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D.C. Barber. Electrical Impedance Tomography.The Biomedical Engineering Handbook: Second Edition.

Ed. Joseph D. BronzinoBoca Raton: CRC Press LLC, 2000

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2000 by CRC Press LLC

68Electrical ImpedanceTomography68.1 The Electrical Impedance of Tissue68.2 Conduction in Human Tissues

68.3 Determination of the Impedance DistributionData Collection Image Reconstruction Multifrequency

Measurements

68.4 Areas of Clinical ApplicationPossible Biomedical Applications

68.5 Summary and Future Developments

68.1 The Electrical Impedance of Tissue

The specific conductance (conductivity) of human tissues varies from 15.4 mS/cm for cerebrospinal fluid

to 0.06 mS/cm for bone. The difference in the value of conductivity is large between different tissues(Table 68.1). Cross-sectional images of the distribution of conductivity, or alternatively specific resistance

(resistivity), should show good contrast. The aim of electrical impedance tomography (EIT) is to produce

such images. It has been shown [Kohn and Vogelius, 1984a, 1984b; Sylvester and Uhlmann, 1986] that

for reasonable isotropic distributions of conductivity it is possible in principle to reconstruct conductivity

images from electrical measurements made on the surface of an object. Electrical impedance tomography

(EIT) is the technique of producing these images. In fact, human tissue is not simply conductive. There

is evidence that many tissues also demonstrate a capacitive component of current flow and therefore, it

is appropriate to speak of the specific admittance (admittivity) or specific impedance (impedivity) of

tissue rather than the conductivity; hence the use of the world impedance in electrical impedance

tomography.

68.2 Conduction in Human Tissues

Tissue consists of cells with conducting contents surrounded by insulating membranes embedded in a

conducting medium. Inside and outside the cell wall is conducting fluid. At low frequencies of applied

current, the current cannot pass through the membranes, and conduction is through the extracellular

space. At high frequencies, current can flow through the membranes, which act as capacitors. A simple

model of bulk tissue impedance based on this structure, which was proposed by Cole and Cole [1941],

is shown byFig. 68.1.

Clearly, this model as it stands is too simple, since an actual tissue sample would be better represented

as a large network of interconnected modules of this form. However, it has been shown that this modelfits experimental data if the values of the components, especially the capacitance, are made a power

D.C. BarberUniversity of Sheffield

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function of the applied frequency!. An equation which

describes the behavior of tissue impedance as a function

of frequency reasonably well is

(68.1)

where Z0 and Z" are the (complex) limiting values of

tissue impedance low and high frequency and fc is a

characteristic frequency. The value of #allows for the

frequency dependency of the components of the model

and is tissue dependent. Numerical values for in-vivo

human tissues are not well established.

Making measurements of the real and imaginary com-

ponents of tissue impedivity over a range of frequencies

will allow the components in this model to be extracted. Since it is known that tissue structure alters in

disease and that R, S, C are dependent on structure, it should be possible to use such measurements to

distinguish different types of tissue and different disease conditions. It is worth noting that although maxi-

mum accuracy in the determination of the model components can be obtained if both real and imaginary

components are available, in principle, knowledge of the resistive component alone should enable the values

to be determined, provided an adequate range of frequencies is used. This can have practical consequences

for data collection, since accurate measurement of the capacitive component can prove difficult.

Although on a microscopic scale tissue is almost certainly

electrically isotropic, on a macroscopic scale this is not so forsome tissues because of their anisotropic physical structure.

Muscle tissue is a prime example (see Table 68.1), where the bulk

conductivity along the direction of the fibers is significantly

higher than across the fibers. Although unique solutions for

conductivity are possible for isotropic conductors, it can be

shown that for anisotropic conductors unique solutions for con-

ductivity do not exist. There are sets of different anisotropic

conductivity distributions that give the same surface voltage dis-

tributions and which therefore cannot be distinguished by these

measurements. It is not yet clear how limiting anisotropy is to

electrical impedance tomography. Clearly, if sufficient data could

be obtained to resolve down to the microscopic level (this is not

possible practically), then tissue becomes isotropic. Moreover, the tissue distribution of conductivity,

including anisotropy, often can be modeled as a network of conductors, and it is known that a unique

solution will always exist for such a network. In practice, use of some prior knowledge about the

anisotropy of tissue may remove the ambiguities of conductivity distribution associated with anisotropy.

The degree to which anisotropy might inhibit useful image reconstruction is still an open question.

68.3 Determination of the Impedance Distribution

The distribution of electrical potential within an isotropic conducting object through which a low-frequency current is flowing is given by

(68.2)

TABLE 68.1 Values of Specific Conductance

for Human Tissues

Tissue Conductivity, mS/cm

Cerebrospinal fluid 15.4

Blood 6.7Liver 2.8

Skeletal muscle 8.0 (longitudinal)

0.6 (transverse)

Cardiac muscle 6.3 (longitudinal

2.3 (transverse)

Neural tissue 1.7

Gray matter 3.5

White matter 1.5

Lung 1.0 (expiration)

0.4 (inspiration)

Fat 0.36

Bone 0.06

Z Z Z Z

j

= +

+

0

1f

fc

FIGURE 68.1 The Cole-Cole model of

tissue impedance.

( ) = 0

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where $is the potential distribution within the object and %is the distribution of conductivity (generally

admittivity) within the object. If the conductivity is uniform, this reduces to Laplaces equation. Strictly

speaking, this equation is only correct for direct current, but for the frequencies of alternating current

used in EIT (up to 1 MHz) and the sizes of objects being imaged, it can be assumed that this equation

continues to describe the instantaneous distribution of potential within the conducting object. If this

equation is solved for a given conductivity distribution and current distribution through the surface of

the object, the potential distribution developed on the surface of the object may be determined. The

distribution of potential will depend on several things. It will depend on the pattern of current applied

and the shape of the object. It will also depend on the internal conductivity of the object, and it is this

that needs to be determined. In theory, the current may be applied in a continuous and nonuniform

pattern at every point across the surface. In practice, current is applied to an object through electrodes

attached to the surface of the object. Theoretically, potential may be measured at every point on the

surface of the object. Again, voltage on the surface of the object is measured in practice using electrodes

(possibly different from those used to apply current) attached to the surface of the object. There will be

a relationship, the forward solution, between an applied current patternji, the conductivity distribution

%, and the surface potential distribution $iwhich can be formally represented as

. (68.3)

If %andjiare known, $ican be computed. For one current patternji, knowledge of $iis not in general

sufficient to uniquely determine %. However, by applying a complete set of independent current patterns,

it becomes possible to obtain sufficient information to determine %, at least in the isotropic case. This

is the inverse solution.In practice, measurements of surface potential or voltage can only be made at a

finite number of positions, corresponding to electrodes placed on the surface of the object. This also

means that only a finite number of independent current patterns can be applied. For N electrodes, N-1

independent current patterns can be defined and N(N-1)/2 independent measurements made. This latternumber determines the limit of image resolution achievable with N electrodes. In practice, it may not

be possible to collect all possible independent measurements. Since only a finite number of current

patterns and measurements is available, the set of equations represented by Eq. (68.3) can be rewritten as

(68.4)

where v is now a concatenated vector of all voltage values for all current patterns, c is a vector of

conductivity values, representing the conductivity distribution divided into uniform image pixels, and

Aca matrix representing the transformation of this conductivity vector into the voltage vector. Since Ac

depends on the conductivity distribution, this equation is nonlinear. Although formally the precedingequation can be solved for cby inverting Ac, the nonlinear nature of this equation means that this cannot

be done in a single step. An iterative procedure will therefore be needed to obtain c.

Examination of the physics of current flow shows that current tends to take the easiest path possible

in its passage through the object. If the conductivity at some point is changed, the current path redis-

tributes in such a way that the effects of this change are minimized. The practical effect of this is that it

is possible to have fairly large changes in conductivity within the object which only produce relatively

small changes in voltage at the surface of the object. The converse of this is that when reconstructing the

conductivity distribution, small errors on the measured voltage data, both random and systematic, can

translate into large errors in the estimate of the conductivity distribution. This effect forms, and will

continue to form, a limit to the quality of reconstructed conductivity images in terms of resolution,

accuracy, and sensitivity.

Any measurement of voltage must always be referred to a reference point. Usually this is one of the

electrodes, which is given the nominal value of 0 V. The voltage on all other electrodes is determined by

measuring the voltage difference between each electrode and the reference electrode. Alternatively, voltage

i iR j= ( ),

v A cc=

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differences may be measured between pairs of electrodes. A common approach is to measure the voltage

between adjacent pairs of electrodes (Fig. 68.2). Clearly, the measurement scheme affects the form of Ac.

Choice of the pattern of applied currents and the voltage measurement scheme used can affect the

accuracy with which images of conductivity can be reconstructed.

Electrical impedance tomography (EIT) is not a mature technology. However, it has been the subject

of intensive research over the past few years, and this work is still continuing. Nearly all the research

effort has been devoted to exploring the different possible ways of collecting data and producing imagesof tissue resistivity, with the aim of optimizing image reconstruction in terms of image accuracy, spatial

resolution, and sensitivity.

Very few areas of medical application have been explored in any great depth, although in a number of

cases preliminary work has been carried out. Although most current interest is in the use of EIT for medical

imaging, there is also some interest in its use in geophysical measurements and some industrial uses. A

recent detailed review of the state of Electrical Impedance Tomography is given in Boone et al. [1997].

Data Collection

Basic Requirements

Data are collected by applying a current to the object through electrodes connected to the surface of theobject and then making measurements of the voltage on the object surface through the same or other

electrodes. Although conceptually simple, technically this can be difficult. Great attention must be paid

to the reduction of noise and the elimination of any voltage offsets on the measurements. The currents

applied are alternating currents usually in the range 10 kHz to 1 MHz. Since tissue has a complex

impedance, the voltage signals will contain in-phase and out-of-phase components. In principle, both

of these can be measured. In practice, measurement of the out-of-phase (the capacitive) component is

significantly more difficult because of the presence of unwanted (stray) capacitances between various

parts of the voltage measurement system, including the leads from the data-collection apparatus to the

electrodes. These stray capacitances can lead to appreciable leakage currents, especially at the higher

frequencies, which translate into systematic errors on the voltage measurements. The signal measured

on an electrode, or between a pair of electrodes, oscillates at the same frequency as the applied current.

The magnitude of this signal (usually separated into real and imaginary components) is determined,

typically by demodulation and integration. The frequency of the demodulated signal is much less than

the frequency of the applied signal, and the effects of stray capacitances on this signal are generally

FIGURE 68.2 Idealized electrode positions around a conducting object with typical drive and measurement elec-

trode pairs indicated.

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negligible. This realization has led some workers to propose that the signal demodulation and detection

system be mounted as close to the electrodes as possible, ideally at the electrode site itself, and some

systems have been developed that use this approach, although none with sufficient miniaturization of

the electronics to be practical in a clinical setting. This solution is not in itself free of problems, but this

approach is likely to be of increasing importance if the frequency range of applied currents is to be

extended beyond 1 MHz, necessary if the value of the complex impedance is to be adequately explored

as a function of frequency.

Various data-collection schemes have been proposed. Most data are collected from a two-dimensional

(2D) configuration of electrodes, either from 2D objects or around the border of a plane normal to the

principal axis of a cylindrical (in the general sense) object where that plane intersects the object surface.

The simplest data-collection protocol is to apply a current between a pair of electrodes (often an adjacent

pair) and measure the voltage difference between other adjacent pairs (see Fig. 68.2). Although in

principle voltage could be measured on electrodes though which current is simultaneously flowing, the

presence of an electrode impedance, generally unknown, between the electrode and the body surface

means that the voltage measured is not actually that on the body surface. Various means have been

suggested for either measuring the electrode impedance in some way or including it as an unknown inthe image-reconstruction process. However, in many systems, measurements from electrodes through

which current is flowing are simply ignored. Electrode impedance is generally not considered to be a

problem when making voltage measurements on electrodes through which current is not flowing, pro-

vided a voltmeter with sufficiently high input impedance is used, although, since the input impedance

is always finite, every attempt should be made to keep the electrode impedance as low as possible. Using

the same electrode for driving current and making voltage measurements, even at different times in the

data collection cycle, means that at some point in the data-collection apparatus wires carrying current

and wires carrying voltage signals will be brought close together in a switching system, leading to the

possibility of leakage currents. There is a good argument for using separate sets of electrodes for driving

and measuring to reduce this problem. Paulson et al. [1992] have also proposed this approach and also

have noted that it can aid in the modeling of the forward solution (see Image Reconstruction). Brown

et al. [1994] have used this approach in making multi-frequency measurements.

Clearly, the magnitude of the voltage measured will depend on the magnitude of the current applied.

If a constant-current drive is used, this must be able to deliver a known current to a variety of input

impedances with a stability of better than 0.1%. This is technically demanding. The best approach to

this problem is to measure the current being applied, which can easily be done to this accuracy. These

measurements are then used to normalize the voltage data.

The current application and data-collection regime will depend on the reconstruction algorithm used.

Several EIT systems apply current in a distributed manner, with currents of various magnitudes being

applied to several or all of the electrodes. These optimal currents (see Image Reconstruction) must be

specified accurately, and again, it is technically difficult to ensure that the correct current is applied ateach electrode. Although there are significant theoretical advantages to using distributed current patterns,

the increased technical problems associated with this approach, and the higher noise levels associated

with the increase in electronic complexity, may outweigh these advantages.

Although most EIT at present is 2D in the sense given above, it is intrinsically a three-dimensional

(3D) imaging procedure, since current cannot be constrained to flow in a plane through a 3D object.

3D data collection does not pose any further problems apart from increased complexity due to the need

for more electrodes. Whereas most data-collection systems to date have been based on 16 or 32 electrodes,

3D systems will require four times or more electrodes distributed over the surface of the object if adequate

resolution is to be maintained. Technically, this will require belts or vests of electrodes that can be

rapidly applied [McAdams et al., 1994]. Some of these are already available, and the application of an

adequate number of electrodes should not prove insuperable provided electrode-mounted electronics

are not required. Metherell et al. [1996] describe a three-dimensional data collection system and recon-

struction algorithm and note the improved accuracy of three-dimensional images compared to two-

dimensional images constructed using data collected from three-dimensional objects.

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Performance of Existing Systems

Several research groups have produced EIT systems for laboratory use [Brown and Seagar, 1987; Smith

et al., 1990; Rigaud et al., 1990; Jossinet and Trillaud, 1992; Lidgey et al., 1992; Riu et al., 1992; Gisser

et al., 1991; Cook et al., 1994; Brown et al., 1994; Zhu et al., 1994; Cusick et al., 1994] and some clinical

trials. The complexity of the systems largely depends on whether current is applied via a pair of electrodes(usually adjacent) or whether through many electrodes simultaneously. The former systems are much

simpler in design and construction and can deliver higher signal-to-noise ratios. The Sheffield Mark II

system (Smith et al., 1990) used 16 electrodes and was capable of providing signal-to-noise ratios of up

to 68 dB at 25 datasets per second. The average image resolution achievable across the image was 15%

of the image diameter. In general, multi-frequency systems have not yet delivered similar performance,

but are being continuously improved.

Spatial resolution and noise levels are the most important constraints on possible clinical applications

of EIT. As images are formed through a reconstruction process the values of these parameters will depend

critically on the quality of the data collected and the reconstruction process used. However practical

limitations to the number of electrodes which can be used and the ill-posed nature of the reconstruction

problem make it unlikely that high quality images, comparable to other medical imaging modalities, canbe produced. The impact of this on diagnostic performance still needs to be evaluated.

Image Reconstruction

Basics of Reconstruction

Although several different approaches to image reconstruction have been tried [Wexler, 1985; Yorkey, et

al., 1986; Barber and Seagar, 1987, Kim et al., 1987; Hua et al., 1988; Cheny et al., 1990; Breckon, 1990;

Zadecoochak et al., 1991; Kotre et al., 1992; Bayford et al., 1994; Morucci et al., 1994], the most accurate

approaches are based broadly on the following algorithm. For a given set of current patterns, a forward

transform is set up for determining the voltages v produced form the conductivity distribution c(Eq. 68.4). Acis dependent on c,so it is necessary to assume an initial starting conductivity distribution c0.

This is usually taken to be uniform. Using Ac, the expected voltages v0are calculated and compared with

the actual measured voltages vm . Unless c0is correct (which it will not be initially), v0and vmwill differ.

It can be shown that an improved estimate of cis given by

(68.5)

(68.6)

where Scis the differential of Acwith respect to c, the sensitivity matrix and Stc is the transpose of Sc. The

improved value of cis then used in the next iteration to compute an improved estimate of vm, i.e., v1.

This iterative process is continued until some appropriate endpoint is reached. Although convergence is

not guaranteed, in practice, convergence to the correct cin the absence of noise can be expected, provided

a good starting value is chosen. Uniform conductivity seems to be a reasonable choice. In the presence

of noise on the measurements, iteration is stopped when the difference between vand vmis within the

margin of error set by the known noise on the data.

There are some practical difficulties associated with this approach. One is that large changes in cmay

only produce small changes inv,and this will be reflected in the structure of Sc, making Stc Scvery difficult

to invert reliably. Various methods of regularization have been used, with varying degrees of success, to

achieve stable inversion of this matrix although the greater the regularization applied the poorer theresolution that can be achieved. A more difficult practical problem is that for convergence to be possible

the computed voltagesvmust be equal to the measured voltagesvmwhen the correct conductivity values

are used in the forward calculation. Although in a few idealized cases analytical solutions of the forward

c S S S v v ct

c ct= ( ) ( )

1

0 m

c c c1 0

= +

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Three-Dimensional Imaging

Most published work so far on image reconstruction has concentrated on solving the 2D problem.

However, real medical objects, i.e., patients, are three-dimensional. Theoretically, as the dimensionality

of the object increases, reconstruction should become better conditioned. However, unlike 3D x-ray

images, which can be constructed from a set of independent 2D images, EIT data from 3D objects cannotbe so decomposed and data from over the whole surface of the object is required for 3D reconstruction.

The principles of reconstruction in 3D are identical to the 2D situation although practically the problem

is quite formidable, principally because of the need to solve the forward problem in three dimensions.

Some early work on 3D imaging was presented by Goble and Isaacson [1990]. More recently Metherall

et al. [1996] have shown images using data collected from human subjects.

Single-Step Reconstruction

The complete reconstruction problem is nonlinear and requires iteration. However, each step in the

iterative process is linear. Images reconstructed using only the first step of iteration effectively treat image

formation as a liner process, an assumption approximately justified for small changes in conductivity

from uniform. In the case the functions Acand Scoften can be precomputed with reasonable accuracybecause they usually are computed for the case of uniform conductivity. Although the solution cannot

be correct, since the nonlinearity is not taken into account, it may be useful, and first-step linear

approximations have gained some popularity. Cheney et al. [1990] have published some results from a

first-step process using optimal currents. Most, if not all, of the clinical images produced to date have

used a single-step reconstruction algorithm [Barber and Seagar, 1987; Barber and Brown, 1990]. Although

this algorithm uses very nonoptimal current patterns, this has not so far been a limitation because of

the high quality of data collected and the limited number of electrodes used (16). With larger numbers

of electrodes, this conclusion may need to be revised.

Differential Imaging

Ideally, the aim of EIT is to reconstruct images of the absolute distribution of conductivity (or admit-tivity). These images are known as absolute (or static) images. However, this requires that the forward

problem can be solved to an high degree of accuracy, and this can be difficult. The magnitude of the

voltage signal measured on an electrode or between electrodes will depend on the body shape, the

electrode shape and position, and the internal conductivity distribution. The signal magnitude is in fact

dominated by the first two effects rather than by conductivity. However, if a changein conductivity occurs

within the object, then it can often be assumed that the changein surface voltage is dominated by this

conductivity change. In differential (or dynamic) imaging, the aim is to image changes in conductivity

rather than absolute values. If the voltage difference between a pair of (usually adjacent) electrodes before

a conductivity change occurs is g1and the value after change occurs is g2, then a normalized data value

is defined as

(68.7)

Many of the effects of body shape (including interpreting the data as coming from a 2D object when in

fact it is from a 3D object) and electrode placing at least partially cancel out in this definition. The values

of the normalized data are determined largely by the conductivity changes. It can be argued that the

relationship between the (normalized) changes in conductivity &cn and the normalized changes in

boundary data &gnis given by

(68.8)

where Fis a sensitivity matrix which it can be shown is much less sensitive to object shape end electrode

positions than the sensitivity matrix of Eq. 68.5. Although images produced using this algorithm are not

gg g

g g

g

gn=

+

=2 1 21 2 mean

g F cn n=

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completely free of artifact that is the only algorithm which has reliably produced images using data taken

from human subjects. Metherall et al. [1996] used a version of this algorithm for 3D imaging and Brown

et al. [1994] for multi-frequency imaging, in this case imaging changes in conductivity with frequency.

The principle disadvantage of this algorithm is that it can only image changes in conductivity, which

must be either natural or induced. Figure 68.3 shows a typical differential image. This represents the

changes in the conductivity of the lungs between expiration and inspiration.

Multifrequency Measurements

Differential algorithms can only image changes in conductivity. Absolute distributions of conductivity

cannot be produced using these methods. In addition, any gross movement of the electrodes, either

because they have to be removed and replaced or even because of significant patient movement, make

the use of this technique difficult for long-term measurements of changes. As an alternative to changes

in time, differential algorithms can image changes in conductivity with frequency. Brown et al. [1994]

have shown that if measurements are made over a range of frequencies and differential images produced

using data from the lowest frequency and the other frequencies in turn, these images can be used to

compute parametric images representing the distribution of combinations of the circuit values inFig. 68.1.For example, images representing the ratio of Sto R,a measure of the ratio of intracellular to extracellular

volume, can be produced, as well as images of fo= 1/2'(RC+ SC), the tissue characteristic frequency.

Although not images of the absolute distribution of conductivity, they are images of absolute tissue

properties. Since these properties are related to tissue structure, they should produce images with useful

contrast. Data sufficient to reconstruct an image can be collected in a time short enough to preclude

significant patient movement, which means these images are robust against movement artifacts. Changes

of these parameters with time can still be observed.

68.4 Areas of Clinical Application

There is no doubt that the clinical strengths of EIT relate to its ability to be considered as a functionalimaging modality that carries no hazard and can therefore be used for monitoring purposes. The best

spatial resolution that might become available will still be much worse than anatomic imaging methods

such as magnetic resonance imaging and x-ray computed tomography. However, EIT is able to image

small changes in tissue conductivity such as those associated with blood perfusion, lung ventilation, and

FIGURE 68.3 A differential conductivity image representing the changes in conductivity in going from maximum

inspiration (breathing in) to maximum expiration (breathing out). Increasing blackness represents increasing conduc-

tivity.

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fluid shifts. Clinical applications seek to take advantage of the ability of EIT to follow rapid changes in

physiologic function.

There are several areas in clinical medicine where electrical impedance tomography might provide

advantages over existing techniques. These have been received elsewhere [Brown et al., 1985; Dawids,

1987; Holder and Brown, 1990; Boone et al., 1997].

Possible Biomedical Applications

Gastrointestinal System

A priori,it seems likely that EIT could be applied usefully to measurement of motor activity in the gut.

Electrodes can be applied with ease around the abdomen, and there are no large bony structures likely

to seriously violate the assumption of constant initial conductivity. During motor activity, such as gastric

emptying or peristalsis, there are relatively large movements of the conducting fluids within the bowel.

The quantity of interest is the timing of activity, e.g., the rate at which the stomach empties, and the

absolute impedance change and its exact location in space area of secondary importance. The principal

limitations of EIT of poor spatial resolution and amplitude measurement are largely circumvented inthis application [Avill et al., 1987]. There has also been some interest in the measurement of other aspects

of gastro-intestinal function such as oesophageal activity [Erol et al., 1995].

Respiratory System

Lung pathology can be imaged by conventional radiography, x-ray computed tomography, or magnetic

resonance imaging, but there are clinical situations where it would be desirable to have a portable means

of imaging regional lung ventilation which could, if necessary, generate repeated images over time.

Validation studies have shown that overall ventilation can be measured with good accuracy [Harris et

al., 1988]. More recent work [Hampshire et al., 1995] suggests that multifrequency measurements may

be useful in the diagnosis of some lung disorders.

EIT Imaging of Changes in Blood Volume

The conductivity of blood is about 6.7 mS/cm, which is approximately three times that of most intratho-

racic tissues. It therefore seems possible that EIT images related to blood flow could be accomplished.

The imaged quantity will be the change in conductivity due to replacement of tissue by blood (or vice

versa) as a result of the pulsatile flow through the thorax. This may be relatively large in the cardiac

ventricles but will be smaller in the peripheral lung fields.

The most interesting possibility is that of detecting pulmonary embolus (PE). If a blood clot is present

in the lung, the lung beyond the clot will not be perfused, and under favorable circumstances, this may

be visualized using a gated blood volume image of the lung. In combination with a ventilation image,

which should show normal ventilation in this region, pulmonary embolism could be diagnosed. Some

data [Leathard et al., 1994] indicate that PE can be visualized in human subjects. Although more sensitive

methods already exist for detecting PE, the noninvasiveness and bedside availability of EIT mean that

treatment of the patient could be monitored over the period following the occurrence of the embolism,

an important aim, since the use of anticoagulants, the principal treatment for PE, needs to be minimized

in postoperative patients, a common class of patients presenting with this complication.

68.5 Summary and Future Developments

EIT is still an emerging technology. In its development, several novel and difficult measurement and

image-reconstruction problems have had to be addressed. Most of these have been satisfactorily solved.

The current generation of EIT imaging systems are multifrequency, with some capable of 3D imaging.These should be capable of greater quantitative accuracy and be less prone to image artifact and are likely

to find a practical role in clinical diagnosis. Although there are still many technical problems to be

answered and many clinical applications to be addressed, the technology may be close to coming of age.

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Defining Terms

Absolute imaging: Imaging the actual distribution of conductivity.

Admittivity: The specific admittance of an electrically conducting material. For simple biomedical

materials such as saline with no reactive component of resistance, this is the same as conductivity.

Anisotropic conductor: A material in which the conductivity is dependent on the direction in whichit is measured through the material.

Applied current pattern: In EIT, the electric current is applied to the surface of the conducting object

via electrodes placed on the surface of the object. The spatial distribution of current flow through

the surface of the object is the applied current pattern.

Bipolar current pattern: A current pattern applied between a single pair of electrodes.

Conductivity: The specific conductance of an electrically conducting material. The inverse of resistivity.

Differential imaging: An EIT imaging technique that specifically images changes in conductivity.

Distributed current: A current pattern applied through more than two electrodes.

Dynamic imaging: The same as differential imaging.

EIT: Electrical impedance tomography.Forward transform or problem or solution: The operation, real or computational, that maps or

transforms the conductivity distribution to surface voltages.

Impedivity: The specific impedance of an electrically conducting material. The inverse of admittivity.

For simple biomedical materials such as saline with no reactive component of resistance, this is

the same as resistivity.

Inverse transform or problem or solution: The computational operation that maps voltage measure-

ments on the surface of the object to the conductivity distribution.

Optimal current: One of a set of a current patterns computed for a particular conductivity distribution

that produce data with maximum possible SNR.

Pixel: The conductivity distribution is usually represented as a set of connected piecewise uniform

patches. Each of these patches is a pixel. The pixel may take any shape, but square or triangularshapes are most common.

Resistivity: The specific electrical resistance of an electrical conducting material. The inverse of con-

ductivity.

Static imaging: The same as absolute imaging.

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Bayford R. 1994. PhD thesis. Middlesex University, U.K.

Boone K, Barber D, Brown B. 1992. Imaging with electricity: Report of the European Concerted Action

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Breckon WR. 1990. Image Reconstruction in Electrical Impedance Tomography. PhD thesis, School of

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Further Information

All the following conferences were funded by the European commission under the biomedical engineering

program. The first two were directly funded as exploratory workshops, the remainder as part of a

Concerted Action on Electrical Impedance Tomography. Electrical Impedance TomographyAppliedPotential Tomography. 1987. Proceedings of a conference held in Sheffield, U.K., 1986. Published in Clin

Phys Physiol Meas 8:Suppl.A. Electrical Impedance TomographyApplied Potential Tomography. 1988.

Proceedings of a conference held in Lyon, France, November 1987. Published in Clin Phys Physiol Meas

9:Suppl.A. Electrical Impedance Tomography. 1991. Proceedings of a conference held in Copenhagen,

Denmark, July 1990. Published by Medical Physics, University of Sheffield, U.K. Electrical Impedance

Tomography. 1992. Proceedings of a conference held in York, U.K., July 1991. Published in Clin Phys

Physiol Meas 13:Suppl.A. Clinical and Physiologic Applications of Electrical Impedance Tomography.

1993. Proceedings of a conference held at the Royal Society, London, U.K. April 1992. Ed. D.S. Holder,

UCL Press, London. Electrical Impedance Tomography. 1994. Proceedings of a conference held in Bar-

celona, Spain, 1993. Published in Clin Phys Physiol Meas 15:Suppl.A.

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