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1390 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 61, NO. 5, MAY 2014

Electrical Tissue Property Imaging at Low

Frequency Using MREITJin Keun Seo and Eung Je Woo∗ , Senior Member, IEEE

Abstract—The tomographic imaging of tissue’s electricalproperties (e.g., conductivity and permittivity) has been greatlyimproved by recent developments in magnetic resonance (MR)imaging techniques, which include MR electrical impedance to-mography (MREIT) and electrical property tomography. Whenthe biological material is subjected to an external electric field,local changes in its electrical properties become sources of mag-netic field perturbations, which are detectable by the MR signals.Controlling the external excitation and measuring the responsesusing an MRI scanner, we can formulate the imaging problem asan inverse problem in which unknown tissue properties are recov-ered from the acquired MR signals. This inverse problem is non-linear; it involves the incorporation of Maxwell’s equations and

Bloch equations during data acquisition. Each method for visu-alizing internal conductivity and permittivity distributions has itsown methodological limitations, and is restricted to imaging only apart of the ensemble or mean tissue structures or states. Therefore,imaging methods can be improved by developing complementarymethods that can employ the beneficial aspects of various existingtechniques. This paper focuses on recent progress in MREIT anddiscusses its distinct features in comparison with other imagingmethods.

Index Terms—Conductivity, electrical impedance tomogra-phy (EIT), magnetic resonance electrical impedance tomography(MREIT), MRI.

I. INTRODUCTION

IMAGING techniques enable scientists and engineers to visu-

alize various physical phenomena and assess them in detail.

Medical imaging shines a metaphorical light on the internal

structures and states of the human body where no visible light is

present. Various techniques can be used to investigate the body,

exploiting differences in the physical and chemical properties

of tissues. The choice of the observation method depends on the

area of interest, with X-ray, MRI, ultrasound, and gamma rays,

each able to augment simple visual examination. The develop-

ment of any new medical imaging tool should be undertaken

Manuscript received September 7, 2013; revised November 25, 2013; ac-cepted December 29, 2013. Date of publication January 9, 2014; date of current

version April 17, 2014. The work of J. K. Seo was supported by the NationalResearch Foundation of Korea grant funded by the Korean government (MEST)(No. 2011-0028868). The work of E. J. Woo was supported by the NationalResearch Foundation of Korea grant funded by the Korean government (MEST)(No. 20100018275). Asterisk indicates corresponding author.

J. K. Seo is with the Department of Computational Science and Engineering,Yonsei University, Seoul 120-749, Korea (e-mail: [email protected]).

∗E. J. Woo is with the Department of Biomedical Engineering, Kyung HeeUniversity, Gyeonggi-do 446-701, Korea (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TBME.2014.2298859

with consideration of its potential uses and its significance to

the diagnosis of certain diseases.

The electrical current is a promising means of visualizing tis-

sue properties such as conductivity (σ) and permittivity (ε). By

subjecting tissue to the influence of an external electric field (E),

we can assess the conductivity of tissue by observing how the

tissue affects the conduction and movement of charged species

(e.g., ions and molecules) under the influence of the applied E.

Permittivity is associated with the polarizations of charged sub-

stances subject to time-varying E. In biological objects, charge

double layers form across cell membranes, which are close to

insulating; these then act as parallel plate capacitors and in-

crease the effective permittivity of a given sample volume at the

macroscopic scale. The permittivity and conductivity of tissue

are affected by ischemia, hemorrhage, edema, inflammation,

cancers, and neural activities, as well as other functional and

pathological conditions. Imaging of the electrical properties of

tissue has potential in diagnosis and in monitoring of disease

progression, and in the detection of anomalies and neural activ-

ities; it has, therefore, remained an active research topic for the

last three decades.

Reconstruction of the admittivity (κ := σ + iωε) distribution

requires Ohm’s law J = κE and estimation of the 3-D distribu-

tions of the ensemble average values of the current densityJ andelectric fieldE inside a given volume or voxel. Generation of the

internal distributions of J and E requires probing the object by

either injecting the current using surface electrodes or inducing

the current using external coils. While direct and noninvasive

methods to measure E and J inside the body are not available,

it is possible to measure the induced internal magnetic flux den-

sity B. A practically feasible method of acquiring data of the

measurable quantity will employ Maxwell’s equations connect-

ing σ,ε,E,J, and B. Note that images can only be produced of

the effective or apparent conductivity and permittivity distribu-

tions that describe the linear relationship between the ensemble

average current density and the electric field in a voxel of finite

size. The effective quantity of σ + iωε at the macroscopic scale

depends on factors associated with the cellular structure such

as molecular composition, shape, and alignment; cellular mem-

branes, intra- and extracellular fluids; and ion concentrations

and mobilities, as well as temperature and the probing method

itself (e.g., probing frequency and the configuration of current

generation).

MRI scanners can noninvasively measure the magnetic fields

generated inside a human body that is subjected to injected

or induced internal currents. Current-injection MRI, which

was developed in the late 1980s, can visualize the internal

current density distribution using a conventional MRI scanner

0018-9294 © 2014 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistributionrequires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.



SEO AND WOO: ELECTRICAL TISSUE PROPERTY IMAGING AT LOW FREQUENCY USING MREIT 1391

Lead Wire

Micro-

Controller

16bit-

DACSwitch

Module

Optical-Rx

(Trigger)Voltmeter

VIC

WG

Electromagnetic Shield Case

MREIT Current Source

DC Power Supply (Battery)

Interface

USB

OpticalTrigger

Interface

Module

Optical-Tx

(Trigger)

Trigger Module

RF Pulse Detector

Coil

Fig. 1. MREIT system. The object to be imaged is placed inside the bore of the MRI scanner with two pairs of electrodes attached to its surface. Currents arethen injected into the object between a chosen pair of electrodes; the z-component of the induced magnetic flux density (Bz ) is measured and used to reconstructcross-sectional conductivity images of the object. To inject currents in a synchronized way with a chosen pulse sequence, one can use the trigger module whichdetects RF pulses using a coil and generates trigger signals to the current source.

augmented by a custom-designed constant-current source[28], [58], [59]. This technique, termed magnetic resonance

current density imaging (MRCDI), motivated early research

into magnetic resonance electrical impedance tomography

(MREIT) in the 1990s, with the aim of reconstructing

conductivity images from acquired current density images.

MRCDI, however, is limited by the requirement of object ro-

tation inside the MRI scanner to acquire all three components

of the induced magnetic flux density vector because the scan-

ner can measure only the z -component when the z -axis is the

axial magnetization direction of the scanner. Serious practical

difficulties arise from this requirement because of the limited

space within the bore, as well as problems associated with tis-sue movement during the rotation. Despite numerous attempts to

overcome these difficulties, drawbacks remain, which seriously

limit the clinical applicability of the method.

The feasibility of this imaging method would be improved

by recovering the conductivity distribution using only the z-

components of the induced magnetic field, thus avoiding the

need for object rotation. According to Maxwell’s equations, the

current density is directly related to the three components of the

induced magnetic flux density B = (Bx , By , Bz ), and the con-

ductivity must be computed from the relationship between the

current density and the electrical field. Therefore, Bz data alone

were considered insufficient for conductivity image reconstruc-

tions, and conductivity imaging using Bz data alone appearedimpossible until 2000.

In 2001, Seo et al. investigated the nonlinear relationship be-

tween conductivity and the measured data via the Biot–Savart

law [61]. Their key observation was that the Laplacian of Bz

data probes changes of the logarithm of the conductivity distri-

bution along any equipotential curve in each imaging slice. In

this method, two different currents are injected into the body

to generate two linearly independent current densities. They

showed that if the area of the parallelogram made by these two

vector fields is nonzero at every position in the imaging slice,

then the spatial change of the conductivity distribution can be

precisely reconstructed. They also rigorously mathematically

proved, using geometric index theory, that the area of the paral-lelogram is nonzero when the two pairs of surface electrodes are

appropriately attached [66]. This proof enabled construction of

a representation formula for the conductivity, which led to the

development of a constructive irrotational MREIT algorithm,

termed the harmonic Bz algorithm [61].

This representation formula exists in an implicit form owing

to the nonlinear relationship between the conductivity and mea-

sured data, but it was designed to use a fixed-point theory. In

other words, the formula has a contraction mapping property

such that an iterative method can be used. This mathematical

analysis formed a basis for subsequent successful tests on an-

imals and humans. MREIT techniques have advanced rapidlyand can now offer high-resolution conductivity images of ani-

mal and human subjects. Fig. 1 depicts the configuration of a

modern MREIT system; in the following sections, we describe

its basic principles and experimental outcomes.

We will start with the basics of electrical tissue property

imaging including brief descriptions on conductivity and per-

mittivity. Introducing two methods to probe the passive material

properties, we will elaborate how to utilize measured boundary

voltage data in electrical impedance tomography (EIT) and in-

ternal magnetic flux density data in MRCDI. Then, we will

focus on MREIT to explain how we can overcome the limi-

tations of EIT and MRCDI. We will restrict the scope of this

paper within these topics, which have been the areas of our maininterests. We will briefly mention other methods such as mag-

netic induction tomography, magnetoacoustic tomography with

magnetic induction (MAT-MI), electrical property tomography

(EPT), and diffusion tensor MRI (DT-MRI), where we need to

make some comparisons.

II. BASICS OF ELECTRICAL TISSUE PROPERTY IMAGING

A. Conductivity and Permittivity

We first consider homogeneous saline solution that contains

mobile ions. The ions randomly move at thermal equilibrium

without any external excitation. Because the conduction of a




current requires a net directional flow of mobile ions (or other

charge carriers), this random movement of ions does not con-

stitute a current flow. The application of an external electric

field would exert Coulomb forces on the ions and induce them

to move either parallel to or antiparallel to the direction of the

field. A greater number of ions or the presence of more mobile

ions in the solution would lead to more overall ionic movement

and hence greater conduction. The induced current is, there-

fore, proportional to the applied field intensity and also to the

concentration and mobility of the ions. The property of conduc-

tivity is essentially determined by these properties of the ions in

solution: their concentrations and their mobilities.

Consider the addition of small spherical cells with thin insu-

lating membranes to such a solution. Also, consider the addition

of connective tissues with different compositions and shapes.

The domain becomes heterogeneous and may reveal some direc-

tional properties, i.e., anisotropy. The anisotropy would depend

on the number, shape, and distribution of the cells and tissues.

The application of the same external electrical field would result

in the ions moving differently; hence, the conductivity wouldbe different.

Changes in the direction of the external electric field can

induce polarization phenomena. Polarization can occur with

immobile molecules; this also occurs when mobile ions move

back and forth on either side of an insulating membrane as the

charge double layer formed across the membrane changes its

polarity. The property of permittivity arises from the polarization

of electric charges and contributes to the displacement current

subject to a time-varying electric field.

B. Potential Applications

The conductivities and permittivities of intact wet living bio-

logical tissue are significantly different from those of an ex-

tracted sample. There is also much variation between indi-

viduals, which necessitates the development of new imaging

techniques to visualize these tissue properties in a quantitative

manner.

Brain ischemia causes cells to swell. Enlarged cells occupy

more space and the tissue undergoes microscopic structural

change. As long as the cell membranes remain intact, ions

cannot penetrate because the membranes are electrical insula-

tors. Ions can move around the swollen cells, but their effective

mobility is decreased, and the conductivity of that region is

decreased [22]. If the cells rupture, the extracellular space in-creases, and conductivity thus increases. During the generation

of action potentials in neurons, the ion flux properties of the

membrane change, resulting in a local change in conductivity.

Sadleir et al. investigated the feasibility of conductivity imaging

to detect fast neural activities [57]. Tumors exhibit significantly

higher conductivity values compared with surrounding normal

tissue [17].

Both conductivity and permittivity change with the frequency

[10], [11], [14]. Some physiological events, such as cell swelling

and neural activity, are detectable only at low frequency be-

cause thin cell membranes are transparent at high frequency.

The change in tissue composition can affect observations at

both low and high frequencies. Multifrequency approaches are

desirable for some applications [36].

In addition to the fact that the electrical tissue properties con-

vey useful diagnostic information, there is also strong interest

in obtaining conductivity and permittivity data from individual

subjects. The collection of such bioelectromagnetic data would

aid accurate forward modeling, which is a precursor for seek-

ing a reliable solution of an associated inverse problem. EEG

and MEG source imaging problems are typical examples as

suggested by Gao et al. [12], [13]. Various electric and mag-

netic stimulations, including RF ablation, deep brain stimula-

tion, transcranial electric or magnetic stimulation, and cardiac

defibrillation, require these values either to understand the un-

derlying mechanism or to optimize the protocols.

C. Probing Methods

Electrical conductivity and permittivity are passive tissue

properties, and can be measured only when an electric cur-

rent is applied. When current flows, distributions of the induced

voltage and magnetic field occur. The properties of conductivity

and permittivity determine how the voltage and magnetic flux

density distributions form inside the object. Noninvasive mea-

surement of the voltage and/or magnetic flux density enables

indirect observation of the admittivity distribution inside the

body, using these data and the underlying physical principles.

Assume that a particular object to be imaged occupies a

3-D domain Ω and that its admittivity distribution in Ω is

κ := σ + iωε under the influence of a time-harmonic electric

field E at angular frequency ω . There are two methods of pro-

ducing J,E, andB inside Ω: the injection of the dc or accurrent

into Ω using a pair of surface electrodes, and the use of an ac cur-

rent flowing in a coil outside Ω to induce eddy-currents inside Ω.

The quantities E,J,B, and κ are related by Maxwell’s

equations

J = (σ + iωε)E = 1

µ0∇ × B (1)

∇ × E = −iωB, ∇ · B = 0. (2)

Introduction of the vector magnetic potential A satisfying

B = ∇ × A and ∇ · A = 0 leads the induced time-harmonic

potential u to be governed by the equation

∇ · (κ∇u) = iω∇κ · A in Ω. (3)

Assuming that κ is isotropic, the relation between κ and B can

be obtained from (1) and (2)

−∇2

B = ∇ ln κ × (∇ × B) − iωµ0 κB in Ω (4)




Fig. 2. Custom-designed 16-channel multifrequency EIT system and its use in chest and phantom imaging experiments. The right diagram shows an exampleof the current injection and voltage measurement protocol. One can sequentially inject the current between all neighboring pairs of electrodes. For each injectioncurrent, the induced voltages between all neighboring electrode pairs are measured.

where µ0 is the magnetic permeability of free space, which is

approximately equal to that of the human body.

Most methods for imaging the electrical properties of tissue

are based on (3) or (4). To recover the admittivity κ, we can

measure either the voltage u in (3) or the magnetic flux density

B in (4). Note that the voltage is measurable noninvasively only

on the boundary, while the magnetic flux density can be detected

either inside or outside of the imaging object.

D. Boundary Measurement Method: EIT

EIT is one of the most studied admittivity imaging meth-

ods using measured voltage data on the boundary. It employs

multiple current sources and voltmeters to inject currents and

measure boundary voltages using multiple surface electrodes

(E j , j = 1, . . . , N ). Its development appears to have been moti-vated by the success of X-ray CT in the late 1970s [1], [4], [8],

[21], [45]. Under the fairly crude assumption that the direction

of J is known roughly, the overall conductivity values along the

lines of current flow can be evaluated from the knowledge of

the current–voltage relation on the boundary.

In the most commonly used EIT technique, N different

currents are injected sequentially using N different adjacent

pairs of electrodes (E j , E j +1 ), j = 1, . . . , N , where we set

E N +1 = E 1 . Using the same or separate N pairs of elec-

trodes (E k , E k + 1 ), k = 1, . . . , N , we measure the voltage dif-

ferences V j k = u j |E k − u j |E k + 1 subject to the jth injection cur-

rent, where u j

denotes the voltage corresponding to the j

th

current that is injected between the electrode pair (E j , E j +1 ).

For simplicity, we ignore the contact impedances underneath

the electrodes in this paper. At low frequency, below 100 KHz,

with the diameter of Ω being less than 1 m, the identity (2) is

approximated as ∇ × E ≈ 0, which leads to −∇u j ≈ E j and

∇ · (κ∇u j ) ≈ 0 in Ω, where E j is the electric field correspond-

ing to the jth current.

The inverse problem of EIT is to provide a cross-sectional

image of κ from the measured current–voltage data V j k for

j, k = 1, . . . , N . Note, the current–voltage reciprocity

V j k = 1

I

Ω

κ∇u j (r) · ∇uk (r)dr = V k j (5)

for j, k = 1, . . . , N , where I = −

E jκ∇u j · dS is the injected

current, dS is the surface element, and r = (x,y,z) is the po-

sition vector. The total number of independent data in an N -channel EIT system is

N (N −1)2 . For N = 32, there are less than

496 independent measurements, which will lead to 496 equa-

tions in a linear system of equations, and thus, we can estimate

at most 496 conductivity values. Such an EIT system could pro-

duce raw images of 22 × 22 pixels. In other words, the effective

pixel size can be as large as 5% of the field of view. Fig. 2

shows a 16-channel multifrequency EIT system developed by

the authors’ group.

For image reconstructions, the domain Ω is discretized into

a computational mesh with elements pm , m = 1, . . . , M . The

value κ on each element pm is assumed to be a constant κm .

The corresponding M × N 2 sensitivity matrix is given by

A = (am n ) , am n :=

pm

∇u j · ∇uk dr (6)

where n = N ( j − 1) + k. The inverse problem of the static

EIT [9] is to find a best fit of the vector κ = (κ1 , . . . , κM )T ,

such that

κ1a1 + · · · + κM aM = V (7)

where am = (am 1 , . . . , am N 2 )T , V = (V 11 , . . . , V N N )T , and

the superscript T denotes a matrix or vector transpose. The sen-

sitivity matrixA is a nonlinearfunction of κ and depends heavily

on the boundary geometry of Ω and the electrode positions. As a

consequence, the current–voltage data V depend mainly on theboundary geometry and the electrode positions, whereas its de-

pendence on a local perturbation of κ is relatively small. Hence,

the problem (7) is nonlinear and severely ill-posed.

Under the strong assumption that the admittivity vector κ is

a small perturbation of a known vector κ0 , we can linearize the

problem (7) by approximating A ≈ A0 , where A0 is the sensitiv-

ity matrix corresponding to κ0 . The computation of A0 requires

the construction of a forward model to compute numerically u j .

In static EIT, it is necessary to have a very accurate knowledge

of the forward model because the computed data V0 = Aκ0 are

very sensitive to modeling errors, including boundary geome-

try errors and electrode position uncertainties. It would be best




Fig. 3. Mathematical framework of MREIT: (top, second from left) real and imaginary parts of k -space data corresponding to the cross-sectional slice Ωz 0 ; (top,second from right) MR magnitude image at the slice Ωz 0 , (top, first from right) four surface electrodes; (bottom, left) typical spin echo pulse sequence for MREIT;(bottom, second from right) conductivity image reconstructed by MREIT; (bottom, right) Bz , 1 and Bz ,2 data.

if the difference V − V0 depends mainly on the perturbation

κ − κ0 , such that V − V0 alleviates the forward modeling er-

rors [25]. However, previous works over the last three decades

have suggested that it is very difficult to eliminate forward mod-

eling errors even when any movement during data acquisition

is neglected. Barber and Brown observed the following [5]: If

electrodes are spaced 10 cm apart around the thorax, variation

in positioning of 1 mm will produce errors of 1% in the data

V. Such a 1% error would likely not allow imaging for clinical

applications.

Time- and frequency-difference EIT can effectively deal with

the forward modeling errors that prevent static EIT from pro-

ducing useful images. Time-difference EIT provides changes in

κ with time from the time changes of the current–voltage data.

Frequency-difference EIT reconstructs changes in κ with fre-

quency from the corresponding changes in V. The difference

EIT methods require reference data V0 measured at a prede-

termined fixed time or frequency. Assuming that V and V0

are measured from the same domain using the same electrodeconfiguration, the differenceV − V0 effectively eliminates for-

ward modeling errors [63]. Therefore, V − V0 is more directly

related to κ − κ0 and can provide useful images even with a

large amount of total errors and the use of the inaccurate sensi-

tivity matrix A0 [68].

Difference EIT, however, cannot provide high-resolution im-

ages because decreasing the element size will also increase the

coherence between column vectors. With increasing discretiza-

tion, |am ·a |am a ≈ 1 for neighboring elements pm and p distant

from the boundary. Robust imaging requires either decreasing

the mesh size or regularization (grouping elements); either re-

sults in larger effective pixels. If κ − κ

0

is known to be sparse,

sparse sensing allows a reasonable coherence so that the spatial

resolution can be increased by decreasing the mesh size taking

account of the “restricted isometry property” [6], [7].

E. Internal Measurement Method: MRCDI

In the late 1980s and early 1990s, Joy et al. [28], [58], [59]developed MRCDI, an MRI-based imaging technique that can

provide an image of J inside Ω. Low-frequency MRCDI em-

ploys the dc current of I mA injected in pulses, whose timing

is synchronized with an MRI pulse sequence. The current is

usually injected between the 90 and 180 RF pulses and also

between the 180 RF pulse and the read gradient, as shown in

Fig. 3.

The injection current I induces an internal magnetic flux

densityB = (Bx , By , Bz ) to perturb the main magnetic field of

the MRI scanner [54]. This perturbation produces extra phase

shift in the MR phase image in such a way that its accumulation

is proportional to the product of Bz

and the current injection

time T c , where the z -axis is in the direction of the main field.

The acquired complex k -space data include the Bz data on each

imaging slice Ωz0 = Ω ∩ r : z = z0

S (kx , ky ) =

Ω z 0

M (r) eiγ B z (r)T c + iδ (r) ei( xk x +y ky ) dS xy

(8)

where M is theMR magnitudeimage, γ = 26.75 × 107 rad/T · s

is the gyromagnetic ratio of hydrogen, T c is the current pulse

width in seconds, and δ is any systematic phase artifact.

Two-dimensional Fourier transformation of the k -space MR

signal S (kx , ky ) provides the complex MR image M(r) :=

M (r) eiγ B z (r)T c

eiδ (r)

. To extract Bz (r) from M(r), we




inject the supplementary current with the opposite polarity to get

M−(r) := M (r) e−iγ B z (r)T c eiδ (r) . Bz can then be calculated

by computing (2γT c )−1 arg (M(r)/M−(r)) and then applying

a phase unwrapping algorithm [15]. For typical examples, see

Fig. 3.

Because an MRI scanner can measure only Bz , acquiring the

other two components Bx and By requires two mechanical ro-

tations while the object to be imaged is inside the bore. With

full knowledge of B = (Bx , By , Bz ), the current density can

be directly computed from Ampere’s law J = ∇ × B/µ0 . Al-

though this current density imaging method is not practicable

due to the requirement of rotations, it provides a noninvasive

method to measure the internal magnetic field at low frequency

in the form of an image with encoded position information.

III. MAGNETIC RESONANCE ELECTRICAL

IMPEDANCE TOMOGRAPHY

To overcome the fundamental limitations of EIT using bound-

ary voltage data only, additional measurements should be incor-

porated in the inverse problem. There are two possibilities for

this: the magnetic field outside the imaging object and the mag-

netic field insidethe object. In MIT, various workshavesought to

utilize theB field outside the domain using coils [16], [37], [77].

However, these methods suffer from low sensitivity—which is

due to the rapid decay of the field strength outside the domain—

and from a tangling of position information due to the mixing

of signals. By contrast, the internal magnetic field measurement

used in MRCDI alleviates both of these technical difficulties at

the expense of using an MRI scanner.

A. MREIT With Subject Rotation

The internal field measurement techniques used in MRCDI

motivated the developers of early MREIT systems to try to

recover σ from J = 1µ 0

∇ × B: Zhang [75] used the line inte-

gral u(P ) − u(Q) =

C 1σ Jdl, where C is a curve joining two

boundary points P and Q, and u is the corresponding potential;

Woo et al. [72] used a least-squares method of finding σ min-

imizing the difference between the measured J and computed

J(σ) = −σ∇u, where the potential u can be viewed as a non-

linear function of σ and the boundary condition; Ider and Bir-

gul [2], [3] used a sensitivity matrix betweenB and σ. However,

none of these early attempts produced high-quality conductivity

images during practical tests.

In the early 2000s, Kwon et al. [38] proposed the J -substitution algorithm based on a 1-Laplacian partial differential

equation

∇ ·

|J|

|∇u|∇u

= 0 in Ω. (9)

This J-based MREIT provided high-resolution σ images by

displaying σ = |J||∇u | [31]. Here, the solution u of (9) with suit-

able boundary data is computed approximately by an iterative

process using ∇ · J

σ n ∇un

= 0 (n = 1, 2 · · ·) with an initial

guess of σ0 = 1. A noniterative conductivity image reconstruc-

tion method termed current density impedance imaging (CDII)

was suggested in [20], [29], and [39]. Some theoretical CDII

studies using a single current density |J| have also been pub-

lished [49]–[51].

All of the J-based MREIT methods have practical difficulties

in imaging experiments because they require rotation of the sub-

ject, which has accompanying technical difficulties such as pixel

misalignment, movement of the internal organs, and distortion

of the boundary geometry. These problems are in addition to the

simple fact that there is no room to rotate a large object inside

the bore of the machine. A new method using only Bz data was

necessary to avoid such problems.

B. MREIT Without Subject Rotation

Bz -basedMREIT aims to reconstruct conductivity imagesus-

ing only Bz data without any rotation of the subject. Before the

creation of the constructive Bz -based MREIT algorithm, most

researchers considered Bz data to be insufficient for conductiv-

ity image reconstructions. Infinitely many conductivities σ can

produce the same B and J values. Considering the structure

σE = ∇ × B and ∇ · B = 0, it appeared that at least two com-

ponents of Bwould be necessary and, therefore, the impractical

rotation of the subject would be unavoidable.

A different view of the inverse problem of recovering σ from

the Bz data was found by Seo et al. [61], who carefully investi-

gated the z-component of the Biot–Savart law

Bz (r) = µ0

4π

Ω

r − r , σ(r)E(r) × z

|r − r|3 dr + B

ex t(r)

(10)

for r ∈ Ω, where Bex t is the magnetic field inside Ω due to

any currents outside Ω, such as external lead wires. In 2001,

they developed the first practically applicable Bz -based MREIT

algorithm based on the following key observation: Bz

data can

probe the change of ln σ in the direction of the vector field

z × J, whereas Bz data cannot probe the change of ln σ in the

direction of J. This observation comes from the identity

−1

µ0∇2 Bz = z × J · ∇ ln σ. (11)

Hence, if we could produce two linearly independent current

densities J1 and J2 , such that (z × J1 ) × (z × J2 ) = 0 in the

image domain Ω, it is possible to probe the change of ln σ in all

transverse directions in each slice Ωz0 = Ω ∩ z = z0 . It would

be best for z × J1 and z × J2 to be orthogonal in the imaging

region [43]. This is the main reason why we usually use two

pairs of surface electrodes E ±1 and E ±2 , as shown in Fig. 3 [52],[53].

C. MREIT Imaging Experiments

The Bz -based MREIT reconstructor, termed as the harmonic

Bz algorithm, was invented based on thefollowing formula [61]:

∇2xy σ =

1

µ0∇ ·

J 1y −J 1x

J 2y −J 2x

−1 ∇2 Bz ,1

∇2 Bz ,2

(12)

where ∇2xy = ∂ 2

∂ x 2 + ∂ 2

∂ y 2 is the transverse Laplacian.

Jeon et al. subsequently developed a noncommercial MREIT

software, the Conductivity Reconstructor using Harmonic




Fig. 4. MREIT animal and human experiments: (first column) canine head, (second column) canine kidney, (third column) canine prostate, and (fourth column)human leg. The MREIT images shown here are equivalent isotropic conductivity images providing contrast information only. Currently, absolute conductivityimages can be reconstructed from an isotropic object only.

Algorithm (CoReHA), to facilitate experimental MREIT studies

[26], [27], [65]. The Bz -based MREIT technique using the har-

monic Bz algorithm is implemented in CoReHA with the fol-

lowing steps:

1) Attach four surface electrodes in such a way as to maxi-

mize the area of the parallelogram made by the two vectors

J1 × z/J1 and J2 × z/J1 in the region of interest.

2) Sequentially pass electric currents I 1 and I 2 through the

two pairs of surface electrodes E ±1 and E ±2 , respectively,

and measure the k-space data S 1 and S 2 using an MRI

scanner.3) Compute Bz ,1 and Bz ,2 from the k-space data S 1 and

S 2 after applying proper phase unwrapping and unit

conversion.

4) Make a geometric model of the imaging domain, which

includes identification of the outermost boundary and the

electrode locations, to impose boundary conditions de-

scribing the current at the boundary. Using this model,

compute J1 and J2 iteratively as functions of σn using the

starting value of σ0 = 1.

5) Segment any problematic regions (such as bones and

lungs), where measured Bz data are defective due to

MR signal void phenomena. Prevent noise propagation

by properly handling such regions.6) Compute σ by solving the Poisson equation (12) with

suitable boundary conditions.

7) Rescale and update the conductivity using additional

information.

As part of the development of MREIT systems, as represented

in Fig. 1, various experiments have been performed post mortem

and in vivo on animal and human subjects [19], [32], [66], [73].

The conductivity images in Fig. 4 clearly show that MREIT

provides unique contrast information that is not available from

conventional MRI or other imaging techniques.

Following the in vivo imaging of the canine brain [33], numer-

ous in vivo animal imaging experiments have been conducted

to image the extremities, abdomen, pelvis, neck, thorax, and

head. Animal models of various diseases are also being investi-

gated. As part of efforts to develop clinical applications of the

technique, in vivo human imaging work is also under way [35].

These trials are expected to generate new diagnostic information

based on in vivo conductivity observations of various biological

tissues [68].

IV. DISCUSSION

MREIT has been developed in an attempt to overcome the

ill-posed nature of the inverse problem in EIT and to providehigh-resolution conductivity images. It provides low-frequency

conductivity images of an electrically conducting object with

a pixel size of about 1 mm. Such high spatial resolution is

achieved by using an MRI scanner to measure internal magnetic

flux density distributions induced by external injected currents.

Theoretical and experimental studies have demonstrated the po-

tential clinical usefulness of MREIT as a bioimaging modality.

Its capability to distinguish the conductivity of different biolog-

ical tissues in vivo is unique.

Future work should aim to overcome two major technical

barriers for the clinical use of the method. First, the amount

of the current passed through an object must be minimized

to a level that does not produce undesirable nerve or musclestimulation. Second, the anisotropy of the conductivity at low

frequency must be properly handled.

The quality of the reconstructed conductivity images depends

greatly on the signal-to-noise ratio (SNR) of the measured Bz

data. The signal, relative to a given amount of random noise

from the MRI scanner, can be enhanced using the current of

higher amplitude because the dynamic range of the induced Bz

is proportional to the current amplitude.

Early experimental studies used current amplitudes as high

as 40 mA to produce clear conductivity images of various parts

of animal subjects, including the head, chest, abdomen, and

pelvis. The development of optimized pulse sequences and the




use of highly sensitive multiple RF coils have decreased the

required current amplitude to 1 mA or below [27], [32], [33],

[35], [46]. Algorithmic enhancementshavealso helpedto reduce

the current amplitude by effectively reducing the noise [26],

[40], [41].

Because current injection at low frequency is unavoidable to

probe conductivity, which is a passive material property, the

level of the generated current density should be limited so that

it does not stimulate nerves or muscles. Large flexible surface

electrodes with a hydrogel layer of varying thickness can pro-

duce a more uniform current density underneath them [71]. By

spreading the current density more uniformly inside the imaging

domain, the amplitude of the total current can be increased for

better quality Bz data. The use of internal electrodes for current

injection also deserves more attention.

Forclinical applications, where thespatial resolution andcon-

ductivity contrast are primary concerns, we recommend using

1 to 5 mA injection currents, and 10 to 20 min scan times. For

example, if we inject 2.5 mA through a uniform current density

electrode with 5×5 cm2 contact area, the internal current den-sity can be well below 1 to 23 A/m 2 , which were estimated as

the threshold to stimulate a nerve with 20-µm diameter [55].

For a given range of Bz measured at a chosen current ampli-

tude, increasing the current injection time T c will also increase

the SNR since the amount of accumulated phase changes in the

MR signal is proportional to the product of Bz and T c [56],

[60]. Increasing the current injection time T c within one pulse

repetition time, however, introduces new problems. Decay in

transverse magnetization during the longer echo time that is

necessary to guarantee a longer T c results in weakening of the

MR signal. This causes deterioration of SNRs in both the MR

phase image and the MR magnitude image.For those applications, where fast functional imaging is

needed, we may significantly reduce the scan time at the ex-

pense of an increased voxel size. In certain cases, we may per-

form quantitative detection of conductivity changes instead of its

image reconstructions and utilize image fusion methods for vi-

sualization. Fast MREIT imaging has been investigated with fast

sequencessuch as EPI andSSFP. The most recent MREIT exper-

imentsutilize optimized pulse sequences designed for multiecho

signals from multiple RF coils [34]. These efforts to reduce the

current amplitude and scan time while maximizing SNR for a

given data collection time require innovative data processing

methods based on rigorous mathematical analyses, as well as

improved measurement techniques.To handle anisotropy, Seo et al. [62] developed an anisotropic

conductivity tensor image reconstruction algorithm that was

very sensitive to measurement noise. The equivalent isotropic

conductivity image may be suitable for certain applications such

as tumor imaging, in which image contrast is the primary con-

cern. However, correct representation of the anisotropy of nerve

or muscle tissues requires consideration of the anisotropy issue

in MREIT.

We may address this problem through the use of additional

information. Given that the water diffusion and conductivity

tensors share the same directional property [70], diffusion ten-

sor images readily available from most clinical MRI scanners

can be incorporated into the conductivity tensor image recon-

structions. Combining DT-MRI with MREIT, we can set the

eigenvectors of the conductivity tensor as those of the diffu-

sion tensor. Since DT-MRI cannot provide any information on

the eigenvalues of the conductivity tensor, we may utilize the

measured current-induced Bz data in MREIT to completely de-

termine the conductivity tensor. This hybrid approach will be

able to deal with the internal conductivity distribution including

both isotropic and anisotropic regions.

The admittivity values of most biological tissues change with

frequency [10], [11], [17]. Observing conductivity and/or per-

mittivity images at both low and high frequencies can strengthen

the diagnostic power of the MR-based electrical tissue property

imaging method. Here, we briefly introduce MAT-MI and EPT

as complementary methods to provide conductivity images in

megahertz range.

In MAT-MI, both static and time-varying magnetic fields are

used to probe the imaging object. The time-varying magnetic

fields induce an eddy current, which generates the Lorentz force

under the static field. Mechanical vibrations of the tissue pro-duce ultrasonic waves to be detected outside the imaging object.

Since the conductivity distribution affects the induced eddy cur-

rent, one may reconstruct its cross-sectional images from the

acquired ultrasonic signals [74]. The latest experimental re-

sults show absolute conductivity images of relatively simple gel

phantoms and biological tissues [23], [24], [44]. As a noncon-

tact method, MAT-MI has a potential to produce high-resolution

conductivity images at variable frequencies in the megahertz

range. There has been no study yet to implement MAT-MI in an

MRI scanner.

In EPT, which can be implemented simultaneously with

MREIT, the input is the conventional RF excitation used inMRI scanning, and the output is the positive rotating magnetic

field H + = (H x + iH y )/2, which can be measured by a B1-

mapping technique [18], [30], [42], [47], [48], [76]. The inverse

problem of EPT is to recover κ from H + and the governing

equation

−∇2H =

∇κ

κ × [∇ × H] − iωκH.

It is easier to implement EPT than MREIT on a clinical MRI

scanner because EPT does not require any additional instru-

mentation, while MREIT requires the attachment of surface

electrodes and an interface with a constant current source. Dual-

frequency conductivity imaging by combining MREIT and EPT

can be implemented simultaneously with a modified spin-echo

pulse sequence [36]. We refer to [64], [67], and [69] for a review

of EPT.

V. CONCLUSION

Electrical tissue property imaging provides unique diagnos-

tic information that is not available from other medical imag-

ing techniques using ultrasound, MR, visible light, X-rays,

or gamma rays. Considering the abundant information em-

bedded in the electrical properties of tissue, particularly con-

ductivity at low frequency, MREIT may open new areas of




research and clinical applications such as in tumor imaging and

neuroimaging.

As is commonly practiced in the field of medical imaging, the

multimodality approach is expected to form a significant part of

future research. Despite the relatively poor spatial resolution of

current EIT images, their high temporal resolution and porta-

bility are advantageous features of EIT for several biomedical

applications [22]. We consider that MREIT and EIT are com-

plementary, rather than competing techniques. Considering the

high spatial resolution of MREIT, Woo and Seo have discussed

its varied applicability in biomedicine, biology, chemistry, and

material science [73]. It is of note that a current density im-

age can be produced for any electrode configuration once the

conductivity distribution is obtained:

1) EIT (≤1 MHz): boundary current→boundary voltage;

2) MREIT (≤1 KHz): boundary current→internal Bz ;

3) MREPT (128 MHz at 3 T MRI): RF excitation →internal

H + = 12µ0

(H x + iH y ).

As summarized previously, EIT could be used when rapid

monitoring of physiological events is required with a focus onfunctional rather than structural information. MREIT and EPT

should be combined to produce multifrequency high-resolution

images of conductivity and permittivity. As these three imaging

methods begin to produce reliable and meaningful in vivo im-

ages, it will be necessary to accumulate large numbers of case

studies of various disease models to obtain useful diagnostic

information.

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