The data

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Topical ReviewR3
are contaminated by systematic artifacts and numerous kinds of noise. Due to these inherent
technical difficulties, reconstructed EIT images suffer from relatively low spatial resolution
and accuracy (Holder 2005). EIT is advantageous when it is enough to visualize changes
of conductivity and/or permittivity distributions with respect to time or frequency. Its high
temporal resolution and portability will be beneficial in some clinical applications. However,
there certainly exists the need for a high-resolution conductivity imaging method.
1.2. Key idea and brief history of MREIT
In the early 1990s, magnetic resonance electrical impedance tomography (MREIT) was
proposed to deal with technical difficulties of EIT. Three different initial trials (Zhang 1992,
Woo et al 1994, Birgul and Ider 1995) were independently attempted. Though none of them
could produce high-quality conductivity images in actual imaging experiments, these early
ideas changed the way we investigate the conductivity imaging problem by suggesting the
supplemental use of internal as well as boundary measurements.
Assuming an externally injected current into an electrically conducting object, we denote
internal conductivity, voltage, current density and magnetic flux density distributions by σ,
u,J = (Jx,Jy,Jz) and B = (Bx,By,Bz), respectively. The key idea of MREIT was based
on a new technique to measure B by using a current-injection MRI technique. Using an
MRI scanner with its main magnetic field in the z direction, the technique enables us to
obtain Bzinside the object in the form of an image. In order to find J using the Ampere law
J = ∇ × B/μ0where μ0is the magnetic permeability of the free space, Bxand Bymust
also be measured and this requires rotating the imaging object twice inside the MRI scanner.
This imaging method, named as magnetic resonance current density imaging (MRCDI), was
originally proposed to noninvasively image J (Joy et al 1989, Scott et al 1991, 1992, Scott
1993) with its own applications (Beravs et al 1997, 1999, Sersa et al 1997, Eyuboglu et al
1998, Gamba and Delpy 1998, Joy et al 1999, Gamba et al 1999, Yoon et al 2003, Joy 2004).
Some early MREIT methods attempted to reconstruct an image of σ from J (Zhang
1992, Woo et al 1994, Eyuboglu et al 2001, Kwon et al 2002a, 2002b). These methods
are, however, difficult to use in practice since rotations of the imaging object are involved.
Noting this difficulty, Birgul and Ider (1995, 1996) and Ider and Birgul (1998) proposed a
method to produce an image of σ from only Bzwithout rotating the object. In 2003, Seo
et al (2003b) invented a new method to reconstruct an image of σ from measured Bzdata sets
subject to multiple injection currents, that is, at least two data sets. The so-called harmonic Bz
algorithm (Oh et al 2003b) has been widely used in subsequent experimental studies. To reach
the stage of an in vivo human imaging experiment, there have been numerous innovations in
theory, algorithm and experimental technique. Non-biological and biological phantoms were
used in validation studies. Postmortem animal imaging has been tried and followed by in vivo
animal and human experiments.
Technical progress in MREIT has shown that high-resolution conductivity imaging
is possible by probing biological tissues using electrical currents and measuring induced
magnetic flux densities using an MRI scanner. Without adding a significant overhead to a
conventional MR imaging procedure, it could become a part of an MRI system and provide
completely new contrast information.
1.3. Structure of the article
Technical development in MREIT requires interdisciplinary research incorporating
mathematical theory and analysis of bioelectromagnetism, an MR imaging method including
RF coil design and pulse sequence, skill for conductivity imaging experiments of

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R4 Topical Review
phantom, animal and human subjects, an image reconstruction algorithm and its numerical
implementation, data processing techniques of denoising, image segmentation and meshing
and others. We will begin with the definition of the MREIT conductivity imaging problem
including its forward and inverse problems. Acknowledging the key measurement quantity of
the induced internal magnetic flux density, we will explain MR imaging and data processing
techniques to obtain its image. We will review several conductivity image reconstruction
algorithms. In this review, however, we will not go into details of associated mathematical
issues. Having described measurement methods and image reconstruction algorithms, we will
summarize results of numerous imaging experiments performed so far using non-biological
phantoms, biological phantoms, postmortem animals, in vivo animals and human subjects.
Discussingtechnicalissuestobeaddressedinfuturework, wewillproposeresearchdirections
of MREIT for possible applications in biomedicine.
2. Problem definition
2.1. Forward problem
We consider an electrically conducting domain ? in R3with its isotropic conductivity
distribution σ and boundary ∂?. Denoting two electrodes attached on ∂? as E1and E2,
we inject a low-frequency current I between them. The induced voltage u in ? satisfies the
following boundary value problem with the Neumann boundary condition:
?∇ · (σ(r)∇u(r)) = 0
where n is the outward unit normal vector on ∂?,g is a normal component of the current
density on ∂? due to I and r is a position vector in R3. On the current injection electrode Ej
for j = 1 or 2, we have?
Setting a reference voltage u(r0) = 0 for r0∈ ?, we can obtain a unique solution u of (1).
Knowing the voltage distribution u, the current density J is given by
J(r) = −σ(r)∇u(r) = σ(r)E(r)
where E = −∇u is the electric field intensity.
We now consider the magnetic field produced by the injection current. The induced
magnetic flux density B in ? can be expressed as
B(r) = B?(r) + BX(r)
where B?is the magnetic flux density due to J in ? and BXis from currents in lead wires and
surfaces of electrodes. From the Biot–Savart law,
B?(r) =μ0
4π
?
Lee et al (2003b) investigated the term BXand suggested experimental and also algorithmic
ways of minimizing its effects. In this review, we will assume that B = B?for simplicity.
From the Ampere law, J in (2) can be expressed as
1
μ0∇ × B(r)
Since we are dealing with the externally injected current with no internal source or sink of the
same kind, we have
1
μ0∇ · ∇ × B(r) = 0
in
on
?
∂?,
−σ∇u · n = g
(1)
Ejg ds = ±I where the sign depends on the direction of current,
and g is zero on the regions of boundary not contacting with the current injection electrodes.
in
?,
(2)
in
?,
(3)
?
J(r?) ×
r − r?
|r − r?|3dr?.
(4)
J(r) =
in
?.
(5)
∇ · J(r) =
in
?.
(6)

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Topical Review R5
As for the case of EIT, we need an MREIT forward solver for algorithm development,
experimentaldesignandverification. Leeetal(2003b)developedathree-dimensionalforward
solver computing distributions of voltage u, current density J and magnetic flux density B.
Given σ, ∂? and electrode configuration, they used the finite element method to numerically
compute u. Computations of J and B can be performed using (2) and (4), respectively. To
validate numerical solutions, they suggested to check the compatibility conditions in (6).
2.2. Inverse problem
We consider the inverse problem of MREIT in two categories. One uses the data of the three
components of B or J for image reconstructions and the other uses Bzonly. We may call them
J-based MREIT and Bz-based MREIT, respectively. The most significant difference is related
to the data collection process. We should rotate an imaging object inside an MRI scanner in
J-based MREIT whereas Bz-based MREIT does not require this.
Assuming that Bismeasured and J iscomputed using(5), weare provided withmeasured
current density data subject to an injection current. Finding σ from the current density is not
as simple as it looks like from (2) since u is a nonlinear function of σ as in (1). Iterative
or single-step conductivity image reconstruction algorithms have been developed for J-based
MREIT. Experimental work is rare since it requires the process of rotating the imaging object
inside the MRI scanner.
We now restrict ourselves to the situation where only one component Bzof B is available.
Extracting the z-component from (4), we can see that Bzis related to σ as
?
or
?
IntheBz-basedMREIT,weobtainmultiplesetsofBzdatasubjecttomultipleinjectioncurrents
and reconstruct an image of σ using an iterative or single-step algorithm. Most experimental
studies so far have been based on Bz-based MREIT since it does not require the object rotation
process.
For any MREIT method, we need at least one voltage measurement to adjust an image of
σ in its absolute values (Kwon et al 2002b, 2006, Ider et al 2003, Liu et al 2007, Nachman
et al 2007). Without the voltage measurement, we can produce an image of σ in terms of its
contrast only. Image reconstruction algorithms to provide a solution of the inverse problem
will be explained in section 4.
Bz(r) =μ0
4π
?
(x?− x)Jy(r?) − (y?− y)Jx(r?)
|r − r?|3
σ(r)?(x − x?)∂u
dr?
(7)
Bz(r) =μ0
4π
?
∂y(r?) − (y − y?)∂u
|r − r?|3
∂x(r?)?
dr?.
(8)
3. Measurement technique
3.1. System configuration
An MREIT system comprises an MRI scanner, constant current source and conductivity
image reconstruction software. The current source is interfaced to the spectrometer of the
MRI scanner for synchronization. We will assume that the scanner has its main magnetic
field in the z-direction. Main magnetic field homogeneity and gradient linearity are especially
important in MREIT. Conventional RF coils including surface and phased array coils can
be adopted as long as there is enough space for electrodes and lead wires. Sensitivity and