Table Of ContentAdvances in Experimental Medicine and Biology 1380
Rosalind Sadleir
Atul Singh Minhas Editors
Electrical
Properties
of Tissues
Quantitative Magnetic Resonance Mapping
Advances in Experimental Medicine
and Biology
Volume 1380
SeriesEditors
Wim E. Crusio, Institut de Neurosciences Cognitives et Intégratives
d’Aquitaine,CNRSandUniversityofBordeaux,PessacCedex,France
Haidong Dong, Departments of Urology and Immunology, Mayo Clinic,
Rochester,MN,USA
HeinfriedH.Radeke,InstituteofPharmacology&Toxicology,Clinicofthe
GoetheUniversityFrankfurtMain,FrankfurtamMain,Hessen,Germany
Nima Rezaei, Research Center for Immunodeficiencies, Children’s Medical
Center,TehranUniversityofMedicalSciences,Tehran,Iran
Ortrud Steinlein, Institute of Human Genetics, LMU University Hospital,
Munich,Germany
JunjieXiao,CardiacRegenerationandAgeingLab,InstituteofCardiovascu-
larScience,SchoolofLifeScience,ShanghaiUniversity,Shanghai,China
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Rosalind Sadleir • Atul Singh Minhas
Editors
Electrical Properties
of Tissues
Quantitative Magnetic Resonance
Mapping
Editors
RosalindSadleir AtulSinghMinhas
SchoolofBiologicalandHealth SchoolofEngineering
SystemsEngineering MacquarieUniversity
ArizonaStateUniversity WallumattagalCampus,
Tempe,AZ,USA MacquariePark,NSW,Australia
ISSN0065-2598 ISSN2214-8019 (electronic)
AdvancesinExperimentalMedicineandBiology
ISBN978-3-031-03872-3 ISBN978-3-031-03873-0 (eBook)
https://doi.org/10.1007/978-3-031-03873-0
©SpringerNatureSwitzerlandAG2022
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Preface
Theelectricalpropertiesoftissuesareafundamentalcharacteristicproviding
auniqueandextremelysensitiveinsightintotheircompositionandfunction.
Whilevaluesforintrinsictissueconductivityandpermittivitymaybedeter-
mined using excised samples or in situ using conductivity cells or probes,
there is increasing interest in imaging the distribution of these properties
within the body. The area of electrical impedance tomography (EIT) has
nowexistedforover40yearsandhasimportantapplicationsinareassuchas
non-invasivelungmonitoringandfunctionalimaging.ThoughEITisavery
sensitive monitoring technique, limitations arise because of the general ill-
posedness of the inverse problem. Current density imaging using magnetic
resonance imaging was first demonstrated by Scott and Joy, working at
the University of Toronto in the early 1990s. The suggestion to use this
approach to image conductivity distributions was also made by this group.
The earliest approaches to imaging both current density and conductivity
proceeded assuming three different measurements, representing the three
components of the magnetic flux density distribution caused by an external
current. In the early 2000s, Seo and Woo contributed to an approach that
involvedmeasuringandusingonlyasinglecomponentofthemagneticflux
density.Ataroundthesametime,Katscherandcolleaguesweredeveloping
practicalstrategiesforimagingconductivityandpermittivitydistributionsat
theLarmorfrequenciesofMRIsystems.Overtheyears,numerousmethods
forreconstructingelectromagneticfieldsandconductivitydistributionshave
been suggested and tested. The currents required to image conductivities at
the lowest frequencies have reduced from over 20mA to around 1.5mA,
andmeasurementsofhumanheadconductivitieshavebeenobtainedinvivo.
High-frequencyconductivitymeasurementsarebeingtestedinclinicaltrials,
andthenewestconductivityreconstructionmethodsinvolvenocurrentadmin-
istration at all, involving only diffusion tensor imaging and high-frequency
conductivitydistributions.Theareaisalsobenefitingfrominterestinstudying
mechanismsandindividualizedtreatmentsinneuromodulationtherapiessuch
astranscranialACandDCstimulation,whichrequiremeasurementofcurrent
densityandelectricfielddistributions.
Thevolumeisorganizedassumingthereaderisanundergraduateorgrad-
uatestudentfocusingonadvancedtopicsinMRI,oraresearcherunfamiliar
withthegeneralareaoftissueelectricalpropertiesandMRI.Chapter1begins
v
vi Preface
with a basic treatment of the factors underlying the electrical properties of
tissues.Apracticalintroductiontothefiniteelementanalysisandelectromag-
neticmodeling,typicallyrequiredduringreconstructions,isgiveninChap.2.
Chapter3coversabasicintroductiontoMRIfocusingonhardware,physics,
mathematicalexpressionsfork-space,pulsesequences,imagereconstruction,
and SNR methods, forming the basis of phase imaging in MRI. Chapters 4
and 5 are concerned with constructing phantoms for conductivity imaging,
andthenexttwochapterspresentacomprehensiveoverviewofMRImethods
forreconstructingcurrentdensity(Chap.6)andconductivity(Chap.7).The
volume concludes with an examination of important factors in measuring
high-frequencyconductivity(Chap.8).
This book arose out of a successful workshop that was held at the 39th
Annual International Conference of the IEEE Engineering in Medicine and
Biology conference which took place at Jeju Island, Republic of Korea, in
2018.WewouldliketothankandacknowledgeourfriendsandmentorsEung
Je Woo, Jin Keun Seo, and Oh In Kwon; our co-authors Camelia Gabriel,
MunishChauhan,SauravZ.K.Sajib,UlrichKatscher,RuthOliver,andNitish
Katoch;andourfamiliesandcolleaguesfortheircontributionstothisproject.
WewouldalsoliketoconveyourgratitudetoMerryStuberandDeepakRavi
atSpringerfortheirassistanceincompilingthisvolume.
Tempe,AZ,USA RosalindSadleir
Sydney,NSW,Australia AtulSinghMinhas
February2022
Contents
1 ElectromagneticPropertiesandtheBasisforCDI,MREIT,
andEPT................................................ 1
RosalindSadleir,CameliaGabrielandAtulSinghMinhas
2 ModelingforElectromagneticCharacterization,Prediction,
andReconstruction ...................................... 17
RosalindSadleir
3 MagneticResonanceImagingBasics ....................... 47
AtulSinghMinhasandRuthOliver
4 PhantomConstructionandEquipmentConfigurationsfor
CharacterizingElectricalPropertiesUsingMRI............. 83
MunishChauhanandRosalindSadleir
5 MRCurrentDensityandMREITDataAcquisition.......... 111
MunishChauhanandRosalindSadleir
6 MagneticResonanceCurrentDensityImaging(MR-CDI) .... 135
SauravZ.K.SajibandRosalindSadleir
7 MagneticResonanceElectricalImpedanceTomography ..... 157
SauravZ.K.SajibandRosalindSadleir
8 Magnetic Resonance Electrical Properties Tomography
(MREPT)............................................... 185
UlrichKatscher,AtulSinghMinhasandNitishKatoch
Index ...................................................... 203
vii
1
Electromagnetic Properties and the
Basis for CDI, MREIT, and EPT
RosalindSadleir,CameliaGabriel,andAtulSinghMinhas
Abstract composition,thatis,ofbiologicalmoleculesand
electrolytesarrangedinanaqueoussolution.Tis-
Theelectromagneticpropertiesofbodytissues
sue electrical properties can be summarized us-
dependonnumerousfactors,themostimpor-
ingelectricalconductivityandpermittivityvalues
tantofwhichareionicconcentrationsand,par-
and their spectra. For most biological materi-
ticularly in the low-frequency regime, mem-
als, the magnetic permeability is close to that of
brane density and geometry. In this chapter,
free space, which implies very weak interaction
thecharacteristicsofthesepropertiesandtheir
withthemagneticcomponentofelectromagnetic
spectra are introduced. The properties mea-
fields at low field strength. The most significant
suredbydifferenttypesofMR-basedmethods
magnetic contrasts in body tissues are related to
aredescribed.
thepresenceofparamagneticiron(inferritinand
deoxygenatedhemoglobin)andcalcium[34].
1.1 ElectricalPropertiesof Tissue response to an incident electromag-
Tissue neticfieldcanthereforebeconsideredasmostly
depending on electrical conductivity or capac-
1.1.1 WhatUnderliesTissue ity (permittivity) properties and can be modeled
ElectromagneticProperties from either perspective. Depending on the tis-
sue composition involved, one approach may be
more natural than another. For example, more
The electromagnetic properties of body tissues
solid tissues tend to have larger charge storage
are characteristic of their cellular structure and
capabilityorpolarizabilityandmaybedescribed
moreappropriatelyusingpermittivityratherthan
R.Sadleir((cid:2)) conductivity.Ineithercase,thepropertycharac-
SchoolofBiologicalandHealthSystemsEngineering, terizing tissue electrical properties is a complex
ArizonaStateUniversity,Tempe,AZ,USA
quantity,andconductiveorcapacitiveproperties
e-mail:[email protected]
maybemeasuredusingin-phase(real)orquadra-
C.Gabriel
ture(imaginary)measurements,respectively.
C.GabrielConsultants,SanDiego,CA,USA
Tissue properties result from multiple influ-
A.S.Minhas
ences including tissue heterogeneity, interfacial
SchoolofEngineering,MacquarieUniversity,
effects, and directionality or anisotropy. At fre-
WallumattagalCampus,MacquariePark,NSW,Australia
e-mail:[email protected] quencies below around 100 kHz, phase shifts
©SpringerNatureSwitzerlandAG2022 1
R.Sadleir,A.S.Minhas(eds.),ElectricalPropertiesofTissues,AdvancesinExperimental
MedicineandBiology1380,https://doi.org/10.1007/978-3-031-03873-0_1
2 R.Sadleiretal.
resultingfromcapacitivetissuecharacteristicsare centrations, this experimental data agrees very
verysmall,andmeasurementsalmostallrelateto well with the resistivity values that may be cal-
conductiveproperties.Theconductiveproperties culatedusingtheexpression
of tissues in this range are mostly due to the
presence of electrolytes in body fluids as well (cid:2) =(cid:2)o −Kc1/2 (1.1)
m m
astheconcentrationandmembranegeometry.At
higherfrequencies,conductivitymostlydepends where (cid:2) is the molar conductivity in S
m
on ionic concentrations. Because tissues contain m−1mol−1 L and where c is the molar conduc-
alotofwater,alltissuesalsoshoweffectsofthe tivity of the electrolyte. K is the Kohlrausch
large absorption energy by of water molecules coefficient, a value that depends on the solvent
around 2 GHz (the same frequency used by mi- andthechargeonionicspeciesaswellasthemo-
crowaveovens). larconcentrationitself.Themolarconductivityof
Thedependenciesofrealandimaginarytissue thesaltatinfinitedilutionis(cid:2)o.Theconductivity
m
electricalpropertiesonfrequencyarerelatedvia ofasolutionanditsconductivityσ arerelatedvia
the Kramers-Kronig relations; therefore, charac-
teristics of conductivity spectra may be intuited σ =(cid:2) c (1.2)
m
from permittivity spectra, and vice versa. The
compound nature of these properties means that Following(1.2),theconductivityofasolution
specialelectricalcomponentsmustbeintroduced broadlyincreaseslinearlywithmolarconcentra-
tobestmodeltissuespectra. tion of electrolyte, but this dependence progres-
In the sections below, we consider ionic con- sively decreases as concentration increases. Fig-
tributions to tissue conductivities, followed by ure1.1showstheconductivityofNaClinsolution
reactiveandfrequency-dependentcharacteristics. (saline) as a function of molar concentration at
Commonlyobservedfeaturesofconductivityand 25 C. Data from this plot were obtained from
permittivityspectrawillbedescribedandproper- published experimental data [13]. In the case
ties of tissues important to imaging electromag- of NaCl dissolved in water, the value for K is
netic properties will be outlined. Last, methods 89.14×10−4 (cid:4)−1 m2mol−1/(mol.L−1)−1/2.The
andimportantconsiderationsformaking“bench- molar conductivity at infinite dilution at 25 C is
top”measurementsoftissuepropertiesforverifi- approximately 126.4 × 10−4 (cid:4)−1m2mol−1. The
cationoftheseimagingmethodswillbesumma- curves start to diverge at a molar concentration
rized,astheyareimportantforreconstructionval- ofaround0.3mol/L(17g/L)whichisalsoabout
idation.Validation,includingconstructingphan- twicetheNaClconcentrationofnormal(0.9%or
tomstotestmethods,isalsodiscussedfurtherin 9 g/L) saline solution. Note that the graph indi-
Chap.4. catesthatatveryhighmolarities,theconductivity
predicted by Eqs.(1.1) and (1.2) actually begins
1.1.1.1 IonicConductivities todecrease,whichisbecausethisapproximation
Becausethewatercontentoftissuesissignificant, breaksdownasconcentrationsbecomehigh.Note
their properties are closely related to those of alsothatatveryhighconcentrations(>6mol/L)
electrolytes in aqueous solution. The most com- ofNaClthesolutionbecomessaturated.
mon ions in the body are sodium and chloride, The conductivity of an aqueous salt solution
withionsofpotassium,bicarbonate,calcium,and willalsotendtoincreasewithincreasingtemper-
magnesium also contributing to the ionic envi- ature because of the decrease in the viscosity of
ronment of intra- or extracellular environments. waterwithtemperature.Thisleadstoanincrease
Properties of electrolytic solutions were investi- in the mobility of ions in solution and hence
gated extensively in the nineteenth century. The in the molar conductivity. This trend underlies
Kohlrausch law describes the dependence of the the observed temperature dependence of tissue
molarconductivityonconcentration.Atlowcon- conductivity.Measurements of tissue properties,
