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Medical impedance tomography and process impedance tomography: a brief review This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2001 Meas. Sci. Technol. 12 991 (http://iopscience.iop.org/0957-0233/12/8/301) Download details: IP Address: 128.148.252.35 The article was downloaded on 09/11/2012 at 13:34 Please note that terms and conditions apply. View the table of contents for this issue, or go to the journal homepage for more Home Search Collections Journals About Contact us My IOPscience

Measurement Science and Technology Volume 12 Issue 8 2001 [Doi 10.1088%2F0957-0233%2F12%2F8%2F301] Brown, Brian H -- Medical Impedance Tomography and Process Impedance Tomography-

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Page 1: Measurement Science and Technology Volume 12 Issue 8 2001 [Doi 10.1088%2F0957-0233%2F12%2F8%2F301] Brown, Brian H -- Medical Impedance Tomography and Process Impedance Tomography-

Medical impedance tomography and process impedance tomography: a brief review

This article has been downloaded from IOPscience. Please scroll down to see the full text article.

2001 Meas. Sci. Technol. 12 991

(http://iopscience.iop.org/0957-0233/12/8/301)

Download details:

IP Address: 128.148.252.35

The article was downloaded on 09/11/2012 at 13:34

Please note that terms and conditions apply.

View the table of contents for this issue, or go to the journal homepage for more

Home Search Collections Journals About Contact us My IOPscience

Page 2: Measurement Science and Technology Volume 12 Issue 8 2001 [Doi 10.1088%2F0957-0233%2F12%2F8%2F301] Brown, Brian H -- Medical Impedance Tomography and Process Impedance Tomography-

INSTITUTE OF PHYSICS PUBLISHING MEASUREMENT SCIENCE AND TECHNOLOGY

Meas. Sci. Technol. 12 (2001) 991–996 www.iop.org/Journals/mt PII: S0957-0233(01)22416-3

Medical impedance tomography andprocess impedance tomography: a briefreviewBrian H Brown

Medical Physics and Clinical Engineering, University of Sheffield,Royal Hallamshire Hospital, Sheffield S10 2JF, UK

E-mail: [email protected]

Received 2 March 2001, in final form 31 May 2001, accepted forpublication 6 June 2001

AbstractThe resurgence of research into medical electrical impedance tomographyabout 20 years ago was soon accompanied by a parallel development inprocess impedance tomography. The interaction between these two researchcommunities was beneficial to both groups. In recent years this interactionhas been very much reduced. This paper briefly reviews the history and thenthe current developments in medical impedance tomography.

Keywords: impedance, imaging, medical tomography, process tomography

1. Introduction

Several titles have been adopted to describe impedanceimaging systems. These include electrical tomography,impedance imaging, resistance imaging, electrical resistancetomography, impedance tomography and applied potentialtomography. The one in widest currency in terms of medicalimaging is electrical impedance tomography (EIT). The titleEIT has the advantage that you can consider it to includeresistive, capacitive and inductive tomographies.

All the proposed impedance imaging systems have a basicmethodology in common. They are all methods of imaging thedistribution of conductivity or permittivity within a volume.This volume might be a part of the human body or it mightbe the contents of a pipeline or vessel in a process controlsituation. There are two basic stages to the production of animpedance image:

(i) the collection of a set of N independent transferimpedances and

(ii) the solution of an inverse problem in order to produce animage from the set of transfer impedances.

This process can be illustrated in a medical context. We canapply a set of electrodes around the chest as shown in figure 1and then make the set of transfer impedance measurementsby applying currents and measuring voltages as illustrated infigure 2. It is easy to show that, if 16 electrodes are used,then only 104 (N(N − 3)/2) independent transfer impedancemeasurements can be made. These measurements can then beused to produce an image such as that illustrated in figure 3.

Figure 1. Electrodes applied for thoracic imaging.

Body tissues have resistivities similar to those ofsemiconductors (Duck 1990). Blood has a resistivity ofapproximately 1.6 � m. Lung has a higher resistivity ofabout 10 � m and this resistivity changes as air is inspired andexpired. It is relatively easy to form an image of the changes inresistivity distribution during respiration. Figure 3 shows suchan image. However, this image illustrates clearly the majordisadvantage of EIT. The spatial resolution is poor becausethere are only 104 independent measurements from which theimage can be reconstructed. This image resolves the two lungsand the cardiac region but the spatial resolution is only of theorder of 30 mm for a thorax which is 300 mm from side to side.However, there are balancing advantages which explain whyEIT is still under investigation and is used in several situations.These advantages include

(i) its low cost,

0957-0233/01/080991+06$30.00 © 2001 IOP Publishing Ltd Printed in the UK 991

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Figure 2. The sequence of transfer impedance measurements used to collect imaging data from 16 electrodes.

Figure 3. An EIT image showing the change in resistivity of thelung during breathing. The maximum change in resistivity is byapproximately 50%.

(ii) that there is no hazard to the patient,(iii) its simplicity of application,(iv) the high speed of data collection (typically 25 frames s−1)

and(v) that tissue/material characterization is possible

This illustration of impedance imaging has used resistiveimaging and a medical image as an example. However,capacitive imaging and inductive imaging are subject to verysimilar constraints. In all cases current is made to pass throughthe volume of interest and the resulting field patterns are usedto produce an image of conductivity or permittivity. A set ofindependent measurements is made and the number of theseconstrains the resolution of the image which can be produced.

The objectives of the medical and process tomographyareas are very different and some of the advantages anddisadvantages are relevant to one area only. However, workersin both areas were quick to see advantages in the developmentof impedance tomography and have put considerable effort intoresearch on the subject.

2. A brief history of impedance imaging

EIT has quite a long history and should no longer be considereda new technique. The first publication of an impedance imagewas that of Henderson and Webster (1978). They used atwo-dimensional matrix of 100 electrodes on one side of thethorax and a single large electrode on the other to produce a

transmission image of the tissues. However, the first publishedtomographic images were those of Brown (1983) and Barberet al (1983). They used 16 electrodes, injection of currentbetween adjacent electrodes and a back-projection method ofimage reconstruction along isopotentials.

Impedance imaging was introduced into process tomogra-phy during the 1980s and Professor Maurice Beck of Manch-ester was instrumental in getting the UK Medical and ProcessTomography groups together on several occasions. This inter-action gave rise to EIT systems being developed along similarlines in both research areas and led to developments such ascapacitive and inductive tomography (Wang et al 1992, Yangand York 1999, Griffiths et al 1999, Korjenevsky et al 2000,McCann et al 1999). The two groups drifted apart again duringthe 1990s but perhaps this publication is evidence that they arenow coming together again in the new millennium.

During the last twenty years there have been manyresearch programmes and a number of general publicationsin both medical and process tomography areas. For example,in the medical EIT area there have been the following.

(i) Two European concerted action programmes on EIT(called Applied Potential Tomography (APT) in theearly years). These gave rise to special issues of thejournal Physiological Measurement between 1987 and1996 following meetings in Sheffield, Lyon, Copenhagen,York, Barcelona, Ankara and Heidelberg.

(ii) A book introducing the technology published in 1990,Electrical Impedance Tomography, ed J G Webster(Bristol: Hilger)

(iii) A book considering the possible clinical applications pub-lished in 1993, Clinical and Physiological Applications ofEIT, ed D S Holder (London: UCL Press).

(iv) A comprehensive review article which appeared followingthe completion of the European Union concerted actionprogrammes in 1997, Imaging with electricity: report ofthe European concerted action on impedance tomography,J. Med. Engng Technol. 21 201–32.

(v) A relatively recent review which followed the 10thInternational Conference on Electrical Bio-impedanceheld in Barcelona, Spain in 1998. Many of thepapers are published as Electrical Bioimpedance Methods,

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Applications to Medicine and Biotechnology, Annals of theNew York Academy of Sciences, volume 873 (1999).

(vi) A very recent review of some medical applications byFrerichs, Physiol. Meas. 21 R1–21 (2000).

(vii) A book called Bioimpedance and Bioelectricity, Basicsby S Grimnes and Ø G Martinsen published by AcademicPress in 2000.

Several reviews and books on the process control applicationsof impedance tomography have also appeared. For example,see

(i) Process Tomography—State of the Art (Beck et al 1998),(ii) special issue on process tomography, Meas. Sci. Technol.

(1996),(iii) a book called Process Tomography: Principles

Techniques and Applications (Williams and Beck 1995)and

(iv) a review, Status of electrical tomography in industrialapplications (York 2001).

There is also a wide range of Web based sourceson medical and process EIT (see www.eit.org.uk andwww.tomography.umist.ac.uk). The volume of medicalresearch into EIT fell during the late 1980s because nomajor medical applications had emerged and it appeared thatthe limits of performance of EIT systems had almost beenreached. However, at that stage the use of multi-frequencyEIT began to be developed and this opened up ways aroundsome of the problems of medical EIT. One major problemin medical EIT is in taking the body shape into account.Body segments have complex shapes and these are the majordeterminants of any set of transfer impedance measurements.However, by using measurements made at one frequency as areference and then measurements made at another frequencyas a data set, it is possible to reduce the effects of bodyshape to a second-order effect. By making multi-frequencymeasurements, it was shown that tissue characterization usingimpedance spectroscopy was possible. Biological tissueshave a complex impedance because of their cellular structure.At low frequencies electrical current flows around cells,whereas at high frequencies the current can penetrate the cellmembranes and hence flow through the intracellular spaces.The significance of this is further expanded in section 4.1.

3. Medical EIT

Opinions regarding what the main research problems inmedical EIT are vary, but the following three appear on mostlists:

(i) taking into account the curved paths of electrical fieldwhen reconstructing images,

(ii) taking into account the body shape and(iii) making sufficiently accurate measurements of the transfer

impedance between electrode or coil combinations.

The first and third of these are common both to processtomography and to medical tomograpy. The second is specificto medical applications. The third problem arises because ofthe nature of EIT. The result of making a transfer impedancemeasurement from a volume conductor is a three-dimensionalintegral. Every part of the volume conductor contributes to

every measurement and hence the contribution from any onevoxel will be small. This means that a large dynamic range isrequired from the measurements. This can be very difficult toachieve, particularly when the effect of electrode impedanceis taken into account. Many researchers have wished thatthe electrodes could be made to disappear. By usingcurrent sources with infinite output impedance and recordingamplifiers with infinite input impedance, the electrodes canbe made to disappear, in that they should not affect themeasurements. However, current sources and amplifiers arenever perfect, so electrode problems remain. One way tosolve the problem is to use inductive tomography, for whichno electrodes are required. Current can be induced into thevolume conductor magnetically and the resultant current inthe tissues produces opposing magnetic fields which can alsobe detected. The instrumentation problems involved are veryconsiderable but this area is a very active one for currentresearch (Tozer et al 1999, Griffiths et al 1999, Korjenevskyet al 2000). There are other improvements to the hardwarewhich can be made to reduce the effects of electrodes andthese will be considered in section 4.

The following list gives some of the medical applicationsof EIT which have been considered:

(i) gastric emptying measurement, particularly for neonates(Vaisman et al 1999) ♠,

(ii) gastric pH measurement (Watson et al 1996),(iii) lung ventilation monitoring (Khambete et al 2000) ♠,(iv) optimization of ventilation during anaesthesia (Frerichs

et al 1999) ♠,(v) assessment of lung water in neonates and in adults with

heart failure (Noble et al 1999) ♠,(vi) detection of pulmonary embolus detection using both

ventilation and perfusion measurement (Leathard et al1994) ♠,

(vii) head imaging with a view to the detection of epileptic foci(Tidswell et al 2001) ♠,

(viii) breast imaging to detect cancer (Kerner et al 2001, Ultchinet al 2001) ♠,

(ix) measurement of tissue temperature during hyperthermia(Conway et al 1992),

(x) measurement of cardiac output (Patterson and Zhang2001, McArdle et al 1993) and

(xi) tissue characterization (Brown et al 2000) ♠.

The subjects marked with a ♠ have been investigated asresearch applications. Nearly all these applications involvethe measurement of changes in impedance. These changesmay be either temporal or frequency changes. One exceptionis the measurement of lung water, but here the changes are verylarge and so can be separated from the effects of body shape.

4. Future research in process and medical EIT

In addition to research into inductive tomography, there appearto be three major areas of change in terms of the technology ofmedical EIT. The first concerns the physical construction of thehardware, the second the use of multi-frequency data captureand the third three-dimensional EIT. The first and third haveseen parallel developments in process and medical EIT. Thesecond may be less relevant to process EIT because most of the

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Figure 4. The isopotentials when current is passed between two electrodes placed at nodes 15 and 55. In (a) the cells are distributedrandomly. It can be seen that the low and high frequency isopotential patterns are similar, although current does penetrate the cells at thehigh frequencies. In (b) the cells have been placed in a layer, in a manner found in some epithelial tissues. In this case both high and lowfrequency ispotential distributions are very different from those seen in (a).

volume conductors involved do not have complex impedancesin the frequency range where measurements are relatively easyto make. However, if biological materials are to be handled inprocesses such as those in biotechnology, then multi-frequencyEIT may well be relevant to process EIT.

4.1. Hardware

Nearly all medical EIT systems have used standard Ag/AgClelectrodes attached to the body and leads to connect to thedata collection electronics. People realized at an early stagethat the leads were very important and that they limited theachievable performance of the data collection system. Boot-strapping has been used widely and even triaxial cables havebeen used, but the limits of performance were probably reacheda few years ago. Shorter leads, or indeed getting rid ofthe leads completely, was the only way to go but peoplehave been quite slow to take this direction. Process EIThas probably led the way here. In part this was because theinvestigation of capacitance tomography made placement ofthe electronics very close to the electrodes absolutely essential.My opinion is that the integration of the current injectionand potential measurement electronics with the electrodeassemblies is vital if further significant improvements inaccuracy of measurement are to be obtained.

4.2. Multi-frequency-impedance spectroscopy

Biological tissues contain cells and this results in the tissueimpedance being complex. Typically the magnitude of thetissue impedance will fall by at least 50% between 10 kHzand 1 MHz. Put simply this is because current starts topenetrate cell membranes as the frequency increases. Thisis illustrated in figure 4(a), in which a mesh model has beenused to plot isopotentials at low and high frequencies. Itis possible to use the idea of differential EIT imaging toobserve changes of tissue impedance with frequency. Byusing a measurement made at one frequency as a referenceand then using measurements made at other frequencies asdata, images showing how impedance changes with frequencycan be obtained. The impedance spectrum for each pixelin the image can then be fitted to a Cole model and henceimages showing the spatial distribution of the Cole parametersdetermined. This has been shown to be an important innovationand allows quantitative measurements of tissue properties tobe imaged.

In medical EIT it is now becoming appreciated that animpedance spectrum can perhaps be related quantitatively tothe structure of tissue. This point is illustrated in figure 4(b), inwhich the cells which were randomly distributed in figure 4(a)have now been placed in a layer. The impedance spectrum

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that results is very much different. An impedance spectrum isdetermined by the arrangement of cells within the tissue. Thisis a very important observation and is the basis for recent workshowing that pre-malignant changes in cervical tissue can bedetected using impedance spectroscopy (Brown et al 2000).Similar changes are being investigated in oesophageal andbladder tissues, for which large finite element tissue modelsare being developed.

4.3. Three-dimensional imaging

Most objects of interest are three-dimensional. However, theimages produced by most EIT research groups have treated theobject as a series of two-dimensional slices, by collecting datafrom electrodes placed around the borders of a plane throughthe object. Unfortunately, unlike other three-dimensionalimaging methods such as x-ray computed tomography, a slicecannot be simply defined in this way in EIT. Electrical currentinjected into a three-dimensional object cannot be confinedto a plane but flows above and below the plane defined bythe electrodes. This means that conductivity distributionsin these regions contribute to the measured signals. Inorder to eliminate this problem, data collection and imagereconstruction must be considered as a fully three-dimensionalproblem. This can be achieved by placing electrodes over thewhole surface of the object. Typically this is done by placingelectrodes in a series of planes around the object. Any pair ofelectrodes, both within and between planes, can be used eitherfor applying current or for making potential measurements.Reconstruction, although involving more measurements andlarger sensitivity matrices, is identical in principle to the two-dimensional case (Metherall et al 1996).

5. Conclusions

EIT is a fast and inexpensive method of imaging materialproperties with many possible applications in both process andmedical fields. However, the two areas of application are verydifferent and have many different constraints. For example, thegeometry is usually well controlled in process instrumentation,in which electrodes may be placed around a regular and rigidstructure. However, electrodes placed around body segmentswill have irregular geometry and the shape may change withtime. It is for this reason that capacitive tomography usingquite large electrodes is a reasonable way forwards for processmeasurements but not for medical measurements. Anotherdifference is that, in many process control situations, theelectrical properties of the fluid are known and the purpose ofthe tomographic measurement is to assess the relative volumesof the flow compartments. In the medical situation the bodytissues have unknown electrical properties, although the rangeof likely values of conductivity and permittivity for particulartissues is known. A further difference between the medicaland process situations is that the dynamic range of valuesfor conductivity and permittivity is often much greater in theprocess area.

Multi-frequency measurements were made in the medicalEIT field as a means of reducing the dependence on body shape.However, the real value of spectral measurements has beenshown to be in tissue characterization. Because body tissues

are cellular, they have a characteristic impedance spectrumwhich can be used to assess the function of particular organs. Itmay be that the use of process instrumentation in biotechnologywill find similar value in the use of tomographic spectroscopy.

Future EIT data collection systems are likely to be muchsmaller and have wider bandwidths than present systems. Theymay be completely wireless and use some of the developmentsin wireless local area network (LAN) systems to return datato a microprocessor. Such systems could well be utilized tocollect data without any ground reference and hence obtainbetter immunity to noise. Impedance tomography is stilla fascinating subject for research and one in which greaterinteraction between the medical and process areas can only beof benefit.

References

Barber D C and Brown B H (ed) 1994 Electrical impedancetomography, special issue of Physiol. Meas. 15 (2A)

——1996 Electrical impedance tomography, special issue ofPhysiol. Meas. A 16 266

Barber D C, Brown B H and Freeston I L 1983 Imaging spatialdistributions of resistivity using applied potential tomographyElectron. Lett. 19 93–5

Beck M S, Dyakowski T and Williams R A 1998 Processtomography—state of the art IEEE Trans. Instrum. Meas.Control 20 163–77

Boone K, Barber D and Brown B 1997 Review: imaging withelectricity: report of the European concerted action onimpedance tomography J. Med. Engng Technol. 21 201–32

Brown B H 1983 Tissue impedance methods Imaging withNon-ionising Radiations ed D F Jackson (Guildford: SurreyUniversity Press)

Brown B H and Barber D C (eds) 1992 Special issue on electricalimpedance tomography of Clin. Phys. Physiol. Meas. 13(suppl A)

Brown B H, Barber D C and Tarrasenko L (eds) 1987 Electricalimpedance tomography—applied potential tomography Clin.Phys. Physiol. Meas. 8 (suppl A)

Brown B H, Tidy J, Boston K, Blackett A D, Smallwood R H andSharp F 2000 The relationship between tissue structure andimposed electrical current flow in cervical neoplasia Lancet355 892–5

Conway J, Hawley M, Mangnall Y, Amasha H and van Rhoon G C1992 Experimental assessment of electrical impedance imagingfor hyperthermia monitoring Clin. Phys. Physiol. Meas. 13A185–9

Duck F A 1990 Physical Properties of Tissue (New York:Academic)

Frerichs I 2000 Electrical impedance tomography (EIT) inapplications related to lung and ventilation: a review ofexperimental and clinical activities Physiol. Meas. 21 R1–21

Frerichs I, Hahn G, Schiffmann H, Berger C and Hellige G 1999Monitoring regional lung ventilation by functional electricalimpedance tomography during assisted ventilation Ann. NYAcad. Sci. 873 493–505

Griffiths H, Stewart W R and Gough W 1999 Magnetic inductiontomography: a measurement system for biological tissue Ann.NY Acad. Sci. 873 335–45

Grimnes S and Martinsen Ø G 2000 Bioimpedance andBioelectricity, Basics (London: Academic)

Hames T J (ed) 1990 Overview of clinical applications Proc.Copenhagen Meeting on Electrical Impedance Tomography(Copenhagen 1990) (Sheffield: University of Sheffield)

Henderson R P and Webster J G 1978 An impedance camera forspatially specific measurements of the thorax IEEE Trans.Biomed. Eng. 25 250–4

Holder D S (ed) 1993 Clinical and Physiological Applications ofEIT (London: UCL Press)

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Kerner T, Hartov A, Soho S, Poplack S and Paulsen K 2001 Usingelectrical impedance spectroscopy to image human breast:practical considerations which influence exam consistency3rd EPSRC Network Meeting, UCL, London

Khambete N D, Brown B H and Smallwood R H 2000 Movementartefact rejection in impedance pneumography using sixstrategically placed electrodes Physiol. Meas. 21 79–88

Korjenevsky A, Cheripenin V and Sapetsky A 2000 Magneticinduction tomography: experimental realisation Physiol. Meas.21 89–94

Leathard A D, Brown B H, Campbell J H, Zhang F, Morice A H andTayler D 1994 A comparison of ventilatory and cardiac relatedchanges in EIT images of normal human lungs and of lungswith pulmonary emboli Physiol. Meas. 15 A137–46

McArdle F J, Turley A, Hussain A, Hawley K and Brown B H 1993An in vivo examination of cardiac impedance changes imagedby cardiosynchronous averaging Clinical and PhysiologicalApplications of EIT ed D S Holder (London: UCL Press)pp 257–68

McCann H, Yang W Q and Polydorides N P 1999 Informationretrieval by electrical capacitance tomography: evaluation ofan alternative algorithm and the importance of boundaryconditions 1st World Congress on Industrial ProcessTomography (Buxton, April) pp 206–10

Meas. Sci. Technol. 1996 Special issue on process tomography 7308–15

Metherall P, Barber D C, Smallwood R H and Brown B H 1996Three-dimensional electrical impedance tomography Nature380 509–12

Noble T J, Morice A H, Channer K S, Milnes P, Harris N D andBrown B H 1999 Monitoring patients with left ventricularfailure by electrical impedance tomography Eur. J. HeartFailure 1 379–84

Patterson R and Zhang J 2001 Using EIT to observe cardiovascularchanges induced by the valsalva manoeuvre 3rd EPSRCNetwork Meeting, UCL, London

Riu P (ed) 1999 Electrical bioimpedance methods, applications tomedicine and biotechnology Ann. NY Acad. Sci. 873

Tidswell A T et al 2001 Electrical impedance tomography of humanbrain activity with a two-dimensional ring of scalp electrodesPhysiol. Meas. 22 177–85

Tozer J C, Ireland R H, Barber D C and Barker A T 1999 Magneticimpedance tomography Ann. NY Acad. Sci. 873 353–9

Ultchin Y, Nachaliel U and Ori A 2001 Indirect calculation of breasttissue impedance values 3rd EPSRC Network Meeting, UCL,London

Vaisman N, Weintrop N, Blumental A, Yosefberg Z and Vardi P1999 Gastric emptying in patients with type 1 diabetes mellitusAnn. NY Acad. Sci. 873 506–11

Wang M, Dicken F J and Beck M S 1992 Improved electricalimpedance tomography system and data collection protocolsProc. 1st European Concerted Action on Process Tomographypp 40–53

Watson S J, Smallwood R H, Brown B H, Cherian P andBardhan K D 1996 Determination of the relationship betweenthe pH and conductivity of gastric juice Physiol. Meas. 17 21–7

Webster J G (ed) 1990 Electrical Impedance Tomography (Bristol:Hilger)

Williams R A and Beck M S 1995 Process Tomography: PrinciplesTechniques and Applications (London: ButterworthHeinemann)

Yang W Q and York T A 1999 New ac-based capacitancetomography system Proc. IEE 146 47–53

York T 2001 Status of electrical tomography in industrialapplications J. Electron. Imaging at press

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