Correspondingauthor:ShaHong.email:sha_hong_2000SimulationStudyofElectrodeSystemOptimizationinElectricalImpedanceTomographyWangYan,RenChaoshi,ZhaoShu,WangLei,ShaHongInstituteofBiomedicalEngineeringChineseAcademyofMedicalSciences&PekingUnionMedicalCollegeTianjin,China.E-mail:sarahyky163.cmAbstractElectrodeliesinthefrontoftheElectricalimpedancetomography(EIT)systemandcontactswithhumanbodydirectly.ItisoneofthemostsensitiveandthepivotalpartsofEITsystem.Thetypeandtheconfigurationofelectrodesysteminfluencethereconstructionimagegreatly,especiallyforthecentralareaofbody,wherethemeasurementsensitivityisverylow.Asimulationplatformisdevelopedtooptimizetheelectrodestructureparameterbasedonthecoerciveequipotentialnodesmodelfortheimagingobjectofthedeepareaofbody.Theinfluencesonthemeasurementsensitivityandtheimagereconstructionqualityhavebeenstudiedusingdifferentelectrodetypesandconfigurations.Thesimulationresultssuggestthatoptimalselectionofelectrodetypesandconfigurationscanhelpfullyincreasetheimagequalityandmeasurementsensitivityoftheimageespeciallyincentralarea.SeveraltypeandconfigurationparameterofEITelectrodethatfitforcentralobjectimagingarealsopresented.Keywords-EIT；electrodesystem；reconstructionquality；measurementsensitivity；simulationevaluationI.0BINTRODUCTIONEITisoneoftheimportantresearchtopicsintodaysbiomedicalengineering1-3.EITelectrodearrayisoneofthemostsensitiveandthepivotalpartsofEITsystem.UsuallytenormoreelectrodesareusedinEITsystem.TheelectrodearrayliesinthefrontoftheEITsystemandcontactswithhumanbodydirectly.Thestructureandperformanceoftheelectrodesystemgreatlyinfluencetheoriginalinformationextraction,realtimepropertyofthesystem,imageresolvingpower,andespeciallytheinformationextractionfromcentralarea,wheretheEITmeasurementsensitivityispoor.Intheearlyoptimumstudyofelectrodeconfiguration,itiswidelyacceptedthatcurrentexcitationelectrodesshouldbeaslargeaspossiblewhilethevoltagemeasuringelectrodesarerequiredassmallaspossible4.PingHua5studiedtheinfluenceofcontactimpedancebetweenelectrodeandskin,andshowedthatthebesteffectcanbeobtainedwhenthetotalwidthofelectrodearrayisabout80-90%oftheimagedareasperimeter.E.J.Woo6usedannularcurrentandvoltageelectrodescovering90%ofthesurface.P.A.T.Pinheiro7reportedthattheoptimumareaunderneaththeelectrodesis80%oftheoverallboundaryareafortheadjacentpatternsand60%fortheoppositeones.WangChaoetal89carriedonthesimulationresearchontheinfluenceofelectrodewidthusingthecoerciveequipotentialnodefiniteelementmethod(FEM)model,andshowedthatthebesteffectwasobtainedwhentheoverlayrateofelectrodesis57.1%.AlthoughcontinuousprogressesonthechoiceofelectrodestructureparameterinEIThavebeenmade,thecompleteandsatisfactoryresulthasnotbeenseensofar.Inpractice,thedesignofEITelectrodestructureandparameterisstillbasedonexperience.AmongEITelectrodes,thecompoundelectrodehasmorecomplexstructure.FourparametersofthecompoundelectroderestricteachotherandtheirinfluenceonEITsystemaremuchcomplex.Theinfluencesofallparametersshouldbeconsideredcomprehensively.Usingonlytheoverlayrateofelectrodesisnotagoodwaytodealwiththecompoundelectrodeoptimizingdesign.InEITmeasurement,thecentralarea,correspondingtodeepareaofbody,isoftentheregionofinterest.Butthemeasurementsensitivityofthecentralareaisrelativelylowerandtheimagequalityisrelativelypoor.HowtoraisethemeasurementsensitivityandimprovetheimagequalityofthecentralareaisakeyprobleminEITmeasurement.TheexcitationpatternisalsoanimportfactorinEITmeasurement.Adjacentexcitationhasmoreindependentmeasurenumber.Oppositeexcitationpatternhaslessindependentmeasure,butthefielddistributionismorereasonablethanthatinadjacentpattern.Inthispaper,asimulationstudyofEITelectrodestructureandparameterdesignaimingattheimagingobjectofcentralareaispresented.Usingthecoerciveequipotentialnodemodelforcompoundelectrode10,asimulationplatformisdevelopedtocarryouttheoptimizingdesignoftheelectrodesystem.Basedonthemodelandtheplatform,theinfluencesoftheelectrodenumber,type,configuration,andexcitationpatternoftheelectrodesystemonthemeasurementsensitivityandtheimagereconstructionqualityhavebeenstudied.ThesimulationstudyofEITimagingwithdifferentdepthsofimagingobjecthasbeenmadewithequipotentialbackprojectionalgorithm.978-1-4244-4713-8/10/$25.002010IEEEII.1BMETHODA.4BFiniteElementModelforComplexElectrodesElectrodeplatesinroundorrectangleshapeareusuallyusedinEIT.Theprojectionsofbothelectrodesonthetomogramplanearealineandthelengthofthelineequalstothewidthoftheelectrodes,calledlineelectrode,asshownin(1)and(2)ofFig.1.Forthecompoundelectrodewithacomplexstructure,theprojectiononthetomogramplaneconsistsof3lines,asshownin(3)and(4)ofFig.1.Theexcitationelectrodeconsistsoftwolines,jinFig.1,ontheleftandtherightrespectively,andthemiddleline,cinFig.1,representsthemeasurementelectrode.Thereare4structureparametersforthecompoundelectrode(Fig.1),theexcitationelectrodewidthj,themeasurementelectrodewidthc,thespacebetweentheexcitationelectrodeandthemeasurementelectrodeb,andthedistancebetweentwoadjacentcompoundelectrodesa.EachofthemispresentedbythecountofFEMnodes.ForanEITelectrodesystemwithcertainboundary(suchas256nodesinthisstudy),whentheelectrodenumbers(32here)andelementsdividedinFEM(1210here)aredetermined,thesumofelectrodewideandthespacebetweenadjacentelectrodesisfixedtoo(8here).Figure1.ThelineelectrodeandcompoundelectrodeinEITAfiniteelementmethod(FEM)ofthecompoundelectrodeusingcoerciveequipotentialnodemodelhasusedtostudytheEITelectrodestructureparameteroptimizing10.B.5BEstimateFunctionsInordertoestimatetheinfluencesofelectrodestructureandparametersonthemeasurementsensitivityandtheimagereconstructionqualityinEIT,themeasurementsensitivityfunctionSandtheimagereconstructionqualityfunctionDaredefinedrespectivelyasfollows.1)10BThemeasurementsensitivityfunctionS%10011010=NiMjijSNMSHereMisthemeasurementnumbercorrespondingofonecurrentexcitation.Nisthenumberofcurrentexcitations.Sijdenotesthemeasurementsensitivityforjthmeasurementinithcurrentexcitation:0101=VVSijSijshowsthatthevoltageofthemeasurementelectrodechangesfromV0toV1whiletheconductanceofacertainregioninthemeasuredfieldchangesfrom0to1.SistheaveragesensitivityofallNtimesofexcitations.Itonlydependsontheelectricfielddistributionduetotheconductancechangeofthemeasuredregion,andisindependentofimagereconstructionalgorithmandhardwareerrors(supposethatsignaltonoiseratioofeachelectrodeisfixed).ThebiggertheSis,thehigherthemeasurementsensitivityis.2)11BTheImageReconstructionQualityFunctionD%100255)()(11=MpSpGpGiMD（p=1,2,M）HereMisthenumberofalltheelementsdividedintheimagingregion.Gs(p)isthegrayvalueofpthelementintheimagingmodel.Gi(p)isthegrayvalueofpthelementinthereconstructedimage.Dshowsthenormalizedaveragevalueofthegreyscaledifferencesbetweenthereconstructedimageandtheimagingmodelofeachelementintheimagingregion.Dsensitivelyreflectsthereconstructedimagequality.UsingD,thedifferencebetweenthereconstructedimageandtheimagingmodelcanbeevaluatedwithoutanyimageprocessing.ThesmallerDis,thelessthedifferencebetweenthereconstructedimageandtheimagingmodelis,thehigherthereconstructedimagequalityis.C.6BImagingModelsInthestudyofthispaperthetotalnumberoffiniteelementsis1210,including734nodes.Thereare256nodesonthecircumferenceofthemeasuredfield.6imagingmodelscorrespondingtodifferentmeasurementdepthhavebeenused(Fig.2).Theimagedobjectmovesfromtheboundarytothecentralareafrommodel1to6,andthemodel6istheimagedobjectofcentralarea,correspondingtodeepareaofbody.III.2BSIMULATIONEXPERIMENTANDRESULTA.7BEffectsofElectrodeNumberEITsystemwith8,16,32,64,128and256pointelectrodesareusedrespectivelyforstudy.TheestimateresultsusingfunctionsDfor6imagingmodelsinFig.1isshowninFig.3.Theimagingresultsofmodel3andmodel6areshowedinFig.4.B.EffectsofElectrodeTypeandStructureParameterThereconstructionimageshavebeenmadeusingthecoerciveequipotentialnodemethodforlineelectrodeandcompoundelectrode.Somecomparisonstudiesoftheparameterinfluencesonmeasurementsensitivityandreconstructionqualitybetweenlineelectrodeandcompoundelectrodehavebeencarriedout.Figure2.ImagingmodelsofdifferentdepthsFigure3.TheeffectsofelectrodenumberonimagequalityFigure4.Imagingresultswithdifferentelectrodenumberformodel3and6Thetotalwidthofbothlineelectrodeandcompoundelectrodearesettothesame.Asanexample,thewidthoflineelectrodeis5FEMnodes,whilecompoundelectrodehas3cases,inwhichthetotalwidthsofthemarealso5FEMnodes.Thefirsta=3,j=1,c=3andb=0,theseconda=3,j=1,c=1andb=1,thethirda=3,j=2,c=1andb=0.Theothercasesofdifferentwidthhavesimilarresult.ThefunctionsSandDofthereconstructionimagescorrespondingtoimagemodel6andmodel3respectivelyhavebeencalculatedandshownintableIandtableII.C.9BEffectofExcitationPatternTheeffectofexcitationpatternofEITonthereconstructedqualityandthemeasurementsensitivityhasinvestigated.Theexcitationpattern,whichdetermineshowthecurrentflowsintotheinterestingarea,influencesthedistributionofelectromagneticfielddirectly.Inthisstudy,theadjacent,intervalandoppositeexcitationmodeareused.Taken32electrodesasanexample,theexcitationcurrentisappliedbytwoelectrodes,andtheintervaloftheelectrodesischangedfrom1to16.Whentheintervalis1,itisadjacentexcitation.Andwhentheintervalis16,itisoppositeexcitation.Othercasesarecalledintervalexcitation,Fig.5.Thereconstructionresultsof32electrodesatintervalsof1,4,8,12,16electrodesrespectivelyhavebeenmadewiththeimagemodelsshowninFig.2.TheeffectsofexcitationpatternonimagequalityandmeasurementsensitivityhavebeenshowninFig.6andFig.7.TABLEI.COMPARISONOFLINEELECTRODEANDCOMPOUNDELECTRODEFORMODEL6TABLEII.COMPARISONOFLINEELECTRODEANDCOMPOUNDELECTRODEFORMODEL3Figure5.Adjacentexcitation,intervalexcitationandoppositeexcitationpatternFigure6.EffectsofexcitationpatternonimagequalityElectrodeTypeandStructureParameterDSLineelectrode:5nodeswide18.7060.003979a=3j=1c=3b=018.5840.003897a=3j=1c=1b=118.5760.003889a=3j=2c=1b=018.5890.003977ElectrodetypeandstructureparameterDSLineelectrode:5nodeswide14.3560.001871a=3j=1c=3b=014.6100.001836a=3j=1c=1b=114.4750.001831a=3j=2c=1b=014.4510.001875510152025308163264128256Delectrodecountmodel6model5model4model3model2model100.0050.010.0150.020.0251481216S%Intervalofcurrentelectrodesmodel6model5model4model3model2model1Figure7.EffectsofexcitationpatternonmeasurementsensitivityIV.3BRESULTSANDDISCUSSIONSFromFig3andFig4,itisshowedthatfornoncentralimagingobject,smallerelectrodenumberwillincreasethereconstructionerror.Butwhentheelectrodenumberturneduptoacertainextent,theimprovementbecamelesssignificant.Theimagequalityisalmostthesamewhenelectrodenumberismorethan64inthestudycondition.Fortheimagedobjectofcentralarea,especiallyformodel6，reconstructionqualityisverysimilar.Whentheelectrodenumberenlargedto128and256,theimagingqualityturnedabitworse.Thissuggeststhatforcentralobject,biggerelectrodenumbercannotbringbetterimagingquality.Inthispaper,the32and64electrodesystemisbetter.IntableI,fortheimagingobjectinthecentralarea,compoundelectrodehashigherimagequality,thanlineelectrode.AndintableII,fortheimagingobjectatsemi-radius,theeffectoflineelectrompoundelectrodeishelpedtoimproveimagequalityofthecentralarea.ThemeasurementsensitivitySoflineelectrodearealmostthesamewiththatofthethirdcaseofcompoundelectrode,andbetterthantheothertwocases,inbothtableIandII.Itmeansthat,ifthetotalelectrodewidthisfixed,themeasurementsensitivityisbetterwhenlargeexcitationelectrodehasbeenused.FromFig.6and7,itcanbeseenthatforeverydepthsofimagingobject,imagequalityturnsworseatintervalsofbiggerdistance,andthemeasurementsensitivityisincreasedsignificantly.Itisthesuggestionthatoptimizingofelectrodesystemaccordingtotheapplicationrequirement,forexampletheimagingobjectofdifferentdepthsandthedifferentexcitationpattern,isveryimportant.ThesimulationstudyofEITelectrodestructureandparameterdesignishelpfultogethighermeasurementsensitivityandgoodimagequality.12BREFERENCES1BarberD.C.andBrownB.H.,“Appliedpotentialtomography”,J.Phsy.E:Sci.instrum.,1984,17,pp.723-733.2Bro