USF Libraries
USF Digital Collections

Advances in Magnetic Resonance Electrical Impedance Mammography

MISSING IMAGE

Material Information

Title:
Advances in Magnetic Resonance Electrical Impedance Mammography
Physical Description:
Book
Language:
English
Creator:
Kovalchuk, Nataliya
Publisher:
University of South Florida
Place of Publication:
Tampa, Fla
Publication Date:

Subjects

Subjects / Keywords:
Electrical Impedance Imaging
Magnetic Resonance Imaging simulations
Boundary value problem
Breast phantom
Breast tissue conductivity
Dissertations, Academic -- Physics -- Doctoral -- USF   ( lcsh )
Genre:
non-fiction   ( marcgt )

Notes

Summary:
ABSTRACT: Magnetic Resonance Electrical Impedance Mammography (MREIM) is a new imaging technique under development by Wollin Ventures, Inc. in conjunction with the H. Lee Moffitt Cancer Center & Research Institute. MREIM addresses the problem of low specificity of magnetic resonance mammography and high false-positive rates, which lead to unnecessary biopsies. Because cancerous tissue has a higher electrical conductivity than benign tissue, it may serve as a biomarker for differentiation between malignant and benign lesions. The MREIM principle is based on measuring both magnetic resonance and electric properties of the breast by adding a quasi-steady-state electric field to the standard magnetic resonance breast image acquisition. This applied electric field produces a current density that creates an additional magnetic field that in turn alters the native magnetic resonance signal in areas of higher electrical conductivity, corresponding to cancerous tissue.This work comprises MREIM theory, computer simulations, and experimental developments. First, a general overview and background review of tissue modeling and electrical-impedance imaging techniques are presented. The experimental part of this work provides a description of the MREIM apparatus and the imaging results of a custom-made breast phantom. This phantom was designed and developed to mimic the magnetic resonance and electrical properties of the breast. The theoretical part of this work provides an extension to the initial MREIM theoretical developments to further understand the MREIM effects. MREIM computer simulations were developed for both idealized and realistic tumor models. A method of numerical calculation of electric potential and induced magnetic field distribution in objects with irregular boundaries and anisotropic conductivity was developed based on the Finite Difference Method. Experimental findings were replicated with simulations.MREIM effects were analyzed with contrast diagrams to show the theoretical perceptibility as a function of the acquisition parameters. An important goal was to reduce the applied current. A new protocol for an MREIM sequence is suggested. This protocol defines parameters for the applied current synchronized to a specific magnetic resonance imaging sequence. A simulation utilizing this protocol showed that the MREIM effect is detectable for a 3-mm-diameter tumor with a current density of 0.5 A/m², which is within acceptable limits.
Thesis:
Dissertation (Ph.D.)--University of South Florida, 2008.
Bibliography:
Includes bibliographical references.
System Details:
Mode of access: World Wide Web.
System Details:
System requirements: World Wide Web browser and PDF reader.
Statement of Responsibility:
by Nataliya Kovalchuk.
General Note:
Title from PDF of title page.
General Note:
Document formatted into pages; contains 179 pages.
General Note:
Includes vita.

Record Information

Source Institution:
University of South Florida Library
Holding Location:
University of South Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 001998408
oclc - 318059430
usfldc doi - E14-SFE0002443
usfldc handle - e14.2443
System ID:
SFS0026760:00001


This item is only available as the following downloads:


Full Text
xml version 1.0 encoding UTF-8 standalone no
record xmlns http:www.loc.govMARC21slim xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.loc.govstandardsmarcxmlschemaMARC21slim.xsd
leader nam Ka
controlfield tag 001 001998408
003 fts
005 20090408095018.0
006 m||||e|||d||||||||
007 cr mnu|||uuuuu
008 090408s2008 flu s 000 0 eng d
datafield ind1 8 ind2 024
subfield code a E14-SFE0002443
035
(OCoLC)318059430
040
FHM
c FHM
049
FHMM
090
QC21.2 (Online)
1 100
Kovalchuk, Nataliya.
0 245
Advances in Magnetic Resonance Electrical Impedance Mammography
h [electronic resource] /
by Nataliya Kovalchuk.
260
[Tampa, Fla] :
b University of South Florida,
2008.
500
Title from PDF of title page.
Document formatted into pages; contains 179 pages.
Includes vita.
502
Dissertation (Ph.D.)--University of South Florida, 2008.
504
Includes bibliographical references.
516
Text (Electronic dissertation) in PDF format.
520
ABSTRACT: Magnetic Resonance Electrical Impedance Mammography (MREIM) is a new imaging technique under development by Wollin Ventures, Inc. in conjunction with the H. Lee Moffitt Cancer Center & Research Institute. MREIM addresses the problem of low specificity of magnetic resonance mammography and high false-positive rates, which lead to unnecessary biopsies. Because cancerous tissue has a higher electrical conductivity than benign tissue, it may serve as a biomarker for differentiation between malignant and benign lesions. The MREIM principle is based on measuring both magnetic resonance and electric properties of the breast by adding a quasi-steady-state electric field to the standard magnetic resonance breast image acquisition. This applied electric field produces a current density that creates an additional magnetic field that in turn alters the native magnetic resonance signal in areas of higher electrical conductivity, corresponding to cancerous tissue.This work comprises MREIM theory, computer simulations, and experimental developments. First, a general overview and background review of tissue modeling and electrical-impedance imaging techniques are presented. The experimental part of this work provides a description of the MREIM apparatus and the imaging results of a custom-made breast phantom. This phantom was designed and developed to mimic the magnetic resonance and electrical properties of the breast. The theoretical part of this work provides an extension to the initial MREIM theoretical developments to further understand the MREIM effects. MREIM computer simulations were developed for both idealized and realistic tumor models. A method of numerical calculation of electric potential and induced magnetic field distribution in objects with irregular boundaries and anisotropic conductivity was developed based on the Finite Difference Method. Experimental findings were replicated with simulations.MREIM effects were analyzed with contrast diagrams to show the theoretical perceptibility as a function of the acquisition parameters. An important goal was to reduce the applied current. A new protocol for an MREIM sequence is suggested. This protocol defines parameters for the applied current synchronized to a specific magnetic resonance imaging sequence. A simulation utilizing this protocol showed that the MREIM effect is detectable for a 3-mm-diameter tumor with a current density of 0.5 A/m¨§, which is within acceptable limits.
538
Mode of access: World Wide Web.
System requirements: World Wide Web browser and PDF reader.
590
Co-advisor: John J. Heine, Ph.D.
Co-advisor: David A. Rabson, Ph.D.
653
Electrical Impedance Imaging
Magnetic Resonance Imaging simulations
Boundary value problem
Breast phantom
Breast tissue conductivity
690
Dissertations, Academic
z USF
x Physics
Doctoral.
773
t USF Electronic Theses and Dissertations.
4 856
u http://digital.lib.usf.edu/?e14.2443



PAGE 1

Keywords:ElectricalImpedanceImaging,MagneticResonanceImagingsimulations,BoundaryValueProblem,breastphantom,breasttissueconductivitycCopyright2008,NataliyaKovalchuk

PAGE 3

Dr.KallergihasgivenmeanopportunitytojointheDigitalMedicalImagingGroupattheH.LeeMottCancerCenteralthoughIhadverylittleexperienceinthisarea.Sheservedasanexampleformebeingsuchaversatileintellectualwithawarmand,atthesametime,strongpersonality.Dr.Kallergiinspiredandmotivatedmewithherenthusiasmandencouragementthroughoutmygraduatestudies. Dr.HeinehasovertakenthehardshipsofbeingmyimmediatesupervisorafterDr.KallergileftforGreece.Hisguidanceincomputersimulationwasessentialtothecompletionofthisdissertation. Dr.RabsonhasagreedtobemyCo-advisoratphysicsdepartmentandbecameacorner-stoneinalltheproblemsandroadblocksthatunavoidablycropupinthecourseofperformingresearch.MystudiesatUniversityofSouthFloridawouldnotbepossiblewithouthishelpwithvisadocumentation.Hisresponsetoallmyquestionsandrequestsapproachedthetimeofe-maildelivery.Iwasalwaysamazedwithhisintellectualabilitiesthatarefarbeyondmyreach. Dr.Wollin,M.D.,P.E.,FACR,despiteofhisnumeroustitlesstruckmewithadown-to-earthpersonality:workingwithhimwasagreatpleasureforme.MagneticResonanceElectricalImpedanceMammographyishiscreation,andIjustassistedhiminitsexperi-mentaldevelopmentandtesting.Hewasthemajoreditorofthisdissertationhelpinginitsprenatalstageswithnumerouscommentsandsuggestions.Dr.Wollindeservesmydeepestgratitudeforhisinvaluablehelpinallaspectsofthiswork. IamalsogratefultoGermanDiaz,MRtechnician,forhelpingconsiderablywithreal-izingtheexperimentaltestsandAnandManohar,amemberofmedicalimaginggroup,forhishelpintheearlystagesofthiswork. IwouldalsoliketothankthePhysicsDepartmentatUSF,especiallyitsrepresentativesDr.MukherjeeandDr.Witanachchi,foracceptingmetotheAppliedPhysicsPh.D.programandforprovidingnancialsupportthroughoutmygraduatestudies. Last,butnotleast,Iwouldliketothankmyfamilyfortheirunderstandingandlove.Theirsupportandencouragementwasintheendwhatmadethisdissertationpossible. ThankYou,ohGod,forgivingmestrengthtonishthiswork.GlorytoYouforeverythingYouhavemercifullyrevealedtome!

PAGE 4

ListofFigures.......................................iv ListofAbbreviations.....................................xii Abstract...........................................xiii Chapter1Introduction.................................1 Chapter2Signicance.................................4 2.1CurrentStageofBreastDiagnosticImaging..................4 2.2MREIMasaPotentialDiagnosticTechnique.................6 Chapter3ElectricPropertiesofNormalandCancerousBreastTissues......7 3.1MicroscopicElectricPropertiesofBiologicalTissue..............7 3.2MacroscopicElectricPropertiesofBiologicalTissue.............11 3.2.1ComplexConductivityandPermittivity................13 3.2.2TissueElectricBehaviorwithFrequency................14 3.2.3TissueConductionModels........................15 3.2.4ElectricPropertiesofBreastCancer..................24 Chapter4ImagingModalitiesBasedonElectricalImpedanceMeasurements...39 4.1ElectricalImpedanceScanning.........................39 4.2ElectricalImpedanceTomography.......................47 4.3MagneticResonanceElectricalImpedanceTomography...........48 Chapter5FundamentalsofMRI............................53 Chapter6TheoreticalDevelopment..........................65 6.1AnalyticalSolutionforMREIMFields.....................66 6.1.1ElectricPotentialEquations.......................66 6.1.2ElectricCurrentDensityEquations...................70 6.1.3AberrationalMagneticFieldEquations................71 6.1.4AberrationalMagneticFieldsinMRI.................74 6.2NumericalSolutionforMREIMFields.....................75 6.3CalculationofMRImagePerturbationduetoAberrationalMagneticField82 6.3.1MREIMEectInuencingFrequencyEncodeGradient(FEEect).83 6.3.2MREIMEectInuencingPhaseEncodeGradient(PEEect)...84i

PAGE 5

7.1BreastPhantomDevelopment..........................90 7.2MREIMApparatus................................93 7.2.1MagneticResonanceSystem.......................93 7.2.2FaradayShields..............................96 7.2.3CurrentProvidingMREIMComponents................100 7.3ImagingSequenceandSliceOrientation....................101 7.4ExperimentalResultsandDiscussion......................101 Chapter8Simulation:DevelopmentandResults...................108 8.1SimulationDevelopment.............................108 8.1.1MREIMSimulationAlgorithm.....................109 8.1.2NumericalCalculationofMREIMFields................113 8.1.3ContrastMeasurements.........................117 8.2SimulationResults:Simple(Idealized)TumorModel.............119 8.2.1ReplicationofExperiment........................120 8.2.2StudyoftheMREIMEects......................122 8.2.3Summary.................................134 8.3SimulationResults:RealisticTumorModels..................141 8.3.1SphericalTumorwithIsotropicandAnisotropicConductivity....141 8.3.2VariousTumorShapeswithAnisotropicConductivity........143 8.3.34-TumorModel..............................143 8.3.4Summary.................................145 Chapter9MREIMEectEnhancement:ReducingtheElectricalCurrentandFutureDirections........................................149 9.1PEEectOptimization.............................150 9.1.1PhaseEncodeMode...........................150 9.1.2ImageAcquisitionMode.........................151 9.1.3DirectionofFEandPE.........................151 9.2CurrentPulseTrainDesign...........................153 9.3SuggestedMREIMProtocol...........................157 9.4FurtherSuggestions...............................165 Chapter10Conclusion.................................167 References..........................................169 AbouttheAuthor..................................EndPageii

PAGE 6

Table2Dielectricpropertiesofbreasttissueatf=10kHz(measuredbyMorimoto,Kinouchietal.1990)..............................30 Table3Meanandstandarddeviationofthemagnitudeofimpedivityinsixgroupsoftissueatf=0:488kHz(measuredbyJossinet1996)...........31 Table4Averagevaluesoflow-frequency-limitresistivityforsixtypesoftissue(cal-culatedbyJossinet1998)............................33 Table5RSZcpeParametersmeasuredatf=(10kHz{10MHz)(fromChauveau,Hamzaouietal.1999).............................35 Table6Realandimaginarypartsofconductivityatf=200Hz(extractedfromScholzandAnderson2000)...........................37 Table7Comparisonofsystemparametersofadditivebreastdiagnosticmethods:Ultrasound(US),ElectricalImpedanceScanning(EIS),andMagneticRes-onanceImaging(MRI)(adoptedfromMalich,Boehmetal.2001).....44 Table8ReportedperformanceofEIS..........................46 Table9EectofTEandTRonimagecontrastinSpinEchoImaging.......60 Table104-Tumormodel..................................146 Table11MREIMdierenceimagescontrast-to-noiseanddetectabilityvaluesforre-alistictumormodels...............................147iii

PAGE 7

Figure2Changesofelectricalpropertiesincancerouscell.............10 Figure3Scanningelectronmicrographofabreast-cancercell...........12 Figure4Anidealizedplotoffrequencyvariationoftherelativepermittivityforatypicalbiologicaltissue(fromSchwan1957)................15 Figure5Asimpliedequivalentelectricalcircuitcorrespondingtotheelectricalbehavioroftissues..............................17 Figure6ApartoftheelectriccircuitwithresistanceRandreactanceX.....18 Figure7ComplexplaneplotofEq.(3.8)......................19 Figure8ElectricalcircuitdevelopedbyCole-Cole(ColeandCole1941)asamodelforthedispersionandabsorptionofmanyliquidsanddielectrics....20 Figure9AgraphicalrepresentationofEq.(3.14)..................21 Figure10AgraphicalrepresentationofEq.(3.13)..................22 Figure11Tissueequivalentcircuitdiagramincorporatingtheconstantphaseele-ment.....................................23 Figure12ReactancerxversusresistancerRplot(\depressedcircle")typicalforbiologicaltissue...............................25 Figure13Locationofthetissuesamplesexcisedfromaspecimenofinltratinglobularcarcinoma(fromSurowiec,Stuchlyetal.1988).........27 Figure14Conductivityofbreastcarcinomaasafunctionoffrequency(adaptedfromSurowiec,Stuchlyetal.1988)....................28iv

PAGE 8

Figure16Typicalimpedivitylociinthecomplexplaneofnon-fattybreasttissues(fromJossinet1998).............................32 Figure17Geometricalpropertiesofconductivityarcs(fromJossinetandSchmitt1999)......................................33 Figure18RSZcpemodel(fromChauveau,Hamzaouietal.1999)......35 Figure19Realandimaginarypartsofconductivityforvarioustypesofbreasttissue(calculatedusingparametersfromJossinet1998).........37 Figure20ElectricalImpedanceScanningPrinciple.................40 Figure21TransScanTS2000..............................41 Figure22TransScanexaminationwindow(fromDiebold,Jacobietal.2005)....42 Figure23Physicalcongurationofthesystemandmeasuringprocedure.....48 Figure24MagneticResonanceElectricalImpedanceTomographyimagingsetup.50 Figure25SystemvariablesintheMREITforwardproblemandillustrationoftype1andtype2reconstructionalgorithms..................51 Figure26(a)Acollectionof1Hnuclei(spinningprotons)intheabsenceofanexternallyappliedmagneticeld.(b)Anexternalmagneticeld~B0isappliedwhichcausesthenucleitoalignthemselvesinoneoftwoorientationswithrespectto~B0.......................54 Figure27(a)Inthepresenceofanexternallyappliedmagneticeld~B0,nucleiareconstrainedtoadoptoneoftwoorientationswithrespectto~B0.(b)Amagneticmomentprecessingaround~B0..................55 Figure28TippingoflongitudinalmagnetizationintotransversemagnetizationbyapplicationoftheRFeld~B1.......................56 Figure29Aftera90RFpulse,~MoscillatesatLarmourfrequencyinthex;yplanedecayingwithtimeT2............................57v

PAGE 9

Figure31PulsetimingdiagramforSpinEchosequence...............61 Figure32SliceorientationinMRI(adoptedfromtraining.seer.cancer.gov).....62 Figure33Adiagramfollowedtoderivetheanalyticalexpressionforaberrationalmagneticeldcreatedinsideandoutsideofahigherconductivesphereembeddedinalowerconductingmediumandsubjectedtoasteady-stateelectriceld..................................65 Figure34AsimpletumormodelusedforanalyticalMREIMdevelopments....67 Figure35AclosedsurfaceandboundingcurvedenedasthesurfaceoftheconeandmouthoftheconeforrR......................72 Figure36Aclosedsurfaceandboundingcurvedenedasthesurfaceoftheconeandmouthofthecone,respectively,forr>R..............73 Figure37Anon-standardmagneticreferenceframewiththeBoremagneticeldalongthe^ydirectionrather^zdirection(theusualconvention).....75 Figure38Aberrationalmagneticeld(Eq.(6.34))plottedfory=z=0......76 Figure39Comparisonofaberrationalmagneticeldimagesobtainedfrom(a)nu-mericalsolutionand(b)analyticalsolution.................79 Figure40Comparisonofmagneticeldplotsthroughy=N=2between(top)an-alyticalsolutionand(bottom)numericalsolution.............80 Figure41Comparisonofmagneticeldstrengthobtainedfromnumerical(column1)andanalyticalsolution(column2)...................81 Figure42FrequencyEncodeeect...........................85 Figure43PhaseEncodeeect.............................89 Figure44SlicedMREIMphantomconstructedoffragrancefreeNeutrogenasoapshowingthesphericalpieceoffat-freehotdogof1cmindiameter(cancersurrogate)...................................91 Figure45EchoPlanarImagingSequenceimages(transversalview)ofasoapphan-tomwithasoapandsaltsolutionasacancersurrogate..........92vi

PAGE 10

Figure47Acircuitdiagramemployingacustommadeconductivitycellusedforconductivitymeasurements..........................94 Figure48Agarsolutionconductivitydependenceongeneratorfrequency......95 Figure49ASiemensMagnetomSymphonyMaestroClass1.5Tsystem(SiemensMedicalSolutionsUSA,Inc.,Malvern,PA)usedfortheimagingexper-iments.....................................96 Figure50ASiemens1.5TSymphony7ChannelBiopsyBreastArrayprovidedbyInvivoCorp.(Orlando,FL)withthestabilizationpaddlesmodiedtoincludetheFaradayshieldelectrodes....................97 Figure51Stabilization/compressionpaddlesoftheMRbreastcoil.........98 Figure52(a)AdiagramofoftheloadedFSsand(b)itsequivalentseriescircuit.99 Figure53Adiagramoftheexperimentalsetup....................101 Figure54Sliceselection,phaseencoding,andfrequencyencodingdirections...102 Figure55Agarphantomimages(sagittalview)acquiredwithanSDSEsequencewiththegeneratorfrequencysettodf=60Hz/pix,i=10A/m2atf300Hz,df=60Hz/pix.........................104 Figure56IdenticalimagesetupasinFig.55.TheMREIMparameterswerechangedtoi=17A/m2atf300Hz,df=60Hz/pix.........105 Figure57IdenticalimagesetupasinFig.55.TheMREIMparameterswerechangedtoi=10A/m2atf350Hz,df=60Hz/pix.........105 Figure58IdenticalimagesetupasinFig.55.TheMREIMparameterswerechangedtoi=10A/m2atf200Hz,df=22Hz/pix.........106 Figure59AblockdiagramforMREIMsimulation..................112 Figure60AnalgorithmfornumericalsolutionforelectricpotentialusingFDM..115 Figure61MaximumerrorinVforeachiterationversusnumberofiterationsforSORscheme..................................116vii

PAGE 11

Figure63MaximumerrorinHforeachiterationversusnumberofiterationsfor!=1.9284489.................................118 Figure64ComparisonofsimulatedMREIMimagesofhigherconductivesphere(R=5mm)embeddedinalowerconductivemediumratio=23andcontrast=10%)withexperimentalresultsforthefollowingparameters:i=10A/m2atf=300:008Hz,df=60Hz/pix,andSD=2......121 Figure65Similarset-uptooneinFig.64.Simulationparameters:i=17A/m2,f=300:004Hz,df=60Hz/pix,ratio=23,contrast=9%,andSD=12....................................123 Figure66Similarset-upasinFig.64:i=10A/m2,df=60Hz/pix,ratio=23,contrast=10%,andSD=9,thedrivingfrequencywassettof=350:004Hz...................................124 Figure67ComparisonofMREIMsimulationimagesforthefollowingsetofpa-rameters:i=10A/m2atf=200:004Hz,df=22Hz/pix,ratio=23,contrast=10%,andSD=10withthecorrespondingexperimentalimages.....................................125 Figure68FrequencyEncodeeectstudy:DependenceofdetectabilityofMREIMsignalontheshiftinx,x=f df.......................128 Figure69FrequencyEncodeeectstudy:DependenceofdetectabilityofMREIMsignaloninitialtumorcontrast.......................129 Figure70FrequencyEncodeeectstudy:DependenceofdetectabilityofMREIMsignalonconductivityratiobetweenthetumorandsurroundingtissue.130 Figure71FrequencyEncodeeectstudy:DependenceofdetectabilityofMREIMsignalonappliedcurrentforthreetumorradii,R=5,2.5,and1.5mm.131 Figure72PhaseEncodeeectstudy:DependenceofdetectabilityofMREIMsignalontheshiftinthe^ydirection,ypix=ffgTRNp,whereTR=2s,andNp=128.................................133 Figure73Combinationofeects:DependenceofdetectabilityofMREIMsignalontheshiftinx,x=f df..........................135viii

PAGE 12

Figure75Combinationofeects:DependenceofdetectabilityofMREIMsignaloninitialtumorcontrast...........................137 Figure76Combinationofeects:DependenceofdetectabilityofMREIMsignalontheconductivityratiobetweenthetumorandsurroundingtissue...138 Figure77Combinationofeects:DependenceofdetectabilityofMREIMsignalonappliedcurrentforthreetumorradii,R=5,2.5,and1.5mm....139 Figure78MREIMsimulationdierenceimagesforcurrentlimitofi=2A/m2forthreetumorradii,R=5,2.5,and1.5mmwithconductivityratioratio=3andinitialtumorcontrast,contrast=0.............140 Figure79ComparisonofMREIMsimulationdierenceimagesobtainedusing(a)analyticaleldsolutions(d=32.5)and(b)numericaleldsolutions(d=30.1)....................................142 Figure80Imagesof(a)conductivity,(b)electricpotential,and(c)magneticeldstrengthatz=N=2andi=10A/m2forasphericalcancerlesionwithisotropicconductivitywithratio=3.MREIMsimulationdierenceimageispresentedin(d)...........................142 Figure81Imagesof(a)conductivity,(b)electricpotential,and(c)magneticeldstrengthatz=N=2andi=10A/m2forasphericalcancerlesionwithrandomlydistributedconductivity(=(0:30:01)S/m)onavariableconductivitybackground(=(0:10:01)S/m).MREIMsimulationdierenceimageispresentedin(d).....................143 Figure82Imagesof(a)conductivity,(b)electricpotential,and(c)magneticeldstrengthatz=N=2foranovalcancerlesionati=10A/m2withrandomlydistributedconductivity(=(0:30:01)S/m)onavariableconductivitybackground(=(0:10:01)S/m).MREIMsimulationdierenceimageispresentedin(d).....................144 Figure83Imagesof(a)conductivity,(b)electricpotential,and(c)magneticeldstrengthatz=N=2foralobularcancerlesionati=10A/m2withrandomlydistributedconductivity(=(0:30:01)S/m)onavariableconductivitybackground(=(0:10:01)S/m).MREIMsimulationdierenceimageispresentedin(d).....................144ix

PAGE 13

Figure85NumericalsimulationofabreastmodelwithfourtumorsdescribedinTable10ati=2A/m2.Imagesatz=N=2:(a)conductivityimage,(b)electricpotentialimage,(c)aberrationalmagneticeldstrengthimage,and(d)MREIMdierenceimageatf=20:004Hz,df=20Hz,SD=2,andcontrast=0...............................146 Figure86Threeschemestocovera2Drectilinearspace:top-to-bottomsequential,centricordering,andreversecentricordering................152 Figure87MREIMdierenceimagewithPEeectonlyobtainedforthreePEmodes:(a)sequential(top-to-bottom),(b)centric,and(c)reversecen-tric.......................................153 Figure88Twotypesofacquisitionfor2Dimaging:sequentialandinterleaved...154 Figure89MREIMdierenceimage(withPEeect)forslice2acquiredwith(a)sequentialand(b)interleavedacquisitionmodes..............155 Figure90MREIMsimulationdierenceimagesforswitcheddirectionofencodingforPEandFEeects.............................155 Figure91MREIMsimulationdierenceimagesforswitcheddirectionofencodingforPEandFEeectscomparedwithimagesobtainedwithconventionalencodingdirectionusedforexperiments..................156 Figure92MREIMsimulationdierenceimagesforcurrentpulsesequencethatisactiveonlyfortheweakestPEgradientapplication............156 Figure93ThecurrentdensityimagingsequencedevelopedbyScottetal.(Scott,Joyetal.1991)................................158 Figure94RectangularbipolarcurrentusedinMREIT(fromGao,Zhuetal.2006)159 Figure95InjectionCurrentNonlinearEncodingpulsesequenceforMREIT(fromKim,Leeetal.2007).............................160x

PAGE 14

Figure97MREIMsimulationdierenceimagesforinitialphaseangledependantonp......................................162 Figure98AschematicdiagramofsuggestedMREIMsequence...........163 Figure99DependenceofdetectabilityofMREIMsignalproducedbysuggestedMREIMsequenceonappliedcurrentforR=5,2.5,and1.5mm....164 Figure100MREIMsimulationdierenceimagesobtainedusingsuggestedprotocolforthelowestcurrentlimitspermittingMREIMeectvisibility.....165xi

PAGE 16

ThisworkcomprisesMREIMtheory,computersimulations,andexperimentaldevelop-ments.First,ageneraloverviewandbackgroundreviewoftissuemodelingandelectrical-impedanceimagingtechniquesarepresented.TheexperimentalpartofthisworkprovidesadescriptionoftheMREIMapparatusandtheimagingresultsofacustom-madebreastphantom.Thisphantomwasdesignedanddevelopedtomimicthemagneticresonanceandelectricalpropertiesofthebreast.ThetheoreticalpartofthisworkprovidesanextensiontotheinitialMREIMtheoreticaldevelopmentstofurtherunderstandtheMREIMeects.MREIMcomputersimulationsweredevelopedforbothidealizedandrealistictumormodels.Amethodofnumericalcalculationofelectricpotentialandinducedmagneticelddistribu-xiii

PAGE 17

AnewprotocolforanMREIMsequenceissuggested.Thisprotocoldenesparametersfortheappliedcurrentsynchronizedtoaspecicmagneticresonanceimagingsequence.AsimulationutilizingthisprotocolshowedthattheMREIMeectisdetectablefora3-mm-diametertumorwithacurrentdensityof0.5A/m2,whichiswithinacceptablelimits.xiv

PAGE 18

MagneticResonanceMammography(MRM)hasemergedasapromisingtechniquefordetecting,diagnosing,andstagingofbreastcancer(Esserman,Hyltonetal.1999).Despiteitsadvantages,MRMsuersfromalowspecicity,thenecessityofgivingintravenouscontrast,alongimagingtimecausedbyfatsuppression,andexpense,whichultimatelyimpactsitsuseinbroadercommunities(Duchesne,Burbanketal.2006).Sincecancerousbreasttissuehasahigherelectricconductivitythanthatofbenignandnormalbreasttissue,electricconductivitymaybeusedasabiomarkerfordetectionofcancer(FrickeandMorse1926;Singh,Smithetal.1979;Surowiec,Stuchlyetal.1988;Jossinet1996;Jossinet1998).1

PAGE 19

Thespecicgoalsofthisworkincludethefollowing:tocollectandanalyzethesupportingmaterialonthedierentiationofnormalandmalignantbreasttissueintermsofelectricalconductivity;todesignanddevelopabreastphantomthatimitatesbothmagneticresonanceandelectricpropertiesofnormalandcancerousbreasttissue;toconductexperimentalphantomimagingtests;toextendtheinitiallydevelopedMREIMtheorytobroadenunderstandingofMREIMeects;todevelopamethodforcalculationofelectricpotentialandinducedmagneticelddis-tributionforarealistictumormodelwithtumorsofirregularboundariesandanisotropicconductivities;todevelopMREIMsimulationforbothidealizedandrealistictumormodels;toreplicateexperimentalphantomimagingresultswithMREIMsimulation;todevelopamethodofquantitativedescriptionofMREIMeects;tostudyMREIMeectsbasedonsimulationresults;tosuggestsequenceprotocolthatwouldproducethemostconspicuousMREIMeectatthelowestappliedelectricenergy. TheaccomplishmentoftheaimsspeciedabovewillserveasaprerequisiteforfurtherMREIMdevelopments,clinicaltesting,andcommercialdevelopment.Whenfullydevel-oped,MREIMhaspotentialtodetectbreastcancerinearlystages,decreasingthefalse-positiverateforMRMandeliminatingunnecessaryinvasive,costly,anddistressingbiopsies. ThisdissertationcontainstenChapters.TheIntroductionoutlinesproblemsincurrentbreastcancerdiagnostics,aproposalforanewimagingtechniquethatiscapableofre-solvingtheseproblems,andalistofspecicaimsforthecourseofthiswork.Thesecond2

PAGE 21

Outofallimagingtechniques,breastMagneticResonanceImaginghasthehighestsen-sitivityandprovidesinformationabouttissuevascularitythatisnotavailablefrommam-mography(Morris2006).BreastMRIperformedforcancerdetectionrequirestheuseofintravenouscontrastagent,suchasGadolinium-DTPA,whichistakenupbyareasofthebreastwiththeincreasedvascularity.Malignantlesionsexhibitanincreasednumberofbloodvesselsandincreasedvascularpermeabilityduetoleakyendothelialcells(Morris2006).Whencontrastisinjected,malignantlesionswillgenerallyenhancerapidlyandstrongly.Malignantlesionsalsodemonstratewash-outthatisdenedasadecreaseofen-hancementafterthepeakhasbeenreached.Wash-outisthoughttoresultfromincreasedvascularpermeabilityandthepresenceofarterio-venousshunts(Morris2006).Ingen-eral,thebreastcancersenhancemorerapidlyandwashoutfasterthanbenignlesions.Alas,inltratinglobularcarcinoma,medullarycarcinoma,andductalcarcinomainsitucan4

PAGE 22

BI-RADS012345IncompleteNegativeBenignProbablySuspiciousHighlyBenignAbnormalitySuspiciousofMalignancy 2004131(7)1316(0)5899(1)474(0)416(84)84(68)2005212(10)1229(0)6191(0)433(2)296(50)70(55)2006368(14)1008(0)6032(6)478(1)275(47)58(46) Table1isavividillustrationoftheareainbreastcancerdiagnosticswhichrequiresimprovement.ThetermBI-RADS(BreastImagingReportingandDataSystem)referstothemammographyassessmentcategories(BreastImagingReportingandDataSystemAtlas2007).BI-RADS4and5aretheparticularcasesthatnecessitateanadjunctivediagnostictechniquetoeliminateunnecessarybiopsies.Asaresultofhighfalse-positiverateofbreast5

PAGE 23

reducingthenumberofFalsePositives(FP)byintroducinganadditionalparameterinimaging,electricalconductivity;eliminatingmanyunnecessaryinvasive,costly,andstressfulbiopsies;makingbreastMRImorecost-eectiveandlesstimeconsumingbyexcludingthene-cessityofintravenouscontrastinjectionandfatsuppression. Ifusedasanadjunctivediagnostictechnique(specicallytargetingBI-RADS4,5,and0),MREIMcansignicantlyreducethehighnegativebiopsyrates.6

PAGE 24

Thischapterpresentstheoutlineofmicro-andmacro-electricpropertiesofbreasttissue.First,ananalysisoftheelectricpropertiesofbiologicaltissueisprovided.Itisfollowedbyareviewofelectricalmodelsformeasuringthedielectricpropertiesofhumantissuewiththeemphasisonbreasttissue.Conductivity/impedivityvaluesmeasuredbyvariousauthorsareprovidedtoobtaintheconductivityratiobetweenmalignantandnormalbreasttissue.3.1MicroscopicElectricPropertiesofBiologicalTissue

PAGE 25

Asarstapproximation,tissuecanbeconsideredtotakeaformofanelectrolytecon-tainingdenselypackedcells.Theextracellularmatrixoccupiesanintermediatepositionbetweenthebloodvesselsandthecellmembraneandactsasatransitandstorageareafornutrients,water,andwaste.Anatomically,theextracellularmediumconsistsoftwosubcompartments:interstitialuid(aminoacids,sugars,fattyacids,coenzymes,hormones,neurotransmitters,salts,andwasteproductsfromthecells)andbloodplasma(Cure1991).Chemically,theextracellularmatrixcontainscations(sodium,potassium,andcalcium)andanions(chloridesandhydrogencarbonate). Normalcellspossesstheabilitytocommunicateinformationinsidethemselvesandamongothercells.Thecoordinationofinformationbythecellsofthebodyisinvolvedintheregulationandintegrationofcellularfunctionsandcellulargrowth.Whencancerarises,cellsarenolongerregulatedbythenormalcontrolmechanisms.Whenaninjuryoccursinabody,normalcellsproliferateandreplacethedestroyedanddamagedcellswithnewcellsorscartissue.Onecharacteristicfeatureofbothproliferatingcellsandcancercellsisthatthesecellshavecellmembranepotentialsthatarelowerthanthecellmembranepotentialofhealthyadultcells(around15mV)(Cone1974). Aftertherepairiscompleted,thenormalcellsintheareaofaninjurystopgrowing,and8

PAGE 28

Figure3showsascanningelectronmicrographofabreast-cancercell(fromtheNCI-SciencePhotoLibrary).3.2MacroscopicElectricPropertiesofBiologicalTissue Ourneedtoobtaintheratiobetweentheconductivitiesofmalignantandnormalbreasttissueresultedinanextensiveliteraturereviewinthisarea(Heine,Kovalchuketal.2008a),11

PAGE 30

@t;(3.1) where~Histhemagneticeld,~Eisthetime-varyingelectriceldintensityoscillatingwithfrequency!,sisstaticconductivity,and"iscomplexpermittivity.TherightsideofEq.(3.1)comprisesthetotalcurrentdensityincludingtheconductionanddisplacementcurrentsandcanbewrittenas~i=s~E+"@~E @t=s~E+j!"~E=~E(3.2) withj=p 1.Complexconductivitycanbeexpressedasfollows:=s+j!"(!);(3.3) wherethecomplexpermittivity"isgivenas"="0j"00:(3.4) Here"0and"00aretherealandimaginarypartsofthecomplexpermittivity,respectively.Throughthefrequencydependenceofthepermittivity,therealandimaginarypartsofcomplexconductivity,0and00,arealsofrequencydependent.Theyaregivenby0=s+!"0"00and00=!"0"0;(3.5) where"0isapermittivityoffreespace.Thus,theimaginarypartofpermittivitydenestherealpartofconductivity,andviceversa. Therehasbeenmuchconfusionintheliteratureoverthecomplexconductivitynomen-clature.Someresearchers(FosterandSchepps1981)includethestaticconductivity,s,intherealpartofpermittivity,sothealternativeformofEq.(3.3)ispresentedas=j!";(3.6)13

PAGE 31

!:(3.7) Sincebothdenitionsareusedintheliterature,oneshouldbecarefulinreferringtothesetermsfromvarioussources. Thechemistryliteraturecontainsmanyreferencestothedielectricconstantofmaterials,whichismeantastherealpartofcomplexpermittivity"0,typically,atlowfrequenciesatwhich"0isessentiallyindependentoffrequency(McAdamsandJossinet1995).Also,someauthorsusetheunit-lesspermittivity,regardingtoitasaratioofthepermittivitytothepermittivityoffreespace.3.2.2TissueElectricBehaviorwithFrequency Sincecurrentpassesthroughthreedierentmedia(ECM,ICM,andCM),thetissuebehavesdierentlycomparedtosimpleRCcircuitsduetothedistinctiveresponseofthesemediatocurrentdensityandfrequency. Becausebothconductivityandpermittivitydependonfrequency,thisdependenceshouldbeinvestigated.Atlowfrequencies(<1kHz),thecapacitivereactanceofthecellmembraneislarge;therefore,thecapacitanceofthecellmembraneactsasaninsulatinglayeratlowfrequenciessothatcurrentowsonlyintheextracellularmedium.Withthefrequencyincrease,theinteriorofcellsbecomesprogressivelyinvolvedintheconduction.Fromabout30kHzto30MHz,thecapacitivechargingofthecellmembraneandthedipolarrelaxationoftheproteinsinthetissuedeterminethepermittivity.Asthefrequencyincreases,insucienttimeisavailableduringeachcycletoallowcompletechargingofthecellmembranes.Asa14

PAGE 32

Theelectricpropertiesofbiologicaltissuesseemtofollowthesamedependenceonfre-quency.AsrstfullydescribedbySchwan(Schwan1957;SchwanandKay1957),therela-tivepermittivityofmosttissueshasafrequency-dependencepatternnormallydividedintothreefrequencydomainsofrelaxation:,,and(Fig.4).The-relaxationisgenerallyconsideredtobeassociatedwithextracellularsurfacepolarizationoflargecells,-relaxationisrelatedtoanincreaseincapacitivecharginganddischargingofthecellmembranes,and-relaxationarisesfromtherelaxationofbulkwaterinthetissue(Schwan1957).Formanyapplications,-and-relaxationregionsareparticularlyinterestingsincemostchangesbetweennormalandpathologicaltissuesseemtoappearinthisfrequencyrange.Moreover,itismorepracticaltodesignameasuringsystemdedicatedtolowfrequencies.

PAGE 33

Cole(Cole1928)inhisearlyworkin1928developedthetissueequivalentcircuitapproach,ndingtheimpedanceofafundamentalcell,andthenexpandedtheworktoasuspensionofhomogenousspheresthatmodeledthebulktissue.ThenoveltyofCole'sstudywasthatitincorporateda\constantphase(CP)impedanceelement"inthecircuitdiagram.Healsoshowedthatanynetworkcontaininganycombinationofresistancesandsinglevariableimpedancewithaconstantphaseangleindependentoffrequencyproducesreactanceversusresistanceplotsintheformofanarcofacirclewithacenterdisplacedalongbothaxes(\depressedcircle"). Thephaseanglebetweentheresistanceandreactance(Fig.6)canbefoundas=tan1(X=R),whichisconstantintheCPelementandresultsinalinearrelationshipbetweenthetwo,R=mX,wheremisaconstant.NotethattheCPelementdoesnotcontaintheexplicitformofreactanceXandbecomesaperfectconductorinthehigh-frequencylimit. TheCole-Colepaperin1941(ColeandCole1941)providedamajorturningpointintheresearchhistoryoftheelectricalpropertiesoftissuesandmembranes.Thedispersionandabsorptionofmanyliquidsanddielectricswerefoundtofollowthisempiricalexpression:""1="0"1 Inthisequation,"isacomplexdielectricconstant,and"0and"1arethedielectricconstantsinthelow-andhigh-frequencylimits,respectively,isageneralrelaxationtime,andisa16

PAGE 35

Onlyinthisspecialcase,at=0,Eq.(3.8)canbeusedtoobtaintherelationbetween"and.AddingthestaticconductiontermtoEq.(3.8)byusingthedenitionofthecomplexconductivityinformofEq.(3.6),wehavethefollowing""1="0"1 With=0,afterseparationofEq.(3.9)intorealandimaginarycomponents,multiplyingtheimaginarycomponentbyj!,wecanndthelimitoftheobtainedexpressionfor!!1:j!"00=lim!!1!2("0"1) 1+(!)2+s=1:(3.10) Equation(3.10)givesthefollowingrelationshipbetweenthepermittivityandconductivityexclusivelywhen=0:1s=("0"1)

PAGE 36

WhenplottedontheNyquistdiagram(Fig.7),Eq.(3.8)representsthearcofacirclewiththecenterdisplacedalongbothaxes,andthedepressionofanarcisrepresentedbyangle=2. Somesourcesassumethatthequantitiessuchaspermittivityandconductivityforthesamecircuitmayberepresentedbythedepressedcirclessimultaneously(Jossinet1996;Jossinet1998;JossinetandSchmitt1999).Toprovetheopposite,wewillrefertotheoriginalworkbyCole-Cole(ColeandCole1941).Figure8showstheelectriccircuitdiagramusedbyCole(ColeandCole1941)tomodelthedispersionandabsorptionofmanyuidsanddielectrics.WewillshowthatthefollowingcircuitresultsintheempiricalEq.(3.8). Sincetheimpedivityoftheleftlegis1 ("0"1)j!+(j!) j!h1+(j!)1i

PAGE 38

ComparingEq.(3.13)withEq.(3.6)wecanwritetheterminbracketsaspermittivity"="0+"1(j!)1 whichisequivalenttoEq.(3.8).Asmentionedpreviously,Eq.(3.14)representsthede-pressedcircleontheNyquistplotdiagramasshowninFig.9.Onthesamehand,thecorrespondingconductivity,derivedfromthesamecircuit,doesnotrepresentthedepressedcircleasshowninFig.10,whichcontradictsthestatementofsomeresearchers(JossinettandSchmitt1999).

PAGE 40

wherez3=r3+jx3representstheconstantphaseelement,andr3=mx3,wheremisaconstant,andx3isnotdenedexplicitly.Lettingz=r+jxandt=r1+r2,separatingEq.(3.15)intorealandimaginarypartswillresultinrtr1r2=(mr1mr+x)x3(3.16)23

PAGE 41

Solvingthissystemofequationswillgivetx2+tr2+mr1txmr1r2xr1trr1r2r=r21r2:(3.18) Atlowfrequencylimit,theimpedivityofthecircuitwillbeduetotheresistivityoftheleftleg(extracellularresistivity);thusr0=r1:(3.19) Athighfrequencylimit,theimpedivityisalsorealandequaltor1=r1r2 Itshouldbenotedthatr1
PAGE 43

In1988,Surowiecatal.(Surowiec,Stuchlyetal.1988)performedin-vitrotestsontumorspecimensfrom7dierentpatientscompletedwithin4hoursafterthesurgery.Therelativepermittivityofinltratingbreastcarcinomaandthesurroundingtissuewasmeasuredatfrequenciesfrom20kHzto100MHzusinganautomaticnetworkanalyzerandanend-of-the-linecapacitivesensor.Itshouldbenotedthatinordertominimizetheelectrodepolarizationeectbelow100kHz,asubstitutiontechniquedevelopedbySchwan(Schwan1963)wasused.Accordingtothistechnique,thetissuewasreplacedbyasalinesolutionofthesameconductivity,anditsdielectricpropertiesweredeterminedatlowfrequencies.Threemaincategoriesoftissueswereconsideredinthisstudy:thecentralpartofthetumor,thetumorsurroundingtissue,andtheperipheraltissue.Figure13showsoneofthespecimenswiththeselectedcylindricalregionscorrespondingtothemeasuredsamples. Thersttypeoftissuerepresentedthebulkofatumor(e.g.,Fig.13,sampleE2)andconsistedofcollagen,elasticbers,andtumorcells.Thesesampleshadlow-frequencyconductivitiesbetween2and4mS/cmwithdielectricconstantsrangingfrom2103to6103. Thesecondtypeofsampleswastakenfromtheinltratingmarginsofthetumorneartheedgeofthelesion(e.g.,Fig.13,sampleE4),wherefewertumorcellsandalargerportionofnormallydistributedcollagenandfatfromthesurroundingunaectedbreasttissuewerepresent.Thedielectricconstantsrangedfrom2:5103to8103at100kHz. Thethirdtypeofsampleswastakenfromtheperipherydistantfromthetumorbyapproximately2cm(e.g.,Fig.13,sampleE1).Thistissueiscomposedofconnectiveandglandulartissue.Thedielectricpropertiesofthethirdtypeoftissuedieredsignicantlyfromtheothertwotypes.Theconductivitiesofnormaltissuewerelessthan1mS/cmwithdielectricconstantlessthan500at100kHz. Asasummaryofthedielectricpropertiesmeasurements,Surowiecetal.(Surowiec,26

PAGE 45

Fromtheplotabove(Fig.14),theconductivitiesofthecentralpartofthetumorandtissuesurroundingthetumorat10kHzrangefrom2mS/cmto6mS/cm.Theconductivityofnormaltissueis0.3mS/cm.Thentheratiosofconductivitiesforcancerousandnormaltissuewillbeinarangefrom6to20atf=10kHz. Sincethemeasurementswereconductedatasignicantlyhigherfrequencyregionthanthatofourpresentstudy(200{300Hz),andSchwan'ssubstitutionalgorithmwasusedfordielectricpropertiesmeasurementsatfrequenciesbelow100kHz,theresultsofSurowiecetal.(Surowiec,Stuchlyetal.1988)studyshouldbeconsideredcarefullyintermsofourwork.28

PAGE 46

FromFig.15,therelativepermittivityofbreastwithmalignanttumorisaround104,andfornormalbreasttissueapproximately3500,makingtheratiobetweentherelativepermittivitiesformalignantandnormaltissue2.5. Anin-vivomeasurementofdielectricpropertiesofbreasttissueswasconductedbyMori-motoetal.(Morimoto,Kinouchietal.1990).Theauthorsusedathree-electrodemeasuringsystemconsistingofacoaxialneedleelectrodeinsertedintothetumor(rightbeforeabiopsywasperformed)andalargereferenceelectrodeplacedontheupperabdominalwall.Theelectricalimpedancewasmeasuredin54patientswithbreasttumors.Thetissue-equivalentmodelconsistedoftheextracellularresistance,Re,inparallelwithaseriescombinationoftheintracellularresistance,Ri,andcapacitanceofcellmembrane,Cm(Fig.5).Thesethreeparameterswerecalculatedonthebasisofabio-equivalentcircuitbymeansofcurve-ttingtechnique(AckmannandSeitz1984).Morimotoetal.madeanassumptionthattheimpedance-spectrumtrajectoryfollowsasemicirclehavingitscenterattherealaxis29

PAGE 47

\thedataof`normalbreasttissue'comprisedthevaluesofmastopathyandmam-marytissuearoundthetumor." Theauthorsstatedthevaluesforthreecomponents,Re,Ri,andCm,atthesinglefrequencyoff=10kHz(seeTable2). TissueTypeTotalImpedanceExtracellularIntracellularMembraneImpedance,Resistance,Resistance,Capacitance,Z,Re;Ri;Cm,pF Breastcancer1,2715081,4455862,4931,4903,5251,879Fibroadenoma8061449541561,1794466,1712,365\Normaltissue"6741577722031,9551,4145,9463,194Fattytissue5,6683,1666,0443,3888,6224,210554262 Accordingtotheauthors,\thevaluesofReandRiinbreastcancerweresignicantlyhigherthanthoseinbenigntumor,andthevalueofCminbreastcancerwassignicantlysmallerthanthatofbroadenoma."Thisstatementcontradictstheconclusionreachedbymostresearchersthattheresistanceofbreastcancerismuchlowerthanthatofnormaltissue.Apossibleargumentheremightlieinthedenitionofnormalbreasttissue,andoneshouldcomparethecancerous-tissueparameterswiththoseforfattytissue.AccordingtoJossinet(Jossinet1998),whoseworkwillbeconsiderednext,\thelow-frequency-limitresistanceofcarcinomawasfoundtobelargerthanthatofallothergroups(i.e.,mammarygland,mastopathy,andbroadenoma),fattygroups,connectivetissueandadiposetissueexcepted."30

PAGE 48

Inhisrstarticle(Jossinet1996),Jossinetinvestigatedthevariabilityofimpedivityinbreasttissuebyassessingthestandarddeviationandthereducedstandarderror.ThemeanandstandarddeviationvaluesofthemagnitudeofimpedivityinthesixgroupsoftissueareshowninTable3.Itwasconcludedthatbelow10kHz,thevariabilitywasattributedtothedispersionofmeasurementerrorsinconjunctionwiththedispersionofthesizeoftheexaminedtissuesamples. TissueTypeMagnitudeofImpedivityatf=0.488kHz,cm Mammarygland246147Connectivetissue1109371Adiposetissue2188338Carcinoma37397Fibroadenoma24570Mastopathy284110 InthesecondstudybyJossinet(Jossinet1998),theobjectivewastodistinguishmalignantandbenigntissuesusingtheCole-Coleparameters.TheCole-Coleparameters,0,1;etc.,werefoundbyttingtheplotsofreactivityversusresistivitytothecirculararcs.It31

PAGE 49

Theanalysisofexperimentaldatashowedtheabsenceofanysignicantdierenceinimpedivity,low-frequencylimitresistivity,0,andfractionalpower,,betweennormalandbenignbreasttissues(Table3).Thelow-frequency-limitresistanceofconnectiveandadiposetissuewasfoundtobelargerthanthatofcarcinoma. JossinetandSchmittattemptedinthethirdstudytodeneandevaluateasetofparam-etersdesignedtocharacterizeanddierentiatebreasttissues.Tissuefrequencyresponsewasdescribedas1+01 andrepresentedonacomplexplaneasacirculararc(Fig17). Eightparameterswereconsidered:low-frequency-limitadmittivity,0;32

PAGE 50

TissueTypeLow-Frequency-LimitRatioofResistivitiesResistivity,ofGivenTissue0,(cm)andCarcinoma Mammarygland2511480.65Connectivetissue12633873.25Adiposetissue23903866.14Carcinoma3891081Fibroadenoma254660.65Mastopathy2921140.75

PAGE 51

fractionalpower,;parameterQLH,0/1;parameterDA,distancetothelow-frequencyintercept;parameter500,magnitudeofphaseangleat500Hz;parameterSHF,high-frequencyslopeinphaseangle;parameterK,integratedphaseratio. Itwasconcludedthatnoneoftheparametersalonewassucientforthediscriminationofanyoneindividualgroupoftissue;thus,severalparameterswereneededfortheclassi-cationofspectra.Buttheresultsofthestatisticalanalysisoftheparametersetsshowedsignicantdierencesbetweenmostofthetissuegroups,especiallybetweencanceroustissueandothergroups.BasedontheerroneousinterpretationoftheCole-Coleempiricalformula(Eq.(3.8)),themeasurementresultsfromJossinet'sworkshouldbeconsideredwithcare.Takingintoaccounttheinverserelationshipbetweenconductivityandresistivity,theex-perimentalimpedivityplotsbyJossinet(Fig.16)resemblethetheoreticallyobtainedplotofEq.(3.13)presentedinFig.10. Chauveauatal.(Chauveau,Hamzaouietal.1999)investigatedex-vivosamplesofnormalandpathologicalbreasttissuesatfrequenciesfrom10kHzto10MHzintherst30minutesfollowingtheexcision.TheRSZcpemodelwhichresemblesourmodelshownonFig.11wasapplied(Fig.18). Theconstantphaseelementwasdenedas:Zcpe=1(C!)(Macdonald1987),whereCisapseudo-capacitance,and=1. Breasttissuewasclassiedintofourtypes:I-normalbreasttissue;II-InvasiveDuctalCarcinoma;III-InvasiveDuctalCarcinomawithstrongstromalreaction;IV-brocysticchanges.34

PAGE 52

CategoryR,S,C,C1;1013F1013F I114020.54961I114020.54961I15801100.87972II95.91091140.55580II7866.2320.490456II71.370.3750.518874III12441.9450.4733133III11545.22500.5148299IV33160180.492540IV28128170.551710 35

PAGE 53

IndexS/RIndexK1=Z01MHz=Z010kHzontherealpartIndexK2=Z001MHz=Z0010kHzontheimaginarypart. Basingontheindicesaboveatwo-categoryclassicationwasmade:Canceroustissue:0:20:85 Thesedierentiationparametersmightnotbeveryapplicabletoimagingtechniquessincetheyarebasedonratiosbetweenparametersmeasuredatdierentfrequencyranges. ScholzandAnderson(ScholzandAnderson2000)intheirstudyofElectricalImpedanceScanning,simulatedtheperformanceoftheElectricalImpedanceScannerandcomparedthesimulationresultswiththeexperimentaldatafromtheTransScanTS2000.Theyemployedthein-vitrostudiesofbreasttissuedielectricpropertiesinthefrequencyregionof488Hzto1MHzcarriedoutbyJossinet(Jossinet1998).TheCole-Coleparameters(FosterandSchwan1989;StuchlyandStuchly1990;Morucci,Valentinuzzietal.1996)derivedfromthesemeasurementswereusedtoextrapolatetheconductivityplotsintofrequencyregionof1108Hz(Fig19). Thevaluesof0and00atf=200HzextractedfromtheirplotsareshowninTable6.Atf=200Hz,therealpartofcarcinomaconductivityis3timeshigherthanthatofthe50/50mixofadiposeandconnectivetissues. Tosummarizethisreview,canceroustissuecanbedistinguishedfromthehealthybreasttissuebyitselectricproperties,specicallyelectricalconductivity,oritsinverse,impedivity.Thequantitativedierentiationofbreasttissueelectricpropertiesprovidesabroadrangeofvaluesvaryingfromstudytostudywhichmightbeduetoanumberofreasons:useofdierenttheoreticalmodelsforbiologicaltissuesimulation,erroneoususageofexperimentalparametersasregardedtothesupportingtheory,experimentalerrors(e.g.,low-frequencydielectricmeasurementerrorsduetopolarization,etc.),dierenttissueclassication(e.g.,36

PAGE 54

TissueType000S/mmS/mm Carcinoma1451Connectivetissue602Adiposetissue351 37

PAGE 55

Malichetal.intheirstudiesofEIS(Malich,Fritschetal.2000;Malich,Boehmetal.2001;Malich,Bohmetal.2001;Malich,Bohmetal.2003)wrotereferringFrickeandMorse,Singhetal.,Surowiecetal.,Jossinetetal.(FrickeandMorse1926;Singh,Smithetal.1979;Surowiec,Stuchlyetal.1988;Jossinet1996;Jossinet1998)that \...incontrasttotheseobservationsinnormaltissue,malignanttumorsshowsub-stantiallyincreasedcapacitanceandconductivityvalues.Invitrostudieshaveshown20{40-foldhighervaluesforbothparametersinmalignantascomparedtonormaltissue(Surowiec,Stuchlyetal.1988)." Consideringtheseguresandconductivityrangesabove,atfrequenciesofinterest(f=[200{300]Hz)wewillaccepttheconductivityratiobetweencancerousandnormaltissuetovaryintherangeof[3{40].Thereisanacuteneedforthemoreaccuratein-vivoconductivitymeasurementsofthenormalandmalignantbreasttissueperformedinthe-relaxationregion.Thisanticipatedstudyshouldprovidearealisticconductivitymodelandin-vivoexperimentsresultinginelectricalparametersmeasuredforvariousnormalandcancerousbreasttissuesamples.38

PAGE 56

Asapioneeringstudy,during1980s,theBreastCenterPistoia(Italy)startedElectricalImpedancebreastimagingwiththe\Mammoscan".\Mammoscan"comprisedan88matrixofsquareelectrodesandproduced4imagesforeachbreast.Sixthousandpatientswerescreened,ofwhich745underwentbiopsy.Alsoallpatientsunderwentanexamina-39

PAGE 58

TransScanTS2000system(TransScanResearchandDevelopmentCo.,Israel;distributedbySiemens,Erlangen,Germany)receivedclearancefromtheUnitedStatesFDAforuseasanadjuncttomammographyincaseswithequivocalmammograms(F-D-CReports1998)andbecametheonlycommerciallyavailablesystemforobtainingelectricalimpedancemeasurementsofthebreast(Fig.21). InaTransScanexamination,analternatingelectriceldisappliedbetweenthepatient's41

PAGE 59

Mellouletal.(Melloul,Pazetal.1999)intheirstudyin1999aimedtoassessthee-ciencyof99mTc-sestamibiscintimammography(SMM)andTransScanTS2000asadjunct42

PAGE 60

Intheirstudyin2000,Malichetal.(Malich,Fritschetal.2000)aimedtoevaluatethereliabilityofEIS(TranScanTS2000)examining52womenwith58sonographicallyand/ormammographicallysuspiciousndings.TwomodesofTranScanperformancewereused:targetedhigh-resolution(forlocalizedlesionexamination)andstandardresolutionmode(foraroutinebreastexamination).Outof58totallesions,29werebenignand29malignant.Inthetargetedmode,thesensitivityandspecicityachievedwere93%and65.5%,respectively,andtenFPswereobserved.Inthelower-resolutionstandardmode,thesensitivitywaslowerandspecicitywashigher,76%and72%,respectively,andeightFPswerereported.Malichatal.(Malich,Fritschetal.2000)pointedoutthelimitationtoasuccessfuluseofElectricalImpedanceScanningsuchassignalsfromsupercialskinlesions,poorcontact,andairbubbles.Also,thedetectionofthelesionsveryclosetothechestwallwasnotalwayspossibleasthemaximaldepthofEISmeasurementswaslimitedto3{3.5cm.Moreover,itwasnotpossibletolocalizeanEIS-positivelesionforbiopsyusingEIS.Malichetal.(Malich,Fritschetal.2000)concludedthatEIScouldbeusefulforpatientswithdensebreastswhereconventionalmammographyfailstoaccuratelydiagnose.Butatthemoment,asnotedbytheauthors, \theEISdidnotseemtoproveadeservedexistenceasanindependentimagingmodality." In2001Malichetal.(Malich,Boehmetal.2001)publishedtheextendedinvestigationoftheUltrasound(US),ElectricalImpedanceScanning(EIS),andMagneticResonanceImag-ing(MRI)asadjunctivetechnologiesbasedon100mammographicallysuspiciouslesions43

PAGE 61

Sensitivity(%)Specicity(%) US7789EIS8163MRI9881 TheEISsensitivityresultswerenotsignicantlyimprovedoverthoseforUS,andtheEISspecicitywassubstantiallylowerthanthatofUSandMRI.Outofeight\border-line"cases(DCISandhyperplasia),EISdetectedve.However,thisnumberwasnotsucienttodrawaconclusion.Therefore,afurtherextensionofthisstudyisneededtoverifytheabovendings.Inthesameyear,amorecomprehensivestudy(Malich,Bohmetal.2001)including240histologicallyprovenbreastlesionsindicatedthattheadditionofEIStomammographyandultrasoundincreasedthesensitivityfrom86.4%to95.1%,buttheaccuracydecreasedfrom82.3%to75.7%.ThestudyalsosuggestedthatEIShasapoordetectionrateof57.1%forDCIS. Assenheimeretal.(Assenheimer,Laver-Moskovitzetal.2001)intheirstudypublishedin2001showedintheirtheoreticalmodelsthatthecurrentsdetectedatthebreastsurfacetranslatedintotwo-dimensionalmapsarerelatedtotheelectricelddistributionwithinthebreast.Theinnitemediummodelwasextendedtotakeintoaccountnitedepthsaswellastheeectsofthehighlyresistiveskin.Furthermore,athree-elementmodelwas44

PAGE 62

Glickmanetal.(Glickman,Filoetal.2002)developedanEISpostprocessingalgorithmthatautomaticallyrecognizedbrightfocalspotsintheconductivitymapofthebreast.Inaddition,thisalgorithmdiscriminatedbetweenmalignantandbenigntissuesusingtwomainpredictors:phaseat5kHzandcrossoverfrequencyatwhichtheimaginarypartofadmittanceisatmaximum.Thealgorithmwastestedusingthetestgroupof87carcinomas,153benigncases,and356asymptoticcases.Sensitivityof84%andspecicityof52%wereobtainedforthetestgroup. In2002,Martinetal.(Martin,Martinetal.2002)studiedcorrelationsbetweenthehistopathologyofthebreastmalignancyandvariationsindepths,intensity,multiplicity,andsimultaneouscapacitance-conductancefeaturesofEIS.Datatakenfrom74patientswitheithersuspiciousordubiousmammographycomprisedthestudy.NosignicantrelationshipwasfoundbetweenthedepthandintensityofEISsignal.Discordanceamongmammogra-phy,EIS,andhistologywasobservedin15(20%)cases,sixofwhichwereperi-menopausalwomen.Benignproliferatinglesionswerediagnosedinsixof15(40%)controversialcases.MammographyandEIShadsimilarratesoffalse-positivendingsinthisstudy. PipernoandLenington(PipernoandLenington2002)intheirstudyin2002examinedthepotentialforusingEISasanindicatoroftheestrogenactivityinthebreast.TS2000wasusedasanexaminingtoolinvestigating86postmenopausalwomen.Thecapacitanceandconductanceweremeasuredatthenipplesectorofeverybreastat200Hzand1100Hz.Thecapacitanceandconductancedecreasedwiththeincreaseofnumberofyearssincethebeginningofmenopause.Womenwhousedestrogenreplacementtherapyhadahighernippleconductance.ThestudyconcludedthatEIScanbeausefulnoninvasivetoolinestrogenlevelmonitoringabletoidentifyahighcancer-riskpatients. In2005,Stojadinovicetal.(Stojadinovic,Nissanetal.2005)evaluatedthefeasibilityofEISforearlydetectioninyoungwomen.Theirstudycomprised29cancersidentiedamong1103women.EISsensitivityandspecicityinwomenyoungerthan40yearswerereportedtobe50%and90%,respectively.EstrogenuseandmenopausalstatuscorrelatedsignicantlywithEISperformance.Stojadinovic'sgroupsupportedtheuseofEISasa45

PAGE 63

WorkbyWersebeetal.(Wersebe,Siegmannetal.2002)alsoaimedtoevaluatethepo-tentialoftargetedEISforclassifyingsuspiciousbreastlesions.Onehundredandseventeenpatientswith129breastlesions(71malignantand58benign)wereexaminedwithEISfollowedbybiopsies.ThesensitivityoftargetedEISwasobservedtobe62%,andspeci-citywas69%.AsconcludedbyWersebeetal.,\EISshowedmediocreoveralldiagnosticaccuracyforclassifyingsuspiciousbreastlesions." ContraryresultswereobtainedbyKneeshawetal.(Kneeshaw,Drewetal.2002),statingthat\EISisabletodierentiatemalignantfrombenigndiseaseassociatedwithclinicallyoccultmicrocalcication."Only35womenwereexaminedresultinginninemalignantcases.FromEISimagingalone,sensitivityandspecicitywere44%and54%.Thedierencebetweenthemeanconductivitiesinmalignantandnormalbreasttissuewassignicant(P=0:034).Table8:ReportedperformanceofEIS. ReferenceBenignMalignantSensitivity(%)Specicity(%) (Kneeshaw,Drewetal.2002)20944.453.8(Glickman,Filoetal.2002)378838452(Wersebe,Siegmannetal.2002)58716269(Malich,Boehmetal.2001)38628163(Malich,Bohmetal.2001)13710387.866.4(Malich,Fritschetal.2000)292993.165.5(Melloul,Pazetal.1999)1031872.267(F-D-CReports1998)5201848068 Inconclusion,asshowninTable8,reportedsensitivityvariesfrom44.4%{93.1%,de-pendingonthestudy;reportedspecicityvariesless,rangingfrom52%to69%.Thevisualinterpretationoftherecordedimagesleadstoastronginterobserverdiagnosticvariability46

PAGE 64

Basedontheinformationreviewed,EISshowspromiseasanadjunctmodality,butstillmoreworkisrequired.Studiesshowthatthespecicityandthesensitivityindetectionareincreasedwhenmorethanonemodalityisused. TheproposedMREIMtechniquecanaddressEISlimitations.ItsadvantagesoverEISincludethefollowing:MREIMcansignicantlyreducethenumberofFPbythesimultaneousinvestigationofmagneticresonancepropertiesandelectricpropertiesofthebreast;MREIMsensitivitydoesnotdependonthelesiondepthinsidethebreast;MREIMdoesnotrequiremanual-probemanipulation;thus,avoidingoperator-dependence.4.2ElectricalImpedanceTomography IntheInstituteofRadioEngineeringandElectronicsoftheRussianAcademyofSci-ences,Cherepeninetal.(Cherepenin,Karpovetal.2001;Cherepenin,Karpovetal.2002)developedanimprovedEITsystemwith256electrodes(arrangedinasquarematrixwithsidesof12cm)pressedagainstthebreastandacoupleofreferenceelectrodesattachedtothepatientwrists.ThiscongurationisshowninFig.23. Themethodofback-projectionswasusedforfast3-Dimagereconstruction.Thisdevicemeasuredonlythemagnitudevoltagevalues,sothephaseinformationwasignored.Twenty-onewomenwereexaminedintwopositions:lyingandstanding.Asaresult,86%of47

PAGE 65

lowresolutionnotallowingdetectionoflesionssmallerthanfewcentimeters,decientelectrodecontact(theinvestigatorsovercamethisissuedevelopingathresh-oldingtechniquetodetectsuchelectrodesanddiscardinformationfromthem),theneedforimagereconstructiontechnique. Duetoanumberofdrawbacks,includingalimitedamountofmeasureddata,lowsensi-tivityofthesurfacevoltagetoconductivitychangesatregionsfarfromelectrodes,andtheill-posednessoftheinverseprobleminvolvedinimagereconstruction,theEITtechniqueisfarfrombeingappliedclinically.4.3MagneticResonanceElectricalImpedanceTomography

PAGE 66

VariousMREITtechniqueshavebeenproposedfordirectcurrent(Scott,Joyetal.1991),alternatingcurrent,(IderandMuftuler1997;Mikac,Demsaretal.2001;Muftuler,Hama-muraetal.2004)andradiofrequencycurrents(Scott,Joyetal.1995).UnlikeEIT,thespatialresolutioninMREITisnotposition-independent.Sinceonlythecomponentofthemagneticuxdensityinthedirectionoftheboremagneticeldcanbemeasured,areconstructiontechniquemustbedevelopedtosolvetheinverseproblemofndingthecon-ductivityorcurrentdensityfromonlyonecomponentofmagneticuxdensity.Itshouldbeemphasizedthatwiththistechnique,onlyrelativeconductivityvaluescanbereconstructedusingthemagneticuxdensitymeasurementsalone.Tondtheabsoluteconductivityval-ues,atleastonevoltagemeasurementfromtheboundaryisrequired.Thereconstructionalgorithmsinthistechniquecanalsobedividedintotwogroupsdependingonthedatatyperequired.Therstgroup(type1)usesmagneticuxdensitydirectly,whereasinthesecondgroup(type2),thecurrentdensitydistributionisrequiredforimagereconstruction. InFig.25,therelationbetweensystemvariablesisexplainedtoillustratethebasisofthisclassication.Foragivenobjectwithconductivitydistribution,,asaresultofappliedpotentialsand/orinjectedcurrentsontheboundaryoftheobject,potentialandelectric49

PAGE 68

Themajordisadvantageoftype1algorithmsisthattond~jfrom~j=(r~B)=0,threecomponentsofmagneticuxdensityshouldbemeasuredusingMRI.Sinceonlythez-componentof~B,alignedwiththedirectionofmainmagneticeld,canbemeasuredbymagneticresonance,theobjectmustberotated.Thiscreatessevereexperimentallimi-tations.ItmayalsobepossibletorotatethemainmagneticeldoftheMRImagnet51

PAGE 69

Birguletal.(Birgul,Eyubogluetal.2003)intheirstudyin2003presentedtheexperi-mentalresultsfor2-DMREITusingthemagneticuxdensityinonedirection.Asalinephantomwasplacedbetweentheelectrodesandimagedwitha0.15TMRIsystem.Are-constructionalgorithmbasedonthesensitivitymatrixbetweenconductivityandonlyonecomponentofmagneticuxdistributionwasapplied.Therelativeerrorsinconductivityvalueswerefoundtobe13%,17%,and14%forthreeconductivitydistributions. TheexperimentalpaperbyOhetal.(OhandHan2003)presentedtheresultsofMREITtestingusingtype1reconstructionalgorithm.TheMREITexperimentwasconductedwitha0.3TMRIsystemonaphantomcomprisingthetwocompartmentswithdierentelec-tricalconductivities:sausagecolumn(imitationofcancer)andelectrolyte(representationofnormalbreasttissue).Thephantomwasrotatedtoobtainthecompleteinformationsetforreconstructionofcurrentdensities.MRcurrentdensityimaging(MRCDI)wasusedtomeasurethecurrentdensityinsidethephantom.Subsequently,theJ-substitutionalgo-rithmwasusedforconductivityimagereconstruction.Theconductivityphantomimagesobtainedwith28mAinjectioncurrentshowedconductivityerrorsof25%. Duetotheseverelimitationsinreconstructiontechniques,MREIT,hasnotproceededbeyondresearch.MREIMholdsapotentialtoovercomethedrawbacksofMREIT,oeringanalternativemoreeectiveapproachthatinvolveslesscomplexityandrisk.52

PAGE 70

2~particlewiththemaximummeasurablecomponentoftheangularmomentumof~

PAGE 71

Equation(5.1)statesthatangularfrequencyisdirectlyproportionaltoappliedmagneticeld. Resonantabsorptionofenergybytheprotonsduetoanexternaloscillatingmagneticeld(radio-frequencyeld)willoccurattheLarmorfrequency.54

PAGE 74

whereMzandM0arethelongitudinalandequilibriummagnetizations,respectively.57

PAGE 75

whereMxyandMxy0arethetransversemagnetizationandtransverseequilibriummagne-tization,respectively(StarkandBradley1999).SpinEcho A180pulseappliedattimeafterthe90pulsecanreestablishsomeofthephasecoherenceanothertimelaterinaspin-echo.SpinechoformalismisdepictedinFig.30.Att=0,allthespinsareinphase.Aftersometime,theystartdephasingduetothespin-spininteractionandinhomogenouselds.Attimet=,the180RFpulsereversesthespinsintomirror-imageposition.Finally,attimet=2,thespinssynchronize(StarkandBradley1999).SpinEchoSequence

PAGE 77

TheexpressionforasignalinSEimagingfromavoxelwithtissueparametersT1,T2,andeectivenumberof1Hnucleiperunitvolume,H,willbeSSE(TE;TR)=H12e(TRTE=2)=T2+eTR=T1eTE=T2;(5.7) whereHisthespin-densityfactor,12e(TRTE=2)=T2+eTR=T1istheT1factor,andeTE=T2istheT2factor(StarkandBradley1999).ByvaryingTRandTE,theSpinEchocanbeusedtohighlightT1,T2,orspin-densityeects(Table9).Table9:EectofTEandTRonimagecontrastinSpinEchoImaging. ContrastTETRSource

PAGE 79

Ifapatientispositionedheadrstandsupineinmagnet,anRFpulseinthepresenceofzgradientcreatesatransverseslice,andxandygradientscreatecoronalandsagittalslices,respectively.Theslicecanbeorientedinanyplanebycombinationofgradientstrengths. RFpulsesperturbthemagnetizationwithinabandwidthofLarmorfrequenciesmatchingthefrequenciescontainedwithintheRFpulse,whichiscalleditsbandwidth(BW).LongerRFpulses,whichhavealowerBW,producethinnerslices.SpatialEncoding TheFrequencyEncode(FE)gradienttypicallyconsistsoftwoportionswithoppositepolarity:aprephasinggradientlobeandreadoutgradientlobe.Thepurposeofaprephasinglobeistopreparethetransversemagnetizationtocreateanechosignal;thepolaritychangebetweentheprephasinglobeandreadoutlobereversesthedirectionsofphaseaccumulationofthespins(Bernstein,Kingetal.2004)(Fig.30).UponfrequencygradientGxapplication62

PAGE 80

Thephaseaccumulatedbyspiniduetothereadoutgradientis'xi=Z!xidt=xiGxt:(5.9) Thenthefrequencyencodedsignalweightedbyspindensity(x)isgivenby(Heine1993)S(t)=Z(x)ej'xdx=Z(x)ejGxxtdx;(5.10) whichindicatesthatthefrequencydistributionisproportionaltodistance,andthesignal'samplitudeisgivenbyspindensityatthislocation. ThephaseofthetransversemagnetizationattheendofPEpulseappliedfortimewillbe'y=Z!ydt=yGy:(5.12) ThePEgradientstepisfoundfrom(Bernstein,Kingetal.2004)Gy=Gy(0)Gy(Np1) whereNpisanumberofPEsteps. TheMRsignalinthetransverseplaneforagivenPEgradientvalueGyp=Gymin+pGyp,assumingauniformsliceselectionandneglectingrelaxation,willbeproportionalto(Heine1993)S(t;Gyp)/ZZx;y(x;y)ej2(Gxxt+Gypy)dxdy:(5.14)63

PAGE 81

t=2BW;(5.15) whereBWisthebandwidth.ThenumberofsamplesfromMRsignalsusuallyrangesfrom128to1024(StarkandBradley1999). Equation(5.14)representstheMRsignalintimedomain,withthexaxiscontainingthefrequencyencodedMRsignalandyaxiscontainingthephaseencodedvalues.Usingcon-tinuousapproximations,thespatialinformationoftheobjectbeingimagedcanbeobtainedthrough2-DFourierTransform:(x;y)ZGypZtS(t;Gyp)ej(Gxxt+Gypy)dtdGyp;(5.16) whereGypisassumedtobecontinuous. Thereconstructedspindensityisamatrixofcomplexvaluessplitintorealandimaginaryimages.Usually,neithertherealnorimaginaryimagesaredisplayedbecausetheimageintensityisdistributedindiscriminatelybetweenthem(StarkandBradley1999).Instead,therealandimaginaryimagesarecombinedintoamagnitudeimage. MostMRimagesarepresentedas2Dplanespartitionedintoagridofpixels.TheintensityofeachpixelrepresentsthestrengthoftheMRsignal.PixelsarealsoreferredasvoxelstoacknowledgethatMRimageisasliceratherthanaplane.Eachvoxelusuallyoccupiestwobytes(16bits)ofmemory,allowing216possibleintensityvalues.Fieldofview(FOV)isthehorizontalorverticalsizeofanimage.Itischosentomatchthesizeoftheanatomicareaofinterest.ItsminimumvalueisdeterminedbythemaximummagneticeldgradientstrengthoftheMRsystem.64

PAGE 82

ThenumericalsolutionfortheaberrationalmagneticeldisprovidedtoexpandanMREIMstudybasedonasimplegeometry/isotropicconductivitymodeltoamorecom-plexirregularshape/anisotropicconductivitydistributionmodel.NumericalsolutionoftheMREIMeldsforasimplegeometrycaseisvalidatedagainstthederivedanalyticalexpres-sionsforMREIMelds.ThisChapteralsoprovidesthetheoreticalexplanationofinducedmagneticeldeectonformationofMagneticResonanceimage.Theinitialdevelopment65

PAGE 83

Sincetherearenofreechargesinaconductingmedium,Poisson'sequationr2V=="(where"isapermittivityofthemedium)reducestoLaplace'sequation:r2V=0:(6.2) Insphericalcoordinates,r2V=1 @sin@V @+1 @'2:(6.3) ThesolutionisoftheformV=V(r;)duetothesymmetryin'. SincethesolutionstoLaplace'sequationareunique,asolutionwhichsatisesalltheboundaryconditionswillsuce.Eq.(6.3)becomes1 @sin@V @=0:(6.4) SeparationofthevariablesyieldsV(r;)=1Xl=0Alrl+Blr(l+1)Pl(cos);(6.5)66

PAGE 85

d(cos)1cos2dPl whichissingle-valuedandcontinuousintheinterval[-1;1].Pl(cos)areknownasLegendrepolynomialsandspeciedbyRodrigues'formulaPl(cos)=1 2ll!dl Forl=1,P1(cos)=1 21!d d(cos)cos21=1 2(2cos)=cos. TheLegendrepolynomialsareorthogonalfunctionsthatformacompletesetofangularfunctions.Theorthogonalityrelationcanbewrittenas1Z1Pl0(cos)Pl(cos)d(cos)=2 2l+1ll0:(6.8) ItfollowsthatEq.(6.5)representsacompletelygeneralaxisymmetricsolutionforEq.(6.2).Withinthesphere,whererR,V2(r;)=1Xl=0AlrlPl(cos);(6.9) wherethetermwithr(l+1)isrejectedbecauseofdivergenceasr!0. Outsidethesphere,r>R,V1(r;)=1Xl=0Blrl+Clr(l+1)Pl(cos):(6.10) FromtheDirichletandNeumannboundaryconditions8><>:1@V1 whereNandTdenoteanormalandtangentialcomponentsforcurrentdensity,~i,andelectriceldstrength,~E.SinceP1(cos)=cos,theonlynon-vanishingBlisB1=E0. Condition@V1

PAGE 86

Boundaryconditions:8<:1@V1 Thissystemofequationscanbesolvedbymeansofthedeterminants:2R32 2R32 2R32 (ratio+2)E0R3:(6.14) Therefore,thenalsolutionforthepotentialsisasfollows:8<:V1=E0r+(ratio1) (ratio+2)E0R3r2cosr>RV2=3E0

PAGE 87

Insphericalcoordinates,~rV=@V @r^r+1 @^+1 @'^':(6.17) Sincethereisnodependenceon^',wewillneglectthelastterminEq.(6.1). Thus,8>>>><>>>>:~Ea=@Va r32cos^r+sin^~Ec=@Vc Theelectriceldstrengthwithinthetumoris3 2+ratiolargerthanthatfarfromthetumorboundary. Thecurrentdensitycreatedbytheelectricelds~Ea,~Eb,and~Ecis8>>>><>>>>:~ia=1E0cos^rsin^rR~ib=1ratio1 r32cos^r+sin^r>R~ic=3E02 Currentdensity~iaisaboundaryjunctioncurrentdensity.Whenratio=1,tworegions(outsideandinsidethesphere)becomeoneregionwiththesamecurrentdensity,andcurrentdensitiesinsideandoutsidethespherewillbethesameandequalto~ia. Thedierencebetweenthecurrentdensitiesinhigherandlowerconductivityregionsisasfollows:ic

PAGE 88

42=2:86;ic 5=1:80:(6.21) Consideringi=1E0asafareldcurrentdensity,thenalexpressionforthegeneratedcurrentdensitiesinsideandoutsidethetumorisgivenby8>>>><>>>>:~ia=icos^rsin^rR~ib=iratio1 r32cos^r+sin^r>R~ic=3iratio whered~lisadierentialdisplacementvectorand,insphericalcoordinates,isrepresentedbyd~l=dr^r+rd^+rsind'^',andd~aisadierentialareavectorrepresentedbyd~a=rsindrd'^+rdrd^'. Thesurfaceoftheconewiththeapexattheoriginischosenasanareaofintegration.Thenon-zerod~ltermisd~l=rsind'^',andI~Hd~l=I~Hrsind'^'=2Z0h'rsind'=2rh'sin;(6.24) whereh'isamagneticeldinthedirectionof^'.Forthesurfaceofthecone,thenon-zerotermisasfollows:d~a=rsindrd'^:

PAGE 89

Figure35.:AclosedsurfaceandboundingcurvedenedasthesurfaceoftheconeandmouthoftheconeforrR,whichwasusedforcalculationsofmagneticeldinsidethesphere. Themagneticeldinsidethesphere(Fig.35)canbefoundusingEq.(6.25)2r(h')2sin=3iratio SolvingEq.(6.26)gives~h2=3i

PAGE 91

ForoutsideRR~iencd~a=RR~ia+~ibd~a=irRR2R0rsin2d'drratio1 Themagneticeldoutsideis~h1=i r3R2ratio Aftersimplication:~h1=isinr Theslopeofaberrationaleldis[2{3]timesgreaterwithinthehigherconductivitytumorthanfaroutsidethetumortakingintoconsideration[3{40]conductivityratios.6.1.4AberrationalMagneticFieldsinMRI Theunitvector^'canbeexpressedthroughtheCartesiancoordinatesas^'=sin'^x+cos'^y; Insidethesphere,theaberrationalmagneticeldalongthe^yaxisis~h2=3i rsin^y=3i

PAGE 92

Outsidethesphere,~h1=isinhr rsin^y+ratio1 rsin^y=i (ratio+2)R3ix r3^y=i (ratio+2)R3ix Finalexpressionsforinducedmagneticeldsinsideandoutsidethesphereare8<:~h1=i (ratio+2)R3x

PAGE 94

FromMaxwell'sequationsr~h=~iandr~h=0,thevectoridentityr(r~h)=r(r~h)r2~hcanbewrittenasr2~h=r~i:(6.36) UsingthepropertyofthecurloperatorandrrV=0,Eq.(6.36)becomesr2~h=r(rV)=(rrV)+(rrV)=rrV:(6.37) Equation(6.37)canbewritteninmatrixformasfollows:r2hx^ir2hy^jr2hz^k=^i^j^k@ @x@ @y@ @z@V @x@V @y@V @z:(6.38) Weareinterestedonlyiny-componentofmagneticeldalignedwiththeboreeldr2hy=@2hy @x@V @z+@ @z@V @x:(6.39) Twosetsofequations,Eqs.(6.35)and(6.39),aresolvedtondthevaluesforaberrationalmagneticeld. Theaboveequationscanbesolvednumericallyusingthenitedierencemethod(FDM).Thenitedierencemethodconsistsinoverlayingtheproblemwithameshoflinesparalleltothecoordinatesystemandndinganapproximatesolutiontothedeningequationattheintersectionpointsonamesh(Binns,Lowrenson,etal.1992).Theapproximationconsistsofreplacingeachderivativeoftheequationbyanitedierenceexpressionrelatingthevalueofunknownvariableatapointwithitsvalueatneighboringpoints. Forthemeshpointlabeledi;j;kanditsimmediateneighbors,usingTaylor'stheoremfortwovariables,thevalueofVatapointcanbeexpressedintermsofitsneighboringvaluesandseparationdistance,e.g.,inxdirection,x,asfollows:V(x+x)=V(x)+xV0(x)+1 2x2V00(x)+:::;V(xx)=V(x)xV0(x)+1 2x2V00(x)+:::(6.40) AddingandsubtractingtheaboveequationsgivesV(x+x)+V(xx)=2V(x)+x2V00(x)+:::;V(x+x)V(xx)=2xV0(x)+::::(6.41)77

PAGE 95

whichresultsinV00i;j;k(x)=(Vi+1;j;k2Vi;j;k+Vi1;j;k) Approximationstothederivativesinthe^yand^zdirectionscanbeobtainedintermsofyandzinasimilarway. Equation(6.35)canbesimpliedasfollows:rrV=r2V+rVr=0:(6.44) TransformingEq.(6.44)totheFDMnotationgivesi;j;kVi+1;j;k2Vi;j;k+Vi1;j;k Equation(6.39)becomeshyi+1;j;k2hyi;j;k+hyi1;j;k Consideringthegridwiththesamestepinthreedirections,x=y=z,Eq.(6.45)canbesimpliedasfollows:i;j;k 4x2(Vi+1;j;kVi1;j;k+Vi;j+1;kVi;j1;k+Vi;j;k+1Vi;j;k1)(i+1;j;ki1;j;k+i;j+1;ki;j1;k+i;j;k+1i;j;k1)=0:(6.47) ThesolutionforVi;j;kcanbefoundasVi;j;k=1 6(Vi+1;j;k+Vi1;j;k+Vi;j+1;k+Vi;j1;k+Vi;j;k+1+Vi;j;k1)+1 24i;j;k(Vi+1;j;kVi1;j;k+Vi;j+1;kVi;j1;k+Vi;j;k+1Vi;j;k1)(i+1;j;ki1;j;k+i;j+1;ki;j1;k+i;j;k+1i;j;k1):(6.48)78

PAGE 96

6hyi+1;j;k+hyi1;j;k+hyi;j+1;k+hyi;j1;k+hyi;j;k+1+hyi;j;k11 24[(i;j;k+1i;j;k1)(Vi+1;j;kVi1;j;k)(i+1;j;ki1;j;k)(Vi;j;k+1Vi;j;k1)]:(6.49) Themeshpointnumericalsolutionsfortheelectricandmagneticeldscanbeobtainedbyaveragingneighboringvaluesandcorrectingthisaveragewiththefactorcontainingthedierencesofneighboringvalues. Figure39comparestheHimagesatz=N=2obtainedfromnumericalcomputationandanalyticalsolutionfori=10A/m2,ratio=20,andR=5mm.Thepairedt-statisticvalueist=1:70withsignicanceof0.96whichgives96%probabilitythattheimageshavethesamemeans(Adams,Ortonetal.2001).Figure40showsmagnetic-eld-strengthplotsforz=N=2andy=N=2obtainedfrom(a)numericaland(b)analyticalsolution.DiscrepanciesbetweennumericallyandanalyticallyobtainedsolutionsarecausedbytheFDMtruncationerrors(Eqs.(6.40){(6.42)),toleranceiniterations(acceptedprecision),etc.FurthercomparisonsforbothsolutionsareprovidedintermsoftheHimagesforplanesz=N=2Rpixandz=N=22Rpix(Fig.41),whereRpix=5pixistheradiusoftumorinpixels.Thet-statisticvaluesandtheirsignicanceforimagesinFig.41werefoundtobe:(a)0.69with0.96signicance,(b)0.70with0.98signicance,(c)0.70with0.96signicance,(d)0.71with0.96signicance,and(e)0.70with0.96signicance.

PAGE 99

ForspinssubjectedtoaboremagneticeldH0,constantgradientelds~G,andtheaberrationaleldalignedwiththeboreeldh(derivedintheprevioussections),thetotaleldHcanbefoundasH=H0+~G~r+hcos(t+'0);(6.50) whereisthedrivingangularfrequency,and'0istheinitialphaseangle. Fromthenuclearmagneticresonancecondition(Eq.5.2),thespinwillhaveaninstanta-neousangularvelocity!=0H=!0+0~G~r+0hcos(t+'0);(6.51) where!0=0H0and0=4107ispermeabilityoffreespace(sincethematerialsimagedbyMRgenerallyhavelowmagneticpermeability(<105),canbereplacedby0).Thespinwillundergoaphaseincrementation'intimeintransverseplanesuchthat'=tZ0!dt=!0t+0Gxxt+0Gypy+0h whereisthetimethePEgradientison.ThetransversesignalisgivenbyS=ZZ(x;y)ej'x;ydxdy;(6.53) where(x;y)istheprotonspindensity.Then,S=ZZ(x;y)ej(Gxxt+Gypy)ej0h(x;y) sin(t+'0)dxdy;(6.54) where(x;y)istheeectivespindensity(includingT1andT2eects(Haacke,Brownetal.1999)).Theaberrationaltermej0h isconsideredsmall(accordingtotheestimationoftheaberrationalmagneticeld(Fig.38))incomparisonwiththemainboreeld.Takingintoaccountthisapproximation,0h

PAGE 100

Usingsin(t+'0)=ej(t+'0)ej(t+'0) 2RR(x;y)ej(Gxxt+Gypy)0h(x;y) ej(t+'0)ej(t+'0)dxdy==0 sin(t+'0)dx:(6.58) TakingintoconsiderationEq.(6.57),S(t)=Zx(x)ejGxxtdx+0 ThesecondtermofEq.(6.59)gives0 Denoting2kx=Gxtand Takingintoconsiderationtheintegralfromthesecondtermandapplyingconvolutionthe-oremgivesZx(x)h(x)ej2kx(xx)dx=ej2kxxZx(x)h(x)ej2kxxdx=ej2kxxP(kx)H(kx);(6.62) whereP(kx)andH(kx)areFouriertransformsof(x)andh(x),respectively.Toobtainthespindensityfunction,theinverseFouriertransformisappliedF1ej2kxxP(kx)H(kx)=RP(kx)H(kx)ej2kxxej2kxxdkx=RP(kx)H(kx)ej2kx(x+x)dkx=(x+x)h(x+x):(6.63)83

PAGE 101

Theperturbationproducesoriginalimageandtwolteredreplicasoftheoriginalimagescaledbyfactorinverselyproportionaltogeneratorfrequencyanddirectlyproportionaltoaberrationalmagneticeldandshiftedbyx. Theshiftisdeterminedbyx=f dfdx(dxisthepixelwidth)orxpix=f dfpixels.E.g.,forf=300Hzanddf=60Hz/pix,theshiftis5pixels. Figure42showsFEinthesimulatedimages(Eq.(6.58))forahigherconductingdisk(ratio=20)withradiusofR=5mm,currentdensityi=10A/m2.Herefrequencyresolutionisdf=60Hz/pix,andgeneratorfrequencywasvariedtoproducetheshiftxpix=f df=1;2;:::;10pixels.TheseresultsarecheckedandveriedagainsttheimagesgeneratedusingEq.(6.64). FromFig.42itfollowsthatFEeectisthemostconspicuousandallowsfortumorshapedierentiationiftheshiftisminimal,e.g.x=[1;R].Aftertheshiftvaluecrossesthera-diuslimit,theshapeoftumorcannolongerbeoutlined.ThisassertionisfurthersupportedinSection8.2.2.FrequencyEncodeeectisdependentonf dfdxfactorandradiuscombina-tion,aberrationalmagneticeldstrengthh(thus,appliedcurrentandconductivityratio),andinitialcontrastofhigherconductingregionanditssurroundings.TheseparameterswillbefurthertestedinSection8.2.2.6.3.2MREIMEectInuencingPhaseEncodeGradient(PEEect) Foraspecicvalueofphaseencode,theaberrationaltermwillgothroughtwostagesinthespinechosequence:accumulationofthephasebeforethe180refocusingpulse,t20;TE

PAGE 102

df=1;2;:::;10pixels(xpixisgivenbelowtheimage).85

PAGE 103

accumulationofphaseafterrefocusingpulsebutbeforetheFE(\read")gradient,t2TE ForthemaximumPEgradientvalue,accumulationofphasebeforethe180pulsegivesTE=2Z0cos(t+'0)dt=1 sinTE Thesecondpartwillcoverthephaseaccumulationfromthe180pulsetothebeginningofechoTETS=2ZTE=2cos(t+'0)dt=1 sin(TETS FortheconsequentPEgradientvalue,thelowertimelimitstartswithTRTR+TE=2ZTRcos(t+'0)dt=1 sin(TR+TE sin(TR+TETS Usingtheinductionmethod,thegeneralizedformulaforthep-thencodelinecanbeob-tained:TRp+TE=2ZTRpcos(t+'0)dt=1 sin(TRp+TE sin(TRp+TETS Addingthesetwotermstogethergives1 2sin((TRp+TE

PAGE 104

2sin(+TE 242sincos(TE 24sin2cos(TE Equation(6.73)canbeexpressedasthesinusoidalfunctionwiththefollowingparameters:1 Asin(+)=1 Asin(TRp+'0+);(6.74) whereA=p Asin(TRp+'0+); Accordingtoperiodicityofsine,sin(TRp+'0+)=sin(2[fTR]p+2ffTRgp+'0+)=sin(2ffTRgp+'0+),where[fTR]andffTRgdenoteintegerandfractionalpartsoffTR,correspondingly.Thephasedierenceangles'0andareconstantsanddonotdependonyorp,theycanbefactoredoutoftheintegrationbecausetheyhavenoeectonmagnitudeimage. Denoting2ky=Gypand2ffTRgp Gyp=y,applyingtheFouriershifttheoremandconvolutiontheoremgives(y)+0A

PAGE 105

Figure43showsthesimulated128128images(Eq.(6.65))forahigherconductingdisk(ratio=20)withradiusofR=5mmatcurrentdensityi=10A/m2.IfTR=2s,theshiftyisproducedbyfractionalgeneratorfrequenciesy=ffgTRNpdy.TheseimageswerecomparedandvalidatedusingthesimulationimagesresultingfromEq.(6.76). ThePEeectisparticularforselectedsequence.ForeachPEline,thephaseaccumulationoccurs,whichinturnmisregistersthespatialfrequenciesin^ydirection.ForaSEsequence,thephaseaccumulationstartsfrom90RFpulsetothebeginningoffrequencyencoding.IfthePEmodeissequential,e.i.,thePEgradientstrengthdiscretelychangesasGyp=GymaxGypwithstepGy=2Gymax Asin(TRp+'0+).ThePEeectissimilartoFEeectproducingtheshift,butin^ydirection.ForthespeciccaseofintegerTR=2s,onlyfractionalfrequenciesproducePEeect,sinceanyintegerfwilleliminateaberrationaltermdependenceonPEindex(1 2nAsin(2nTRp+'0+)=1 2nAsin('0+))andwillnotinuencethemagnitudeimage.PhaseEncodeeectdependsonthefractionalpartofgeneratorfrequency,theaberrationaleldstrength(atthetumorboundaries),appliedcurrent,conductivityratio,andinitialcontrast. PhaseEncodeeectforotherthansequentialphaseencodemodesandimageacquisitionmodesisconsideredinSection9.1.88

PAGE 107

Initially,fragrancefreeNeutrogenasoapwasselectedasthematerialequivalenttohealthybreasttissue.Thesoapelectricalconductivitywasmeasuredtobe0.03S/mat1kHz.Twotypesofphantomswereconstructedwiththesoap:(a)soapphantomthatcontaineda90

PAGE 108

Theimagingresultsshowedthatthesoapphantomwiththesoapandsaltsphericalinsertwasunstableandpronetodiusion(Fig.45).Thephantomsweremadeafewhoursbeforetheimagingtoeliminatethediusionofthesaltintothesurroundingsoap. Thethirdtypeofphantomwasconstructedusingagargelasapliablematerialequivalenttohealthybreasttissueandapieceoffat-freehotdogasacancersurrogate.Theagarsolution(1.4g/100mL)wasplacedinanelectricallyconductive(2000measuredfor0.1thicknessandareaof1cm2)610in2atpolybag(AssociatedBagCo.)thatrepresentedaskinsurrogate.Thecalculatedresistivityforthiscarbonplasticwasc=2105cm.Thebaghadthesimilarresistivepropertiesandthicknesstohumanskin(Lee,Kimetal.2002).AphotographoftheagarphantomplacedinthecarbonpolybagisshowninFig.46. TheconductivitycellwasconstructedfromPVCpipe(D=1inandl=1in)and2stainlesssteelsheetstomeasuretheconductivityoftheagarsolution.Hotagarsolutionwas91

PAGE 110

A1 Furthermore,conductivitydependenceonthefrequencywasinvestigated(Fig.48)show-ingasteadybehaviorofconductivitywithfrequencychange. Theagarphantomprovedtobemorestableandshowedconsistencyintheimagingresults.Itsimulatedthemagneticresonanceandelectricpropertiesofnormalandmalignantbreasttissueandwascosteectiveandeasytoreplicate.Itwasmadefreshbeforeeachimagingexperiment. Varioussequencesweretestedforthreephantoms,e.g.,SDSE,EPISE,T2ash,etc.AchoiceofSDSEsequencewasmotivatedbyitssimplicityintermsofMREIMtheoreticalandsimulationdevelopments.Duetotheproblemswithsoapphantomdesigns(Fig.45)theagarphantomwasusedforfurtherMREIMtesting.7.2MREIMApparatus

PAGE 113

AlthoughtheMREIMapparatuswasdesignedforphantomtesting,itwasalsoimportanttoexploretheproblemofthepatient-FSscouplingthatwouldseparatetheskinfromthemetalelectrodestosatisfyrequirementsofclinicaluseandregulatoryagencyapproval.FromEq.(6.54),lowerfrequencieswillproduceamoreobservableeect.Tochosethefrequencyrangeforexperimentaltesting,frequenciesusedforimpedance-basedimagingtechniqueswereconsidered.TheTransScan2000'soperationalfrequencyis200Hz.Atthisfrequency96

PAGE 115

TheresistanceofeachcomponentinFig.122(b)canbeestimatedbymakinganap-proximationfortheFSs-phantomcontactareaandgeometryofthephantom.Thecontactareawasestimatedas100cm2withavariationof1cminbothlengthandheight,which98

PAGE 117

Figure53showsadiagramoftheelectriccircuitusedtosupplytheelectriccurrenttothephantomthroughtheconductivelycoupledFSs.100

PAGE 120

TheT1andT2relaxationparameterswerenotmeasuredexplicitlybutweredeemedappropriatebyvisualobservation.ThestrongbackgroundsignalfromtheagaronT1weightedFLASHlocalizerimages(scoutimages-notshown)andmoderatesignalontheSDSEimages(seeFigs.55{58)simulatedafattybreast,andthelowsignalfromthecancersurrogateonT1weightedFLASHandhighersignalonSDSEsimulatedamalignancy.Likewise,theT2ofthebackgroundmaybeestimatedbecauseofthelongTRusedintheexperimentalsequences(asdescribedbelow).Therefore,theMRIrelaxationparameterswerevisuallywithintherangeoftheexpected. Withdfsetto60Hz/pix,currentdensityrangingfrom10to17A/m2,andfrequenciesvaryingfrom300to350Hz,thedierenceimageswithcurrentoandon(Figs.55{57)(b)-(a)and(b)-(c),showtheeectoftheperturbationaroundthecancersurrogate.Theexpectedsignalwasnotobservedwhendfwassetto22Hz/pixandfwassetto200Hz(Fig.58). ThetoprowimagesinFig.55showthatthecancersurrogatehasacceptablecontrastrelativetothebackground,andtheshieldsarenotperceptibleanddonotdegradetheMRimageacquisition.ThisisanindicationthattheFSsarecompatiblewiththeMRcoil,andthatthephantomandMREIMequipmentarecompatiblewithMRsystem. SlightinterferencepatternsareapparentintheimagesinFig.56,whichwereprobablyduetoradiofrequencyleakageintototheFSselectricalleadsduetopoorshielding.TheRFleakageisnotpresentinotherexperimentswherethecurrentdensityislower.Also,theMREIMeectislessapparentthaninFig.55,eventhoughthecurrentdensityishigherhere.Thiscanpossiblyexplainedbytheinuenceofnoise. Figure57showstheimagesacquiredwiththefollowingparameters:i=10A/m2atf350Hz,df=60Hz=pix.NoiseisgreaterthaninFig.55. ThemissingeectinFig.58ispredictedbythesupportingtheoryduetotheinterplayofthefrequencyresolutiondf,signalgeneratorfrequencyf,andradius(x=f dfdx2R)inuencedbynoise. Inconclusion,acustomdesignedanddevelopedMREIMapparatuswasabletovalidate103

PAGE 126

phaseencodegradientstrengthincrementationpandtimeincrementationt,N=Np=Nt=128;spatialxandyincrementationk,L=4N=512; PhaseEncodestepcanbefoundasGy=2Gxmax Variableparameters: suggestedfrequencyfromtheTransScanTS-2000performance(200Hz),lowfrequencyrangeduetotheuseofrealcomponentofconductivity(region),useofconductivecouplingforthephantom-FSssystem,109

PAGE 127

fromEqs.(6.58)and(6.65),itfollowsthattheaberrationaltermislargeratlowergeneratorfrequencies. ToobservetheshiftduetoPEeectatTR=2s,thegeneratorfrequencyisrequiredtobefractional,ypix=ffgTRNp(seeSection6.2.2).GeneratorfrequencywaslinkedtofrequencyresolutiondftoobtaintheshiftduetoFEeect,xpix=f df;experimentalvalues:100{170mAforthecontactareaof1010cm2,whichisequivalentto10{17A/m2;radiusofacancersurrogateinthebreastphantomwasR=5mm,whichwasusedasdefaultforMREIMeectstudy;-

PAGE 128

basedonexperimentalimages,contrastbetweenthetumorsurrogateandsurroundingagarmediumwasapproximately10%.Forarealisticmodelofabreastwithvarioustumorshapesandanisotropicconductivity,thenumericalsolutiontoaberrationalmagneticeld(Eq.(6.49))wereincorporated.AnalgorithmforthenumericaleldsolutionsisprovidedinthefollowingSection.111

PAGE 130

Step9:TakingtheMagnitudeoftheRawImagetoObtaintheFinalResult.8.1.2NumericalCalculationofMREIMFields whereE0=i=normalisasteady-stateelectriceldstrength.Withanassumptionthatconductivityishomogenousontheperipheryofthecuboid,theboundaryconditionsfor113

PAGE 131

2normalE0x(0)H(N1;y;z)=1 2normalE0x(N1)H(i;0;z)=1 2normalE0x(i)H(i;N1;z)=1 2normalE0x(i)H(i;y;0)=1 2normalE0x(i)H(i;y;N1)=1 2normalE0x(i);(8.2) wherenormalistheconductivityofhealthybreasttissue. Foragivenconductivityprole,thesolutionwasdividedintotwopart:(1)electricpoten-tialdistribution(Eq.(6.48))and(2)they-componentofmagneticeldstrength(Eq.(6.49)).Thetolerance(acceptedprecision)was104and106forelectricpotentialandmagneticeldstrengthwiththemaximumiterationnumberof103.Equation(8.3)displaystheformatusedforiterations:Vi;j;k=(1!)Voldi;j;k+!Vi;j;k;(8.3) where!isaconvergencefactor.Equation(8.3)denotestheSuccessiveOver-Relaxation(SOR)methodif!>1.InaccordancetoKahantheorem(Kahan1958),thesystemofequationsisconvergentwhen!isintheopenrangeof(0;2).When!=1,theSORmethodsimpliestotheGauss-Seideliterationmethod,whereforagiveniterationtheelementsthathavealreadybeencomputedforthisiterationareused.Foreachiterationini;j;k,thedierencebetweentheoldandnewvalueofVi;j;kischecked;themaximumdierenceforagiveniterationiscalledtheerror.Iftheerrorislessthanpre-assignedtolerancevalue,theiterationisstoppedandtheconvergedsolutionforVisconsideredasthesolutiontotherstpartoftheproblem.The\price"forthegivensolutionisrepresentedbythenumberofiterationsperformed. PlotsofmaximumiterationerrorversusthenumberofiterationsforVareshowninFigs.61and62,andforHshowninFig.63. Todecreasethe\price"foraconvergedsolution,thechoiceof!wasestimatedbytheformula(Mitra2007):!=4 2+r N12;(8.4)114

PAGE 134

q 22sig+1 22bg;(8.5) whereSsig,Sbgandsig,bgarethemeanpixelintensitiesandtheirstandarddeviationsforobjectandbackground,respectively.DetectabilitywascomputedwithRose'sformula(Rose1948):

PAGE 136

ThresholdvaluesofdweretakenfromRose(Rose1948)andBrightetal.(Bright,New-buryetal.1997):Contrast-to-noiseratioanddetectabilitywerecomputedfordierenceMREIMsimulationimages(subtractionimageofmagnitudeimagesobtainedwithcurrentonandcurrento).Theregionofinterest(ROI)fortheobjectwasoutlinedbythecoordinatesofthehigherintensitydiskinthetemplateimage.TheROIofthesameshapeandnumberofpixels(Npix)wasusedtocapturethesignalfrombackground.8.2SimulationResults:Simple(Idealized)TumorModel

PAGE 137

Figure64showsthesimulatedMREIMimagesandtheircomparisonwiththeexperimen-talndingsforthefollowingexperimentalparameters:i=10A/m2,f300Hz,df=60Hz/pix,SD=1:97,andcontrast=10%.Inthesimulation,SD=2wasused.Theexper-imentalimagesshowthatPEeect(shiftinthe^ydirection)ismorepronouncedthantheFEeect(shiftinthe^xdirection).Toreproducethisscenario,theshiftinverticaldirectionwassettoypix=2,whichresultedinfractionalfrequencyffg=ypix 2128=0:008Hz.Theshiftin^xdirectionisgivenasxpix=f df=300 60=5pix,whichisequivalenttothetumorradiusinpixels.Fortheshiftequalorlargerthantumorradius,twoadditionalaberrationalimagesofthetumordonotoverlap(Fig.42). ExperimentalimagesinFigs.65and66showadierentaspectofPEandFEeectscom-bination.TheMREIMparameterswerethesameasinthepreviousexperiment(Fig.64):df=60Hz/pix,TR=2s,andTE=50ms,butinFig.65,theappliedcurrentwasincreasedtoi=17A/m2,andinFig.66,thegeneratorfrequencywasincreasedtof350Hz.AnalysisofexperimentalimagesinFigs.65and66showedthatthenoisevarianceis6and4.5timeshigherincomparisonwiththepreviousexample(SD=12inFig.65andSD=9inFig.66). ResultsobtainedinFigs.65and66canbeexplainedbyconsideringthemagnitude120

PAGE 139

FindingthepowerofPV1andPV2,subtractingandtakingthesquarerootwillgiveq Notethattheresultingsignalisnotjustadditivenoisebutalsocontainssignaldependentnoiseterms.Subtractionimagesnolongerdisplaytheshift,butshowtheaberrationintheareaofhighersignal(higherconductingregion). InFig.67,experimentalsubtractionimageofcurrentonandoshowsnoMREIMeect.Here,theMREIMacquisitionparameterswerechangedtodf=22Hz/pixandf=200Hz,andtheshiftduetoFEeectisxpix=f df9pixels,whichisalmostequaltotumordiameter.AberrationalreplicationsoforiginaltumorduetoFEeectareseparatedenoughtobelostinnoise.Noisevarianceinexperimentalimageswasfoundtobe10.8.2.2StudyoftheMREIMEects TheMREIMsimulationprogramprovidedtheoptionofselectivelyturningon/oFEandPEeects.Theparameterswereoptimizedtoproducethemostconspicuouseectatthelowestappliedcurrent.ThisstudywasbasedonthesimpletumormodelusingasimpleSDSEsequence(usedinexperiment)withthefollowingsequenceparameters:TR=2s,TE=50ms,Np=128,fov=12:8cm,dx=1mm,andGymax=22mT/m.ThisparameteroptimizationbasedontheSDSEsequencecanbeusedinfutureformorecomplexsequencesandassistindesigninggeneratorpulsesequencestime-coupledtoMRsequencestoproducethemostconspicuousMREIMeect.122

PAGE 142

df9pixels.125

PAGE 143

sintdxdy;(8.10) whichgives(x;y)0 wherex=f dfand=2f. FromEq.(6.34),weconcludethattheentireimageshiftssincemagneticeldstrengthforbothregionsisproportionaltox.Subtractingtheimagesobtainedwithcurrentonandoyields0 TheFEeectdependson(a)theshiftin^x,x=f dfdx,anditsrelationtotumorsize,(b)aberrationalmagneticeldstrength,whichinturndependsonappliedcurrentandconductivityratio.InuenceoftheseparametersonFEeectdetectabilityistestedinFigs.68{71. TheFEeectdetectabilityischaracterizedasthefunctionoftheshiftproducedbyf dfratio(Fig.68).Fivefrequencyresolutionswereusedtoexploredetectabilitybasedontheexperiments:df=20,40,60,80,and100Hz/pix.Theshiftx=1producedthehighestdetectabilityforallfrequencyresolutions.Detectabilityisthehighestwithf=20Hzanddf=20Hz/pix.Lowerfrequencyresolution,df,produceshighersignal-to-noiseratio.Also,dfisproportionaltoFEgradientstrength.Atlowergradientstrengths,theaberrationalmagneticeldhasastrongereect.ThegeneratorfrequencyisalsopreferableinlowerrangesincetheaberrationalterminEq.(8.10)isinverselyproportionalto.Lowergeneratorfrequencyagreewiththereal-valueapproximation.Also,theFSscouplingisbasedonlowergeneratorfrequencies. ThebehavioroftheFEeectasafunctionofshiftxandtumorradiuscanbeobservedinFig.42.Whenx>R,theaberrationalreplicasofhigherconductingregiondonot126

PAGE 144

ConsideringresultsfromFig.68,wewillusef=20Hzanddf=20Hz/pixforinvestiga-tionofFEeectbehaviorwithotherMREIMparameters.Figure69showsthedependenceoftheFEeectdetectabilityoninitialtumorcontrast.Themaximumcontrastvalueof10%wasestimatedfromexperimentalimages.Contrastismeasuredasconrast=SinSout Figure70showstheFEeectdetectabilityasafunctionofconductivityratioofthetumorandsurroundingtissues.Therearenotissuesinbreastthatarelessconductivethanconnectiveandadiposetissue(seeTables2{5).Takingthisintoconsideration,theconductivityratiowasvariedfrom1to40.FromFig.70,theFEeectdetectabilitypassedthevisibilitythresholdatconductivityratioof2.Startingwithratio=17,thedetectabilityoftheFEeectreachedtheplateau.Ourexperimentswereconductedusingabreastphantomwithratio=23. Appliedcurrentlimitsforthisspecicsequencewerefoundforthelowestcancerdier-entiationconductivityratioratio=3andthreetumorradii,R=5,2,5,and1.5mmbasedonthecontrastdiagraminFig.71.Forallthreeradii,thelowestcurrentdensitywas2A/m2.Aspredictedbytheory(Eq.(6.34)),thedetectabilitydependenceoncurrentdensityislinearsincetheaberrationalmagneticeldstrengthisdirectlyproportionaltocurrentdensity.PEEect

PAGE 145

df.Simulationimagesweregeneratedforthefollowingparameters:R=5mm,contrast=10%,ratio=20,SD=2,andi=10A/m2.Dottedcoloredlinesdenote(red)visibilitythreshold,(green)detectionthreshold,and(yellow)shapeoutlinethreshold.128

PAGE 149

TheaberrationaltermforaSpinEchosequencewillgothroughtwostagesofphaseaccu-mulation:before180pulseandafter180pulsewithanoppositesign.Thisaccumulationofphaseisparticularforasequence,PEmode,andacquisitionmode.ItwillbestudiedfurtherinChapter9.FortheSDSEsequence,Eq.(8.13)canberewrittenasfollows: whereAisafactordependingonsequencetimingparametersTEandTS(inverselypro-portionaltodf)andgeneratorfrequencyf(seeEq.(6.74)). ItisrequiredforPEeecttobeobservableatintegerrepetitiontimeTR=2stosupplycurrentatfractionalfrequencies.Inthiscase,theshiftinywillbeproduced,y=ffgTRNpdy,whereffgisafractionalpartofgeneratorfrequency.Theresultingimagewillcontaintheoriginalimageandtwoaberrationalversionsoforiginalimage(scaledby0A Becauseaberrationalmagneticelddependsonyonlyattheboundariesoftumor,PEeectconsistsinshiftingtheboundariesofhigherconductingareas(Fig.43).Forsmallershifts,insubtractionimagestheintensityofareainsideandoutsidethetumorvanishesexceptfortheboundaries.Withtheshiftincrease,theboundariesaresmearedout,andwhenyreachesR,twoseparatereplicasofhigherconductiveregioncanbeobserved.UnlikeFEeect,theseaberrationalimageshaveoppositeintensity,suchthat,whenadded,theydiminish. Figure72provestheaboveassertionshowingdetectabilitydiagramasafunctionofshiftin^y.Thevaluesofdetectabilityarewellbelowvisibilitythresholdandaremostlyinuencedbynoise. Asaconclusion,PEeectinuencestheboundariesofhigherconductingtumor,andsmallershiftsin^yarepreferableintermsofcarryingtheinformationabouttumorlocation.132

PAGE 151

Figures73{77showdetectabilityplotsforcombinationsofFEandPEeects.Theanal-ysisissimilartotheoneusedforFE.First,xandythatproducethemostconspicuouscombinedeect(Figs.73{74)arefound. ThecombinationofFEandPEeectsischaracterizedasfunctionoftumorcontrast(Fig.75),conductivityratio(Fig.76),and,nally,currentdensitylimitsarefoundforthreetumorradiiusingratio=3andcontrast=0.Theoptimizedvaluesofshiftwerefoundtobexpix=1andypix=1fordf=20Hz/pix,resultingingeneratorfrequencyoff=20:004Hz.Overall,thecontrastdiagramsforcombinedMREIMeectresembledthoseforFEeectforthereasonsspeciedinprevioussection.Minimumcurrentlimitsremainedthesameforcombinedeects,i=2A/m2forR=5,2.5,and1.5mm(Fig.77).Figure78providesthesimulationdierenceimagesforsphereswiththreedierentradiiwithlowconductivityratioofratio=3atthelowestcurrentlimitofi=2A/m2thatpermitstumorvisibility.AdditionofPEeectallowsforbetterdierentiationofthetumorbyenhancingthetumorboundaries.8.2.3Summary MREIMimagesweresimulatedforexperimentalparametersthatreplicatedtheexper-iment:(Experiment1,Fig.64)i=10A/m2atf=300:008Hz,df=60Hz/pix,andSD=2(dexp=7:8,dsim=7:1),134

PAGE 152

df.Simulationimageswereacquiredwiththefollowingparameters:ypix=1,ffg=0:004Hz,i=10A/m2,R=5mm,contrast=10%,ratio=20,andSD=2.Dottedcoloredlinesdenote(red)visibilitythreshold,(green)detectionthreshold,and(yellow)shapeoutlinethreshold.135

PAGE 157

(Experiment2,Fig.65)i=17A/m2atf=300:004Hz,df=60Hz/pix,andSD=12(dexp=5:1,dsim=5:4),(Experiment3,Fig.66)i=10A/m2atf=350:004Hz,df=60Hz/pix,andSD=9(dexp=5:8,dsim=6:2),(Experiment4,Fig.67)i=10A/m2atf=200:004Hz,df=22Hz/pix,andSD=10(dexp=dsim=0:6);2. FrequencyEncodeeectconsistsincreatingtheimageconsistingofthreeterms,originalimageandtwolteredreplicasoforiginalimagescaledbyfactorinverselyproportionaltofanddirectlyproportionalaberrationalmagneticeldandshiftedbyxpix=f df.ThemaximumMREIMsignaldetectabilityisobservedatx=1anddf=20Hz/pix;3. PhaseEncodeeect(forSDSEsequence,sequentialmode)consistsincreatingtheimageconsistingofthreeterms,originalimageandtworeplicasoforiginalimagescaledbyafactorinverselyproportionaltofanddirectlyproportionaltoA(Amax=2)andaberrationalmagneticeld,andshiftedbyypix=ffTRgNp.PhaseEncodeisstudiedfordierentacquisition/PEmodesinSection9.1;4. FrequencyEncodeandPhaseEncodeeectsconspirelinearly;5. ForcombinedFE+PEeects:140

PAGE 158

optimumgeneratorfrequencyandfrequencyresolutionaref=20:004Hzanddf=20Hz/pix;initialtumorcontrastdoesnotinuencetumordetectability.TheMRsequencecanbedesigneddisregardingrequirementofhightumorcontrast;MREIMeectisdetectableforconductivityratioaslowasratio=2;minimumcurrentdensityrangefortumordetectabilityisi=1{2A/m2forthefollowingtumorradii,R=5,2.5,and1.5mm,withlowconductivityratioofratio=3andcontrast=0.8.3SimulationResults:RealisticTumorModels Thedeviationinconductivityvaluesisaddedtosimulaterealisticanisotropicconduc-tivitybreasttissue.Figure81showstheeldimagesandMREIMdierenceimagesfor141

PAGE 160

roundovallobularirregular. TheMREIMeectisinvestigatedforoval,lobular,andirregularcancerouslesions.Figures82{84showtheMREIMeldimagesandcorrespondingMREIMdierenceimagesforoval,lobular,andirregularshapes.ResultingdetectabilityvaluesareprovidedinTable11.8.3.34-TumorModel

PAGE 162

FromtheMREIMsimulationresultsfornumericallycomputedaberrationalmagneticeldvalues,thefollowingconclusionscanbedrawn:1. MREIMsimulationimagesincorporatingnumericallycomputedaberrationalmagneticeldproducedaperceptibleeectscomparabletothoseobtainedwithanalyticalH;145

PAGE 163

TumorsCoordinatesRadius,Conductivity,PathologyofcentermmS/m Tumor1(N=2;N=2;N=2)91:00:01malignant61:50:01malignant32:00:01malignantTumor2(N=3;N=3;N=2)52:00:01malignantTumor3(2N=3;2N=3;N=2)31:00:01malignant21:50:01malignant12:00:01malignantTumor4(N=3;2N=3;N=2)50:20:01benign

PAGE 164

0:10:0128.682oval102020-0:30:01 0:10:0125.383lobular102020-0:30:01 0:10:0128.484irregular102020-0:30:01 0:10:0124.285tumor1,22020<91:00:01 0:10:016.5round<61:50:01 0:10:01<32:00:01 0:10:0185tumor2,2202052:00:01 0:10:018.6round85tumor3,22020<31:00:01 0:10:016.4round<21:50:01 0:10:01<12:00:01 0:10:0185tumor4,2202050:20:01 0:10:010.7round

PAGE 165

Eectsareperceptibleforatumormodelwithanisotropicconductivityinsideandout-sidethetumor;detectabilityvalueslightlydropped(5%)ascomparedtocorrespond-ingresultsforamodelwithhomogenoussurroundingtissue;3. Eectsweresimulatedforvarioustumorshapes,i.e.oval,lobular,irregular,etc.De-tectabilityforabovetumorshapesdecreasedslightlycomparedtothecorrespondingdetectabilityforsphericaltumor;4. Eectsweresimulatedfor4-Tumormodelconsistingofsphericaltumorswithhigher-conductivitybulkofatumorandlower-conductivitymargins.Thedetectabilityvalueforatumorwith1 0:10:01wasdetectedwithd=6:4atthefollowingparameters:i=2A/m2,f=20Hz,df=20Hz,SD=2,andcontrast=0;benigntumor4withradiusR=5mmandratio2couldnotbedetected(d=0:7); Inconclusion,MREIMsignalisobservableforzero-contrast,lowappliedcurrent,andlowconductivityratioforvariousshapesandconductivitydistributionsaslongastheconductivityratiosareintherangeofthoseforcancerousandbenignlesions.148

PAGE 166

Inourexperiment,thevoltagedropacrossthephantomwasapproximately20V,whichcreatesanelectriceldofabout4V/cm.Theelectriceldstrengthisontheorderofeldstrengthsusedinotherexperimentalclinicaltrialsfordisruptingcancercelldierentiation(Miller2007);TheIEC601standardlimitofappliedauxiliarycurrentis0.1mAatf<10Hzand1mAatf>10kHz(IEC2001);AmericanNationalStandard:safecurrentlimitsforelectromedicalapparatusis0.5mAforperceptiblecurrent(AAMI1993);EISTransScan2000operatesat5mAfor4747mm2,whichresultsinanappliedcurrentdensityofi=2:26A/m2.TransScan2000operateswithupto30frequenciesintherangefrom58Hzto5kHz(ScholzandAnderson2000);ToachieveMRI-comparableresolutioninpostmortemexperimentsonacaninehead,MREITrequiredaminimumcurrentof40{50mA(Kim,Leeetal.2007).149

PAGE 167

BasedonMREIMeectanalysisprovidedinChapter8,forasimpleSDSEsequence,theFEeectconsistsinproducingtwoaberrationalimages,replicasoftheoriginalimage,scaledandshiftedbyafactorthatisproportionaltogeneratorfrequencyandinverselyproportionaltofrequencyresolution.SinceFEoccursinonedirection,theFEeectinaSDSEsequencepermitsfurtheroptimizationonlybymanipulationofk-spacedata,i.e.,ltering/shiftingbeforeimagereconstruction.ThePEeectinSDSEsequence(sequentialPEmode,sequentialacquisitionmode)consistsinproducingtheshiftoforiginalimageequaltoffTRgNpandforTR=2sisobservableonlyatfractionalfrequencies.ThePEeectismorepronouncedattheboundariesoftumor,sincetheaberrationalmagneticeldisdependantonyattheboundaries(ifPEoccursinydirection).PhaseEncodingisnotlimitedtoasequentialmode;thus,moreoptionsarisetooptimizePEeect.Besides,PEgradientstrengthvariesthroughouttheacquisitionandpassesthroughsmallvaluesofGy 2(1281)mT/m=0:17mT/m(FEgradientisGx=df dx=0:47mT/mfordf=20Hz/pixanddx=1mm).ThenativeMRacquisitionismoresusceptibletomagneticeldperturbations,e.g.,theaberrationaleldgradientin^xdirectionaty=0,Gaber=0:0026mT/minsidethetumorandGaber=0:00126mT/moutsidethetumorforlowestdetectablelimitsforMREIMsignal(ratio=3andi=2A/m2)(Section8.3.4). ThisChapterdiscussesdierentoptionsofeectoptimizationbyinvestigatingvariousPEmodes,acquisitionmodes,generatorpulsesequencetime-coupledtoMRsequence,etc.Theanalysisisperformedwithsimulationsforthesimpletumormodel(R=5mmandratio=3).9.1PEEectOptimization9.1.1PhaseEncodeMode

PAGE 168

Tseq]. Figure89showsthesimulationresultfortheinterleavedacquisitionmode(slice2).SincephaseaccumulationoccurswithintegermultiplesofTRbutshiftedbyconstantphaseangle,theeectproducedbytheinterleavedacquisitionmodeissimilartosequentialacquisitioneect.9.1.3DirectionofFEandPE

PAGE 170

Figure91comparessimulationMREIMimagesfori=2A/m2,f=20:004Hz,df=20Hz/pix,ratio=3,SD=2,andcontrast=0forFEinthe^xdirection,PEinthe^ydirectionwiththedierenceimagesobtainedwithencodinginoppositedirections.Thedetectabilityvalueincreasedafterswitchingthegradientencodedirections.9.2CurrentPulseTrainDesign Intheexperiments,thegeneratorwasinoperationduringtheentireimageacquisition.Thephaseaccumulationbefore180refocusingpulseandafter180pulsewillhaveoppositesigns.Ifthecurrentisappliedsuchthatitchangespolarityat180pulse,thephaseaccumulationwillpreserveitssignaftertheip.Thiswasimplementedbyanumberof153

PAGE 174

Ageneratorfrequencyoff20HzcanbeconsideredastheoneprovidingtwoDCelectricpulsesthatchangepolarityatthe180RFpulse,sinceTE 2s=1 2(1 2Ti,whereTiistheperiodofsignalgeneratorpulse. ToinvestigatetheMREIMeectforhigheralternatingfrequencies,apulsetechniquedevelopedbyMikacetal.issuggested(Mikac,Demsaretal.2001)(Fig.96(b)).UsingthesameprincipleofapproximatingACwithachanging-polarityDCpulse,insertingrefocusingRFpulsesbetweeneachpairofelectricpulsesofoppositepolaritywillenableconstructiveaccumulationphaseshifts,and,inprinciple,shouldproducemoreconspicuouseectinPE. ThereisanoptionofstartingacurrentpulsewithadierentinitialphaseanglewitheachTR(initialphaseangle'0isdependantonp).Figure97showshowMREIMdierenceimageschangewithaddingPEdependantinitialphasetocurrentwaveform.Forexample,for'0= Forsagittalslices:sliceencodeinthe^zdirection(alongappliedelectriceld),FEencodeinthe^ydirection(alongtheboreeld),andPEencodeinthe^xdirection;-

PAGE 179

Ingeneral,thegeneratorfrequencyshouldbechosensuchthatpolarityofappliedcurrentipsat180refocusingpulseatt=TE Appliedcurrentlimitsarefoundusingthecontrastdiagramforthreetumorradii,R=5,2.5,and1.5mmwithconductivityratioofratio=0:30:01 0:10:01.TheminimumcurrentallowingforMREIMeectvisibilitywasfoundtobei=0:4A/m2forR=5mmandi0:5A/m2forR=2:5and1.5mm,whichisequivalenttotherangeof4{5mAfor1010cm2breast-FSscontactarea. Figure100showsthesimulationdierenceimagesobtainedwiththelowestcurrentlimitsatwhichMREIMisstilldetectable.Theimagesweregeneratedfollowingtheprotocolsuggestedabove.162

PAGE 181

0:10:01,andSD=2.Dottedcoloredlinesdenote(red)visibilitythreshold,(green)detectionthreshold,and(yellow)shapeoutlinethreshold.164

PAGE 182

0:10:01,contrast=0,andSD=2.9.4FurtherSuggestions Half-FourierImagingPhaseCorrectionMethod TheMREIMaberrationalelddistortsthesymmetryofk-spacedatabyaccumulatingphase.ThisphaseaccumulationcanbefoundusingphasedataestimationasinHalf-Fourierimaging(Bernstein,Kingetal.2004). Half-Fourierimagingwasdevelopedbasedonthefactthatforrealfunction(x),itsfrequencyrepresentationS(k)isredundantduetoitsHermitiansymmetry.Insteadofacquiringallk-spacelines,onlyn0n
PAGE 183

n0),wheren0n
PAGE 184

AsMREIMisbasedontheconductivitydierencesbetweenmalignantandnormalbreasttissue,areviewoftheelectricpropertiesofthebreasttissuewasprovidedintheformofasurveythatcanbeusedasareferenceforfurtherdevelopmentofbio-impedancebasedapplications(Heine,Kovalchuketal.2008a).Althoughtheconductivityratiobetweencancerousandnormalbreasttissuevariesintherangeof3{40(Chapter3),extensivein-vivoresearchisrequiredatthelowerfrequenciestospecifytheconductivepropertiesofbreasttissueintheMREIMapplicationranges. Anovelbreastphantomwasdesignedanddeveloped,andphantomMREIMimagingtestswereconducted.Thecustom-madephantomrealisticallyreproducedmalignancyandnormalbreasttissueintermsofconductivepropertiesandrelativesignalintensitiesinMREIMimages.TheMREIMapparatuswasabletovalidatetheMREIMtheoryproducingtheMRmagnitudeimageswiththedierentialsignatureofahigher-conductingcancersurrogate(Heine,Kovalchuketal.2008b). AMREIMsimulationprogramwasdeveloped.Usingthisprogram,theexperimentalphantomimagingresultswerereplicatedandexplainedbysupportingtheoreticaldevelop-ments. Amethodforcalculationofelectricpotentialandinducedmagneticelddistributioninobjectswithrealistictumorshapesandanisotropicconductivitieswasdeveloped.ThesimulationbasedonthedevelopedmethodshowedthattheMREIMsignalisdetectablefortumorswithrealisticshapesandconductivitydistributions.TheMREIMeectdetectabil-167

PAGE 185

MREIMeectswereinvestigatedusingacontrastdiagrammethod.AnMREIMsequenceprotocolthatproducesadetectableMREIMeectatthelowestappliedelectricenergywassuggested.Accordingtosimulationresults,utilizingthisprotocol,theminimumappliedcurrentatwhichadetectableMREIMeectfora3mm-diametertumorisfoundtobe0.5A/m2,whichmeetssafetystandards. ToproduceaclinicallyviableMREIMproduct,asignicanteortshouldbeputintofurtheroptimizationofimagingsequences(EPI,GSE,FLASH,RODEO,etc.)atminimumcurrentwithoutcompromisingpatientsafetyorsignalquality.Optimizationofthehard-wareincludes:(a)atemporallystableandmoresophisticatedphantomcontainingvariousbreastabnormalities,(b)MR-compatiblepowersuppliesandFaradayshieldsincorporatedincommerciallyavailableMRsystems.Infuturework,prototypeFSscomponentsandpowersupply,includingallconnectinghardware,shouldbeprofessionallymanufacturedtomeetbothMRsafetyandclinicalpatient-safetystandards.Thisequipmentwillper-mitmoreexacttestingthatwillleadtoclinicalhuman-subjectexperimentationtovalidateMREIMapplicability. Intheworkpresentedhere,themagnitudedatawasanalyzed,becausethephasedatawasnotaccessible.Futureworkshouldinvestigatephasecontrastwiththephasedataaswellasmagnitudecontrast. TheworkontheMagneticResonanceElectricalImpedanceMammographyprojecthasresultedinpatentapplication,publications,presentations,andabstracts(Wollin2004;Ko-valchuk,Kallergietal.2006;Kallergi,Wollinetal.2006a;Kallergi,Wollinetal.2006b;Heine,Kovalchuketal.2008a;Heine,Kovalchuketal.2008b).168

PAGE 186

AckmannJJandSeitzMA1984MethodsofcompleximpedancemeasurementsinbiologictissueCritRevBiomedEng11281-311 AdamsSV,OrtonPZandScottV2001ClisQuickReview:Statistics(NewYork,NewYork:WileyPublishing,Inc.) AssenheimerM,Laver-MoskovitzO,MalonekD,ManorD,NahalielU,NitzanRandSaadA2001TheT-SCANtechnology:electricalimpedanceasadiagnostictoolforbreastcancerdetectionPhysiolMeas221-8 BernsteinMA,KingKFandZhouZJ2004HandbookofMRIpulsesequences(Amsterdam;Boston:AcademicPress) BeutelJ,KundelHL,andVanMetterRL2000HandbookofMedicalImaging:Volume1.PhysicsandPsychophysics(Bellingham,Washigton:SPIEPress) BinnsKJ,LawrensonPJandTrowbridgeCW1992Theanalyticalandnumericalsolutionofelectricandmagneticelds(Chichester[England];NewYork:Wiley) BirgulOandEyubogluBM2003Experimentalresultsfor2Dmagneticresonanceelectricalimpedancetomography(MR-EIT)usingmagneticuxdensityinonedirectionPhysMedBiol483485-504 BirgulO,EyubogluBMandIderYZ2001Newtechniqueforhighresolutionabsoluteconductivityimagingusingmagneticresonanceelectricalimpedancetomography(MR-EIT)SPIEPhysicsofMedicalImaging2880-8169

PAGE 187

BirgulOandIderYZ1995Useofmagneticeldgeneratedbytheinternaldistributionofinjectedcurrentsforelectricalimpedancetomography.In:IXthIntConfonBio-Impedance,pp418-9 BlochF,HansenWWandPackardM1946NuclearinductionPhysRev69127 BreastCancerFactsandFigures2007-2008(Atlanta:AmericanCancerSociety,Inc.) BreastImagingReportingandDataSystem(BI-RADS)Atlas2007(Reston,VA:AmericanCollegeofRadiology) BrighamEO1988ThefastFouriertransformanditsapplications(EnglewoodClis,N.J.:PrenticeHall) BrightDS,NewburyDEandSteelEB1997VisibilityofobjectsincomputersimulationsofnoisymicrographsJMicroscopy18925-42 CharmanRA1996Clayton'sElectrotherapy,edSKitchen,Bazin,S.(London,UK:SaundersCompanyLtd.) ChauveauN,HamzaouiL,RochaixP,RigaudB,VoigtJJandMorucciJP1999Exvivodis-criminationbetweennormalandpathologicaltissuesinhumanbreastsurgicalbiopsiesusingbioimpedancespectroscopyAnnNYAcadSci87342-50 ChenX,LehmanCDandDeeKE2004MRI-guidedbreastbiopsy:clinicalexperiencewith14-gaugestainlesssteelcorebiopsyneedleAJRAmJRoentgenol1821075-80 CherepeninV,KarpovA,KorjenevskyA,KornienkoV,MazaletskayaA,MazourovDandMeisterD2001A3Delectricalimpedancetomography(EIT)systemforbreastcancerdetectionPhysiologicalmeasurement229-18 CherepeninVA,KarpovAY,KorjenevskyAV,KornienkoVN,KultiasovYS,OchapkinMB,TrochanovaOVandMeisterJD2002Three-dimensionalEITimagingofbreast170

PAGE 188

ColeKS1928ElectricimpedanceofsuspensionsofspheresJ.Gen.Physiol.1229-36 ColeKS1932ElectricphaseangleofcellmembranesJ.Gen.Physiol.15641-9 ColeKSandColeRH1941Dispersionandabsorptionindielectrics.I.AlternatingcurrentJ.Chem.Phys.9341-51 ConeCD,Jr.1970VariationofthetransmembranepotentiallevelasabasicmechanismofmitosiscontrolOncology24438-70 ConeCD,Jr.1974TheroleofthesurfaceelectricaltransmembranepotentialinnormalandmalignantmitogenesisAnnNYAcadSci238420-35 ConeCD,Jr.1985TransmembranePotentialandCharacteristicsofImmuneandTumorCells(BocaRaton,Florida:CRCPress) CopeFW1978AmedicalapplicationoftheLingassociation-inductionhypothesis:thehighpotassium,lowsodiumdietoftheGersoncancertherapyPhysiolChemPhys10465-8 CureJC1991Cancer:anelectricalphenomenon.Resonant1 DuchesneN,BurbankFandDuchesneSeds2006BreastDiseases:Detection,Intervention,andTherapy(St.Bruno,Canada:DTRInc.) EssermanL,HyltonN,YassaL,BarclayJ,FrankelSandSicklesE1999Utilityofmag-neticresonanceimaginginthemanagementofbreastcancer:evidenceforimprovedpreoperativestagingJClinOncol17110-9 EyuboluBM,LeighJSandReddyR2002Magneticresonance-electricalimpedancetomog-raphy.(US:6397095)171

PAGE 189

FosterKRandScheppsJL1981DielectricpropertiesoftumorandnormaltissuesatradiothroughmicrowavefrequenciesJMicrowPower16107-19 FosterKRandSchwanHP1989Dielectricpropertiesoftissuesandbiologicalmaterials:acriticalreviewCritRevBiomedEng1725-104 FrahmJ,MerboldtKDandHanickeW1988DirectFLASHMRImagingofMagneticFieldInhomogeneitiesbyGradientCompensationMagneticResonanceinMedicine6474-480 FrickeHandMorseS1926TheelectriccapacityoftumorsofthebreastJ.CancerRes.10340-76 GabrielC1996CompilationofthedielectricpropertiesofbodytissuesatRFandmicrowavefrequencies.In:Occupationalandenvironmentalhealthdirectorate,RadiofrequencyRa-diationDivision,(Texas(USA):BrooksAirForceBase) GaoN,ZhuSA,HeB2006Anewmagneticresonanceelectricalimpedancetomography(MREIT)algorithm:theRSM-MREITalgorithmwithapplicationstoestimationofhumanheadconductivityPhysMedBiol513067-83 GlickmanYA,FiloO,NachalielU,LeningtonS,Amin-SpectorSandGinorR2002NovelEISpostprocessingalgorithmforbreastcancerdiagnosisIEEEtransactionsonmedicalimaging21710-2 HaakeEM,BrownRW,ThompsonMR,VenkatesanR1999MagneticResonanceImaging:PhysicalPrinciplesandSequenceDesign(NewYork:Wiley) HeineJJ1993ComputerSimulationsofMagneticResonanceImagingandSpectroscopy.In:PhysicsDepartment(Tampa:UniversityofSouthFlorida) HeineJJ,KovalchukNandWollinE2008a(underreviewinMedicalPhysics)MagneticRes-onanceElectricalImpedanceMammographyPart2:Tissuemodelsandeldequations172

PAGE 190

HeywangSH,ViehwegPandHeiningA1997ContrastenhancedMRIofbreast:Accuacy,value,solutionsEuropJRadiol2494-108 IderYZandMuftulerLT1997MeasurementofACmagneticelddistributionusingmag-neticresonanceimagingIEEEtransactionsonmedicalimaging16617-22 IEC2001InternationalStandard:MedicalElectricalEquipment-Part1-2:GeneralRequire-mentsforSafety(DocumentIEC60601-1-2) JossinetJ1996VariabilityofimpedivityinnormalandpathologicalbreasttissueMedBiolEngComput34346-50 JossinetJ1998TheimpedivityoffreshlyexcitedhumanbreasttissuePhysiolMeas1961-75 JossinetJandSchmittM1999AreviewofparametersforthebioelectricalcharacterizationofbreasttissueAnnNYAcadSci87330-41 KahanW1958Gauss-SeidelmethodsofsolvinglargesystemsoflinearequationsIn:PhDThesis(Toronto:UniversityofToronto) KallergiM,WollinE,HeineJJ,KovalchukNandManoharA2006aLectureNotesinCom-puterScience,(Berlin/Heidenberg:Springer)pp468-74 KallergiM,WollinE,HeineJJ,KovalchukNandManoharA2006bMagneticResonanceElectricalImpedanceMammography:APilotStudy.In:8thIWDM,edSAstley,etal.(Manchester,UK:Springer-Verlag) KhangHS,LeeBI,OhSH,WooEJ,LeeSY,ChoMH,KwonO,YoonJRandSeoJK2002J-substitutionalgorithminmagneticresonanceelectricalimpedancetomography(MREIT):phantomexperimentsforstaticresistivityimagesIEEETransMedImaging21695-702173

PAGE 191

KneeshawPJ,DrewPJandHubbardA2002Electricalimpedancescanning:anewimagingtechniqueforevaluatingmicrocalcicationsinthebreast?BreastCancerRes420 KovalchukN,KallergiM,WollinE,HeineJJ,ManoharAandRabsonD2006MagneticResonanceElectricalImpedanceMammography:AFeasibilityStudy.In:48thAnnualMeetingAAPM,(Orlando,US:Med.Phys.)p2183 KraftKA,FatourosPP,ClarkeGDandKishorePR1987AnMRIphantommaterialforquantitativerelaxometryMagnResonMed5555-62 KwonO,WooEJ,YoonJRandSeoJK2002Magneticresonanceelectricalimpedanceto-mography(MREIT):simulationstudyofJ-substitutionalgorithmIEEETransBiomedEng49160-7 LeeJW,KimDM,LimHG,ParkIYandChoJH2002AcharacteristicsofhumanskinimpedanceincludingatbiologicalactivepointsITC-CSCC-2002 LineyGP,TozerDJandTurnbullLW1999Asimpleandrealistictissue-equivalentbreastphantomforMRIJMagnResonImaging10968-71 MacdonaldJR1987ImpedanceSpectroscopy:EmphasizingSolidMaterialsandSystems(NewYork:Wiley) MadsenELandFullertonGD1982Prospectivetissue-mimickingmaterialsforuseinNMRimagingphantomsMagnResonImaging1135-41 MalichA,BoehmT,FaciusM,FreesmeyerMG,FleckM,AndersonRandKaiserWA2001aDierentiationofmammographicallysuspiciouslesions:evaluationofbreastultrasound,174

PAGE 192

MalichA,BohmT,FaciusM,FreessmeyerM,FleckM,AndersonRandKaiserWA2001bAdditionalvalueofelectricalimpedancescanning:experienceof240histologically-provenbreastlesionsEurJCancer372324-30 MalichA,BohmT,FaciusM,KleinteichI,FleckM,SaunerD,AndersonRandKaiserWA2003Electricalimpedancescanningasanewimagingmodalityinbreastcancerdetection-ashortreviewofclinicalvalueonbreastapplication,limitationsandperspectivesNuclearInstrumentsandMethodsinPhysicsResearchA49771-81 MalichA,FritschT,AndersonR,BoehmT,FreesmeyerMG,FleckMandKaiserWA2000Electricalimpedancescanningforclassifyingsuspiciousbreastlesions:rstresultsEuropeanradiology101555-61 MartinG,MartinR,BrievaMJandSantamariaL2002Electricalimpedancescanninginbreastcancerimaging:correlationwithmammographicandhistologicdiagnosisEuro-peanradiology121471-8 McAdamsETandJossinetJ1995Tissueimpedance:ahistoricaloverviewPhysiolMeas16A1-13 MelloulM,PazA,OhanaG,LaverO,MichalevichD,KorenR,WollochYandGalR1999Double-phase99mTc-sestamibiscintimammographyandtrans-scanindiagnosingbreastcancerJNuclMed40376-80 MikacU,DemsarF,BeravsKandSersaI2001MagneticresonanceimagingofalternatingelectriccurrentsMagneticresonanceimaging19845-56 MillerJ2007Electriceldshavepotentialasacancertreatment.In:PhysicsToday,pp19-20 MitraAK2007FiniteDierenceMethodfortheSolutionofLaplaceEquation[www:public:iastate:edu=akmitra=aero361=designweb=Laplace:pdf]175

PAGE 193

MorimotoT,KinouchiY,IritaniT,KimuraS,KonishiY,MitsuyamaN,KomakiKandMondenY1990Measurementoftheelectricalbio-impedanceofbreasttumorsEurSurgRes2286-92 MorrisEAed2006BreastMRI(St.Bruno:DTRInc.) MorrisPG1986Nuclearmagneticresonanceimaginginmedicineandbiology(Oxford:Ox-fordUniversityPress) MorucciJP,ValentinuzziME,RigaudB,FeliceCJ,ChauveauNandMarsiliPM1996BioelectricalimpedancetechniquesinmedicineCritRevBiomedEng24275 MuftulerLT,HamamuraM,BirgulOandNalciogluO2004Resolutionandcontrastinmagneticresonanceelectricalimpedancetomography(MREIT)anditsapplicationtocancerimagingTechnologyincancerresearch&treatment3599-609 NieperHA1985Dr.Nieper'sRevolutioninTechnology,MedicineandSociety(Oldenburg,Germany:MITVerlag) OhSHandHanJY2003Electricalconductivityimagingbymagneticresonanceelectricalimpedancetomography(MREIT)MagnResonMed50875-8 OhSH,LeeBI,ParkTS,LeeSY,WooEJ,ChoMH,SeoJKandKwonO2004Magneticresonanceelectricalimpedancetomographyat3TeslaeldstrengthMagnResonMed511292-6 OhSH,LeeBI,WooEJ,LeeSY,ChoMH,KwonOandSeoJK2003ConductivityandcurrentdensityimagereconstructionusingharmonicBzalgorithminmagneticresonanceelectricalimpedancetomographyPhysMedBiol483101-16 OhmineY,MorimotoT,KinouchiY,IritaniT,TakeuchiMandMondenY2000NoninvasivemeasurementoftheelectricalbioimpedanceofbreasttumorsAnticancerRes201941-6176

PAGE 194

PipernoG,FreiEHandMoshitzkyM1990Breastcancerscreeningbyimpedancemeasure-mentsFrontMedBiolEng2111-7 PipernoGandLeningtonS2002Breastelectricalimpedanceandestrogenuseinpost-menopausalwomenMaturitas4117-22 PolkCandPostowWeds1986CRCHandbookofBiologicalEectsofElectromagneticFields(BocaRaton,FL:CRCPress) PurcellEM,TorreyHCandPoundRV1946ResonanceabsorptionbynuclearmagneticmomentsinasolidPhysRev6937-8 Rakow-PennerR,DanielB,YuH,Sawyer-GloverAandGloverGH2006Relaxationtimesofbreasttissueat1.5Tand3TmeasuredusingIDEALJMagnResonImaging2387-91 ReichenbachJR,VenkatesanR,YablonskiyDA,ThompsonMR,LaiSandHaakeEM1997TheoryandApplicationofStatisticFieldInhomogeneityEectsinGradientEchoImagingJMagnResonImaging7266-279 RoseA1948ThesensitivityperformanceofthehumaneyeonanabsolutescaleJOptSocAm38196-200 ScholzBandAndersonR2000Onelectricalimpedancescanning-principlesandsimulationsSiemensElectromedica20006835-44 SchwanHP1957ElectricalpropertiesoftissueandcellsuspensionsAdvBiolMedPhys5147-209 SchwanHP1963PhysicalTechniquesinBiologicalResearch,edWLNastuk(NewYork:Academic)pp327-407 SchwanHPandKayCF1957TheconductivityoflivingtissuesAnnNYAcadSci651007-13177

PAGE 195

ScottGC,JoyMLG,ArmstrongRLandHankelmanRM1995RotatingframerfcurrentdensityimagingMagnResonMed33355-69 SeegerPGandWolzS1990Succesfulbiologicalcontrolofcancer:BycombatagainstthecausesGesamtherstellung:NeuwiederVerlagsgesellschaftmbH SijbersJ,denDekkerAJ,VanAudekerkeJ,VerhoyeMandVanDyckD1998EstimationofthenoiseinmagnitudeMRimagesMagneticresonanceimaging1687-90 SinghB,SmithCWandHughesR1979InvivodielectricspectrometerMedBiolEngComput1745-60 SlichterCP1978PrinciplesofMagneticResonance(NewYork:Springer)ChVII StarkDDandBradleyWG1999Magneticresonanceimaging(St.Louis:Mosby) StevickJW,HardingSG,PaquetU,AnsorgeRE,CarpenterTAandWilliamsGB2008GaussianProcessModelingforImageDistortionCorrectioninEchoPlanarImagingMagneticResonanceinMedicine59598-606 StojadinovicA,NissanA,GallimidiZ,LeningtonS,LoganW,ZuleyM,YeshayaA,Shi-monovM,MelloulM,FieldsS,AllweisT,GinorR,GurDandShriverCD2005Electricalimpedancescanningfortheearlydetectionofbreastcancerinyoungwomen:preliminaryresultsofamulticenterprospectiveclinicaltrialJClinOncol232703-15 StuchlyMAandStuchlySS1990ElectricalPropertiesofBiologicalSubstances(EaglewoodClis,NJ,USA:PrenticeHallInc.)178

PAGE 196

WalshMandLeeM1991AreviewoffalsenegativemammographyinsymptomaticpopulationClinicalradiology4413-5 WersebeA,SiegmannK,KrainickU,FersisN,VogelU,ClaussenCDandMuller-SchimpeM2002DiagnosticpotentialoftargetedelectricalimpedancescanninginclassifyingsuspiciousbreastlesionsInvestigativeradiology3765-72 WollinE2004ApparatusandMethodforMagneticResonanceMeasurementandMappingofElectricalImpedanceComplexPermittivityandComplexConductivityasAppliedtoDetectionandDetectionofSamplePathology.(Int.PatentNo.WO2004/019763 WorldHealthOrganizationCancerFactSheetN2972006WorldHealthOrganization ZhangN1992Electricalimpedancetomographybasedoncurrentdensityimaging.In:DeptofEE,MSThesis(Toronto:UniversityofToronto)179