![Single-pole Debye parameters for the dielectric property curves for each tissue type [64].](https://www.researchgate.net/publication/356951243/figure/tbl3/AS:1099638572625928@1639185674565/Single-pole-Debye-parameters-for-the-dielectric-property-curves-for-each-tissue-type-64_Q320.jpg)
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Sensors2021,21,8265.https://doi.org/10.3390/s21248265www.mdpi.com/journal/sensors
Article
Developmentof3DMRI‐BasedAnatomicallyRealistic
ModelsofBreastTissuesandTumoursforMicrowave
ImagingDiagnosis
AnaCatarinaPelicano
1,
*
,†
,MariaC.T.Gonçalves
1,
*
,†
,DanielaM.Godinho
1
,TiagoCastela
2
,M.LurdesOrvalho
2
,
NunoA.M.Araújo
3
,EmilyPorter
4
andRaquelC.Conceição
1
1
InstitutodeBiofísicaeEngenhariaBiomédica,FaculdadedeCiências,UniversidadedeLisboa,
CampoGrande,1749‐016Lisbon,Portugal;dmgodinho@fc.ul.pt(D.M.G.);rcconceicao@fc.ul.pt(R.C.C.)
2
DepartamentodeRadiologia,HospitaldaLuzLisboa,LuzSaúde,1500‐650Lisbon,Portugal;
tacastela@hospitaldaluz.pt(T.C.);lorvalho@hospitaldaluz.pt(M.L.O.)
3
CentrodeFísicaTeóricaeComputacional,FaculdadedeCiências,UniversidadedeLisboa,
CampoGrande,1749‐016Lisbon,Portugal;nmaraujo@fc.ul.pt
4
DepartmentofElectricalandComputerEngineering,TheUniversityofTexasatAustin,2501Speedway,
Austin,TX78712,USA;emily.porter@austin.utexas.edu
*Correspondence:acpelicano@fc.ul.pt(A.C.P.),mctgoncalves@fc.ul.pt(M.C.T.G.)
†Thefirsttwoauthorscontributedequallytothepaper.
Abstract:Breastcancerdiagnosisusingradar‐basedmedicalMicroWaveImaging(MWI)hasbeen
studiedinrecentyears.Realisticnumericalandphysicalmodelsofthebreastareneededfor
simulationandexperimentaltestingofMWIprototypes.Weaimtoprovidethescientific
communitywithanonlinerepositoryofmultipleaccuraterealisticbreasttissuemodelsderived
fromMagneticResonanceImaging(MRI),includingbenignandmalignanttumours.Suchmodels
aresuitablefor3Dprinting,leveragingexperimentalMWItesting.Weproposeapre‐processing
pipeline,whichincludesimageregistration,biasfieldcorrection,datanormalisation,background
subtraction,andmedianfiltering.Wesegmentedthefattissuewiththeregiongrowingalgorithm
infat‐weightedDixonimages.Skin,fibroglandulartissue,andthechestwallboundarywere
segmentedfromwater‐weightedDixonimages.Then,weapplieda3DregiongrowingandHoshen‐
Kopelmanalgorithmsfortumoursegmentation.Thedevelopedsemi‐automaticsegmentation
procedureissuitabletosegmenttissueswithavaryinglevelofheterogeneityregardingvoxel
intensity.Twoaccuratebreastmodelswithbenignandmalignanttumours,withdielectric
propertiesat3,6,and9GHzfrequencieshavebeenmadeavailabletotheresearchcommunity.
Thesearesuitableformicrowavediagnosis,i.e.,imagingandclassification,andcanbeeasily
adaptedtootherimagingmodalities.
Keywords:realisticnumericalmodels;breasttumourmodels;dielectricproperties;image
segmentation;breastmodelrepositoryformicrowavediagnosis
1.Introduction
Femalebreastcancerwasthemostcommoncancerdiagnosedworldwidein2020,with
over2.26millionnewcases[1].Breastcancerwasalsoreportedthefifthdeadliesttypeof
cancerin2020,andthecancerwiththehighestmortalityrateinthefemalepopulation[1].
Earlydetectionandinterventionhavebeenidentifiedasdeterminingfactorsinthe
reductionofbreastcancermortalityratesandarethekeyfactorsforasuccessfultreatment
outcome,therebyimprovingthequalityoflifeofcancerpatientsandsurvivalrates[2].
ThemostcommonimagingmodalityforbreastcancerdetectionisX‐ray
mammography[2,3].Althoughmammographyisstillthego‐toimagingmethodfor
cancerscreening,itdoesnotprovidereliableresultsforwomenwithdensebreasts,which
Citation:Pelicano,A.C.;
Gonçalves,M.C.T.;Godinho,D.M.;
Castela,T.;Orvalho,M.L.;
Araújo,N.A.M.;Porter,E.;
Conceição,R.C.Developmentof3D
MRI‐BasedAnatomicallyRealistic
ModelsofBreastTissuesand
TumoursforMicrowaveImaging
Diagnosis.Sensors2021,21,8265.
https://doi.org/10.3390/s21248265
AcademicEditor:VangelisSakkalis
Received:29October2021
Accepted:3December2021
Published:10December2021
Publisher’sNote:MDPIstaysneu‐
tralwithregardtojurisdictional
claimsinpublishedmapsandinstitu‐
tionalaffiliations.
Copyright:©2021bytheauthors.Li‐
censeeMDPI,Basel,Switzerland.
Thisarticleisanopenaccessarticle
distributedunderthetermsandcon‐
ditionsoftheCreativeCommonsAt‐
tribution(CCBY)license(http://crea‐
tivecommons.org/licenses/by/4.0/).
Sensors2021,21,82652of27
arecommonamongyoungerwomen[4].Sensitivityofmammographyexamsrangefrom
62.9%,forwomenwithextremelydensebreasts,to87.0%,inwomenwithmostlyfatty
breasts.Specificityhasbeenreportedtorangefrom89.1%to96.9%forthesamebreast
types[5].Besidesshowingdifferentsensitivitiesdependingontissuedensity,
mammographyalsorequirestheuseofionizingradiation,andanuncomfortablebreast
compression.
MicrowaveImaging(MWI)hasbeenidentifiedasatechniquethatcantacklethe
shortcomingsofX‐raymammography[6,7].InMWI,anexternalelectromagneticfieldis
appliedontotheregionofinterestinthebody,resultinginelectromagneticscattering
generatedbytissueswithdifferentdielectricproperties.Theconductivityandrelative
permittivityarethemostrelevantdielectricpropertiesofbiologicaltissues,wherethe
latterisintrinsicallyrelatedtothewatercontentpresentinthetissuesample.Inrecent
years,MWIsystemshavebeenstudiedforearly‐stagebreastcancerdiagnosis[8–10]due
tothecontrastbetweenthedielectricpropertiesofcancerousandhealthybreasttissuesat
microwavefrequencies[11].Canceroustissuesdifferfromhealthytissuesdueto
permeabilitychangesintumourcellmembranecausinganincreaseofwaterflowtothe
interiorofthecell.Hence,theextraquantitiesofwateranddissolvedionsinsidethe
cancerouscellsleadtogreatervaluesofrelativepermittivityandconductivitywhen
comparedtohealthycellsofthesametissuetype[12–15].Inadditiontobeinga
comfortableandnon‐invasiveimagingmodality,MWIdevicesarealsoportable,low‐cost,
user‐independent,uselow‐power,andtherefore,aresuitableforscreeningprogrammes.
Simulationsandexperimentsmimickingtherealisticconditionsandrealisticpatients
ofaclinicalexamareessentialforthedevelopmentandvalidationofMWIdiagnostic
systems,aswellasthedevelopmentoftherapeuticdevices,suchasthoseformicrowave
hyperthermiaandablation[16,17].Hence,realisticcomputationalandphysicalmodelsof
breasttissuesandtumourswiththerespectivedielectricpropertiesestimatedat
microwavefrequenciesareofutmostimportance.
Realisticmodelsofhealthybreasttissuesarecurrentlyavailableinpublic
repositories,however,duetotheircomplexshape,tumourmodelsareoften
oversimplified.Malignantbreasttumoursgenerallyhaveanirregularshapesurrounded
byspiculeswhereasbenigntumourspresentroughlyroundedorellipticalshapes[18,19].
Therefore,weaimtoprovidethescientificcommunitywitharepositoryofmultiple
anthropomorphicmodelsofbreasttissueswithrealisticbenignandmalignantbreast
tumours.
Inthisstudy,weuseMRIexamstodeveloptheanatomicallyrealisticmodelsofthe
breast,andestimatethedielectricpropertiesoffat,fibroglandular,skin,muscle,and
tumoroustissuesofthisregion.Additionally,wedevelopedarobustsegmentation
pipelinesuitabletosegmenthighlyheterogeneoustumoursfromMRIexams.The
developedsemi‐automaticimageprocessingpipelineincludesthefollowingsteps:(i)
Imagepre‐processing,(ii)Imagesegmentation/Featureextraction,comprisingthebreast
region(skin,breast/chestwallboundary,fatandfibroglandulartissues)andthebreast
tumour,andfinally,(iii)Estimationoftissuedielectricproperties.Thesecondaimofour
workistoaddressthelackofrealisticbreasttumourphantomsforMWIprototypetesting.
Hence,wehavebeenpreparingaccuratemodelsofthebreastwhichwillbeusedto
simulatetissueresponsetomicrowaveradiationandlater3Dprintedforexperimental
testing.Inshort,ourworkaimsto:
providethescientificcommunitywitharepositoryofmultipleanthropomorphic
modelsofbreasttissuesandtumours;
addressthelackofrealisticphysicalbreasttumourphantomsforMWIprototype
testing.
Thispaperisorganisedasfollows:firstly,wepresentrelatedworkalreadyconducted
concerningbreastandbreasttumourmodels;then,wedetailthematerialsusedandthe
methodologydevelopedforimagepre‐processing,segmentation,andestimationof
Sensors2021,21,82653of27
dielectricproperties;then,wepresenttheresultsofourproposedmethodology,followed
byadiscussion,andfinally,wehighlightthemainconclusionsofourwork.
RelatedWork
Wintersetal.[20]designedtwonumericalMRI‐derivedmodelsofthebreastsurface.
Later,apublicrepositorywithninenumericalbreastphantomscontainingrealistic
distributionsofskin,fat,glandularandmuscletissuewascreated[21];theSTLfilesto3D
printthesemodelswaslaterpublishedin[22].Morerecently,ananthropomorphicbreast
modelrepositoryincludingrealisticmodelsofskin,fatandfibroglandulartissues,anda
modelofa10mmmalignanttumourwasmadeavailablein[23].However,the
segmentationofthetumourvolumewasachievedbymanualcroppingandthresholding
techniques.
Studiesincludingnumericalbreasttumourmodelsoftenoversimplifytheir
representationbyusingspherical[24–26],andcross‐ andpeanut‐shapednumerical
models[14].Amoresophisticated3Dbreastmassmodelwasdevelopedin[27]usinga
growthmodelwithadensecentreandfadingboundariesfromanellipsoidvolumewhich
resultedinastellatepattern.
MostofthephysicalbreasttumourmodelsreportedintheliteraturetotestMWI
systemspresentanunrealisticsimplifiedshape,generallyspherical,elliptical,and
cylindrical:in[22],sphericalglassbulbswith5,10and15mmradiicontainingsaline
solutionswereusedtomimictumourtissuesinphantomstudies;anellipsoidcontainer
withinternaldimensions10and20mmwas3Dprintedin[28]tostudythefeasibilityof
aradar‐basedbreastMWIdrysetup;a20mmsphericalphantomfilledwitha10:90ratio
ofwatertoglycerinewasusedtoemulateabreasttumourin[29];twocylindricalshaped
tumourphantomswith10and20mmdiametersand30mmheightweretestedin[30];
andin[31],asmallcylindricalplasticcontainerfilledwithwaterwasusedasabreast
tumourphantominexperimentaltests.
Breasttumourshavebeenmodelled,morerealistically,withGaussianRandom
Spheres.Thesewereusedforvalidationtestsofamicrowaveimagingdevicein[32],and
fortumourclassificationusingaMWIprototypesystemin[33].In[34],realisticbenign
andmalignantbreastphantomswerecarvedbyhand,resultinginapproximatespherical
andspiculatedmodelsforbenignandmalignanttumours,respectively.Weemphasize
thatnoneofthemodelsreportedintheliteraturewerebasedonaccurateanatomical
representationsoftumours.
Asummaryofpreviouslydevelopedmethodologiestocreatebreastmodelshasbeen
recentlypublishedin[35].
2.MaterialsandMethods
2.1.Dataset
ThisstudywasapprovedbytheScientificandEthicalCommissionofHospitalda
Luz—Lisboa,underreferencesCES/44/2019/ME(19September2019)and
CES/34/2020/ME(6November2020).ThebreastMRIexamscollectedatHospitaldaLuz—
Lisboawereanonymisedbeforeprocessingandinformedconsentwasobtainedfromall
patients.
Thecurrentdatasetofthison‐goingstudycomprisesexamsfrom16patients,witha
totalof29tumours:15benignand14malignant.Inthispaper,weselectedbreastmasses
scoredwithBI‐RADS2and3[1](benigntumours)andBI‐RADS5and6(malignant
tumours)[1].
Womenwereimagedinapronepositionina3.0TMAGNETONVidaclinical
MagneticResonance(MR)scan(SiemensHealthineers,Erlangen—Germany)witha
dedicatedcoilforthebreast(SiemensBreast18coil,SiemensHealthineers,Erlangen—
Germany).TwoMRIsequenceswerecollected:DynamicContrastEnhanced(DCE)
transversalthree‐dimensional(3D)T1‐weighted(T1‐w)FastLowAngleShot3D(fl3D)
Sensors2021,21,82654of27
SpectralAttenuatedInversionRecovery(SPAIR)sequence;andDirectcoronalisotropic
3DT1‐wfl3DVolumetricInterpolatedBreath‐holdExamination(VIBE)Dixonimage
sequence(T1‐wDixon).
DCE‐fl3Dconsistsofafat‐suppressionsequencewithsixsetsofimages:apre‐con‐
trastimage,acquiredbeforetheinjectionofgadoliniumintravenouscontrastagent,and
fivepost‐contrastconsecutiveimageswherehighlyvascularisedtissues,suchastumours,
areenhanced.Digitalsubtractionsofeachpost‐contrastimagefromthepre‐contrastim‐
agearealsoavailable.Thedigitalsubtractionsenhancetumourregionsduetothecontrast
uptakeinthoselocationsandannulhypersignalregionspresentinthepre‐contrastimage.
Theseimagespresenthighresolutioninallanatomicalplanesandhaveisotropicvoxels.
Eventhoughourdatasetincludesimageswithdifferentspatialresolutions(0.99mm×0.99
mm×1mmand1.04mm×1.04mm×1mm),weonlyuseimageswith0.99mm×0.99mm
×1mminthispaper.WechosethesubtractionDCE‐fl3Dimage(SUB‐DCE‐fl3D)thatbest
revealsthewholetumourregionfortumoursegmentation.Onemustnotethatlargertu‐
moursrequiremoretimedelayforcontrastenhancementtobeobserved.
TheT1‐wDixonsequencereliesonthedifferenceinresonancefrequencybetween
hydrogennucleiboundtowaterandfat.Thisdifferenceallowsobtainingfoursetsofim‐
agesinasingleacquisition:in‐phase,oppositephase,fat‐only,andwater‐onlyimages.For
thisstudy,weusedfat‐only(F),water‐only(W),andin‐phase(I)imagestoretrievestruc‐
turalinformationofthebreast.Toderivethedielectricpropertiesofthetissuesinthe
breast(fat,fibroglandular,skin,andbenignandmalignanttumours),weusedtheT1‐w
Dixon‐Iimages,asthefatandfibroglandulartissuesareeasiertodistinguishintheirhis‐
tograms.Theseimageshadisotropicvoxels(0.99mm×0.99mm×1mm)andwereac‐
quiredinthecoronalplane.
2.2.Pre‐ProcessingPipeline
Thissectiondetailseachstepofthepre‐processingpipelineappliedtobreastMRI
imagesbeforetissuesegmentation.
2.2.1.ImageRegistration
WeusedtwodifferentMRIsequencestosegmentthebreasttissues:thetransverse
SUB‐DCE‐fl3Dsequence(fortumoursegmentation)andthecoronalT1‐wDixonsequence
(forthesegmentationoffat,fibroglandular,skin,andthebreast/chestwallboundary,pre‐
dominantlycomposedofmuscle);hencethealignmentofthetwoimagesisrequired.We
usedtheInsightToolkit(ITK)implementation(SimpleITK’s)[36]ofalinearregistration
withlinearinterpolationtoregistertheSUB‐DCE‐fl3Dsequence(movingimage)tothe
T1‐wDixonsequence(staticimage).T1‐wDixonwasconsideredthestaticimagedueto
itshigherinformationcontentregardingthedifferentbreasttissues.Theapplicationof
thelineartransformationresultedinimageswithdimensionsandresolutionofthestatic
image,andinthesamespatialreferential,allowingtheircorrectsuperimposition.
2.2.2.BiasFieldCorrection
MRIimagesarepronetothebiasfieldartefact[37],whichcausesunreliableintensity
variationswithinvoxelsofthesametissue.Astheaccuracyofintensity‐basedimagingpro‐
cessingalgorithms,suchassegmentationandclassification,isgreatlyaffectedbythebias
fieldartefact,apre‐processingstepaddressingitseffectsandcorrectionisrequired[38].
Anonparametricnonuniformsignalintensitynormalisation(N3)algorithm,pro‐
posedbySledetal.[39],usesaGaussianmodeltocorrectthebiasfieldwithouttheneed
foraprioriknowledge.Later,animprovementofthistechniqueledtothedevelopment
oftheN4algorithm[40],whichusesamulti‐scaleoptimisationapproachtocomputethe
biasfield.Thisalgorithmhasshownpromisingresultsinremovingthebiasfieldfrom
breastMRIimages[41].Thebiasfieldartefactcorrectionwasappliedtoallimagesusing
theSimpleITKN4BiasFieldCorrectionImageFilterimplementation[40].
Sensors2021,21,82655of27
2.2.3.DataNormalisation
Subsequently,theimageswerescaledbetween0and255usingtheMinimum‐Maxi‐
mum(Min‐Max)normalisationapproach,followingEquation(1):
𝑣
𝑛𝑒𝑤𝑛𝑒𝑤
𝑛𝑒𝑤,(1)
where𝑣′and𝑣aretheoriginalandscaledvaluesofeachvoxelrespectively;𝐴isthevol‐
umedata,andmax𝐴andmin𝐴arethemaximumandminimumvaluesof𝐴,respec‐
tively.𝑛𝑒𝑤and𝑛𝑒𝑤arethe[new]maximumandminimumvaluesofthe
scaledrange,respectively[42].
2.2.4.ImageFiltering
MRIimagesarepronetonoiseduetoimageacquisitionerrors,whichcorruptstheir
qualityanddeterioratestheperformanceofintensity‐basedautomaticsegmentationalgo‐
rithms.Salt‐and‐Peppernoise,commonlypresentinMRIimages,consistsofrandomly
distributedcorruptedvoxelswhichwereeithersettohavethevalue0orthemaximum
intensityvalueofthevoxelsintheimage[43].Themedianfilterisawell‐knownnon‐
linearfilterwhichallowsthereplacementofthevalueofavoxelbythemedianofthegray
levelsinitsneighbourhoodandhasbeenprovenveryeffectiveinthepresenceofSalt‐
and‐Peppernoise[44].Besidesremovingnoise,theimplemented3‐by‐3‐by‐3medianfil‐
ter,appliedtotheSUB‐DCE‐fl3Dimages,alsosmoothsvoxelsignalintensitydifferences
betweentumorousandnon‐tumoroustissues.However,wedidnotapplythemedian
filterforinfra‐centimetrictumours,asitproducessubstantialchangesinthesizeand
shapeoftumours.
2.3.ImageSegmentation
Accuratebreasttissuesegmentationisofparamountimportancetoobtainanatomi‐
callyrealisticnumericalandphysicalbreastmodels.Mosttissuesegmentationalgorithms
relyonthediscontinuityorsimilaritypropertiesoftheimage’sintensityvalues[44,45].
Severalprocessingpipelineshavebeendevelopedtoidentifythedifferenttissuesofthe
breastanduseacombinationofbothpropertiestoachieveacorrectsegmentation.Dis‐
continuity‐basedapproachesforbreasttissuesegmentationrelyontheidentificationof
air‐breastandbreast‐chestwallboundaries[46,47],whilesimilarity‐basedtechniques
mostlyrelyonthresholding[48],region‐growing[47],andclustering[49,50].Energy‐
basedapproaches,suchasactivecontour,havealsobeenproposedtosegmenttheskinof
thebreast[51].
Wedetailthesegmentationmethodologyusedforthedifferentbreasttissuesinthis
section.Figure1representsasimplifiedschematicofthestepsfollowedtoobtainamask
ofthebreastregion.
Sensors2021,21,82656of27
Figure1.Simplifiedschematicoftheprocessingstepstoobtainthemaskofthebreastregion.
2.3.1.BreastRegion
WeusedT1‐wDixon‐FandT1‐wDixon‐Wimagestogenerateabinarymaskofthe
breastregion.Wechosetheseimagessincefatisrepresentedwithhigh‐intensityvalues
intheT1‐wDixon‐Fimages,whilefibroglandular,skin,andmusclehavehigh‐intensity
valuesintheT1‐wDixon‐Wimages.Wepresenttheresultsfromourprocessingpipeline
inSection3.2.1,forclarity.
1. Step1:Fatmask+removaloforgansinsidethethoraciccavity
Theorgansinsidethethoraciccavity,suchastheheart,lungs,stomach,andliver,
presentedlow‐intensityvaluescomparedwiththehigh‐intensityvaluesofthefattissues
intheT1‐wDixon‐Fimage.Hence,weusedtheseimagestoexcludethemfromthebreast
regionmask.
Firstly,weneededtolocatethesternumintheT1‐wDixon‐Wimage.Todothis,we
identified,ineachframe,thevoxelswithanintensityhigherthanthemeanintensityof
theT1‐wDixon‐Wimage.Wethenpickedthecoordinatesoftheouter‐mostidentified
voxelandusedthesetolatercomputetheseedtogrowthefatregion.
Weappliedaregiongrowingalgorithm,implementedusingSimpleITK’sNeighbor‐
hoodConnectedImageFilter,totheT1‐wDixon‐Fimagetoidentifythevoxelsconnected
totheseedandwhoseneighboursliewithinauser‐definedintensityrange.Weautomat‐
icallycalculatedtheintensityrangeassignedtofattissue.Thelowerlimithasbeeniden‐
tifiedbyotherauthors[47]asthesumofthemeanandthreetimesthestandarddeviation
valuesofthevoxelintensitiesofnon‐fatsuppressedbreastMRIimages,wherefat,fibro‐
glandular,muscle,andskintissuesarerepresentedwithmediumtohigh‐intensityvalues.
Sinceonlyfathashigh‐intensityvaluesintheT1‐wDixon‐Fimage,weadjustedthelower
limitoftheintensitytothesumofthemeanandstandarddeviationvaluesofthevoxel
intensities.Wesettheupperlimittothemaximumintensityvoxeloftheimage.Inbreast
MRIimages,withnoclearseparationbetweenthefattissuesofthebreastandtheinner
partofthethoraciccavity,theregiongrowingalgorithmmaynotcorrectlysegmentboth
Sensors2021,21,82657of27
fattissues.However,theapplicationofmorphologicalwatershedtransformfrommarkers
[52](themarkerimageobtainedfromtheoutputoftheregiongrowingalgorithmbyap‐
plyingadistancetransform)totheregiongrowingalgorithmoutputsuccessfullydistin‐
guishesthetwotypesoffat.
2. Step2:Skin+Fibroglandular+Fatmask
Weincludedtheskinbydilatingthefatmask.Accordingto[53],thethickestskin
areaofthebreastcorrespondstotheareolarregionwith2.040.31mm.Withavoxel
spacing,inmillimetres,of0.9965 0.99651,weperformedadilationusingastructur‐
ingelementofradius3.Thedilatedmaskwaswhitedoutontheanteriorpartofthebody
andthenmultipliedbytheT1‐wDixon‐Wimagetoincludethefibroglandulartissue.We
binarizedtheresultingimagebythresholding,usingstatisticalinformation(meanand
standarddeviation)oftheimage,andaddedthebinarizedimagetothedilatedmask.The
thresholdwasdefined,inEquation(2),as:
𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 𝑚𝑒𝑎𝑛
.(2)
Tobinarizetheimage,wehadtoconsiderthefollowing:thethresholdhadtobe
higherthanthemeanvoxelintensitytoremovethebackgroundvoxelsintroducedbymul‐
tiplicationwiththeT1‐wDixon‐Wimage,butnotexcessivelyhighthattheholesleftfrom
thefatmaskwerenotfilled,especiallyinthenipplearea.Fromthisstep,weobtainamask
thatincludestheskin,fat,andfibroglandulartissue.
3. Step3:Maskevaluation
Asourmethodologyusesthesternumcoordinatesasreference,areaswhereatu‐
mourinvadesthepectoralismusclearenotincludedinthebreastregionmask.Aninva‐
sivetumourintroducesanasymmetryinthebreast;hence,theobtainedbreastmaskand
itsflippedimage(flippedalongthesagittalplane)areevaluated.Wechosethemean‐
squarederror(MSE)metric(Equation(3))toevaluatethedifferencesbetweenthemask
anditsflippedimage:
𝑀𝑆𝐸
∑
𝐴
𝐵
100,(3)
where𝑛representsthenumberofdatapoints,ivariesfrom1ton,𝐴isthemask,and𝐵is
theflippedimageofthemask.
Thelowerthemean‐squarederror,themoresimilararetheimagesunderevaluation.
Weconsideredthatamean‐squarederrorvaluehigherthan10%indicatedthepresence
ofaninvasivetumour.
4. Step4:Maskforanexamwithaninvasivetumour(optional,whenMSE>10%)
Foramean‐squarederrorvaluehigherthan10%,weaddedthebreastregionmask
anditsflippedimage.Then,wecomparednon‐coincidingareastotheT1‐wDixon‐Iimage
andreassignedvoxelswithintensitylowerthanthemeanvoxelintensityoftheT1‐w
Dixon‐Iimageto0.Afterthisprocess,thebreastmaskbecomessymmetricinthe
breast/chestwallboundaryregion(maskforinvasivetumours).Tocloseanyholesleft
fromtheprocessofreassigningthevoxelsto0,weappliedSimpleITK’sBinaryFillholeI‐
mageFiltertothesymmetricbreastmask.
5. Step5:Segmentationofskin+breast/chestwallboundary
Weusedthebreastmaskcontourtoidentifytheskinandthebreast/chestwallbound‐
ary.Wescannedittoretrievethefirstwhitevoxelfromlefttoright,righttoleft,andtop
tobottominthesagittalplane.Theresultingimagecorrespondedtoa1‐voxel‐thickskin
contour,wheresomeareasinthesagittalcentreofthebody,betweenthebreasts,were
notincluded.A1‐voxel‐thickbreast/chestwallboundarycontourcorrespondedtothe
largest‐connectedcomponentresultingfromthesubtractionbetweenthebreastmaskcon‐
tourandtheskincontour,followedbyblackingoutthevoxelsintheanteriorpartofthe
body,abovethesternum.
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Thefinalskincontourcorrespondedtothelargestconnectedcomponentofthesub‐
tractionbetweenbreastmaskcontourandthe1‐voxel‐thickbreast/chestwallboundary
contour.Weobtainedthefinalbreast/chestwallboundarycontourbysubtractingthefinal
skincontourfromthebreastmaskcontour.
AsmentionedinSection2.3.1,wedilatedthefatmaskobtainedfromapplyingregion
growingtotheT1‐wDixon‐Fimage,usingastructuringelementofradius3.Asaresult,
itisnecessarytodilatethecontoursbythesamestructuringelementtoestimatetheskin
andbreast/chestwallboundarytissues.Afterthedilation,wemultipliedtheresultingim‐
agebytheoriginalmasktoremovethe“excessive”breastarea.
Foraninvasivetumourexam,weadjustedthemethodtoidentifythebreast/chest
wallboundarytissuesbybuildinguponthebreastregionmaskthatwasmadesymmetric
inthesagittalplane.Weobtainedthebreast/chestwallboundarytissuesbysubtracting
themaskforinvasivetumoursandthe“original”mask(themaskobtainedbeforeitsad‐
ditionwithitsflippedimage,asobtainedinStep4),followedbydilationwithastructur‐
ingelementofradius3.Althoughthebreast/chestwallboundaryispredominantlymus‐
cle,itmayincludeothernearbytissues.
6. Step6:Skinevaluation
Sincetheskinhasvaryingthicknessthroughoutthebreast—rangingfrom2.35mm
intheareolarregionto1.52mminthelateralquadrant[53]—weneededtoadjusttheskin
masktoportrayanaccurateskinthickness.Firstly,wemultipliedtheT1‐wDixon‐Wim‐
agebythenegatedfatmasktoobtainanimagewithskinandfibroglandulartissue.Then,
webinarisedtheresultingimagebythresholding,andmultipliedthebinarisedimageby
thedilatedskincontour.
7. Step7:Fibroglandulartissuesegmentation
Withthefattissue,skin,andbreast/chestwallboundaryseparatelysegmented,the
fibroglandulartissuecanbeidentifiedbysubtractingthosetissuesfromthewholebreast
mask.Inthiswork,wefurtherappliedtheGaussianMixtureModeldescribedin[53]to
segmentbothfatandfibroglandulartissuesintosub‐categories(low,median,andhigh),
allowingtoincorporatetissueheterogeneity,asreportedin[54].
2.3.2.TumourSegmentation
Accuratetumoursegmentationisofutmostimportancefortumourevaluationand
extractionofitscharacteristics.Thistaskisverychallengingasbreastlesionswidelyvary
inshapeandintensitydistribution.Strategiesbasedondataclustering,particularlyunsu‐
pervisedclusteringmethodssuchasK‐meansandFuzzyC‐means,havebeenusedfor
breasttumoursegmentationusingMRIexams[55–58].Suchmethodsgroupasetofdata
objectsofthewholeimage/volumeintoclustersbymaximizingintraclasssimilarityand
minimizinginterclasssimilarity.TheproposedapproachesusingK‐meansin[55,56]and
FuzzyC‐meansin[57,58]outperformedstandardtechniquesandshowedhighaccuracy
insegmentingbreasttumours.Asemi‐automaticalgorithmusingamarker‐controlledwa‐
tershedmethodproposedin[59]wasprovenmoreefficientinconnectingdisjointareasin
lesionscomparedtoclassicalK‐meansclusteringandGaussianMixtureModelclustering
[60].Thakranetal.[61]developedanautomaticmethodologyforbreasttumoursegmen‐
tationbasedonOtsuthresholding.
Allpreviousmethodologiesrelyonintensityvaluesofthewholeimagetoobtainthe
regionofinterest(tumour),astheyweredevelopedundertheassumptionthat,generally,
biologicaltissuesarefairlywellseparatedwithinagrayscaleimage.However,inthecase
ofheterogeneousstructurescomprisingawiderangeofintensityvalues,suchashetero‐
geneousmalignanttumours,thesemethodscannotincludeallvoxelscomprisingthetu‐
mourwithinthesamecluster,leadingtopoorsegmentationofthetumourvolume.
Inthiswork,weuseda3Dregiongrowingalgorithm,basedon[62],toaddresstu‐
mourswithvoxelsspreadingoverawiderangeofintensityvalues.Aspreviouslymen‐
tionedinStep1,thismethodusesaseedtogrowtheregiontoadjacentpointsbasedon
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anintensitythresholdcriterion.Suchcriteriondefinestheintensityrangeofthevoxelsin
thegrowingregionastheseedintensityvalue±threshold.
InSUB‐DCE‐fl3Dimages,tumourregionsgenerallypresenthigherintensitieswhen
comparedtoneighbouringtissues,soweusedthehighestintensityvoxelastheseedin
theregiongrowingalgorithm.Forthat,onemustselectaslice(pertumour)inwhichthe
algorithmshouldchoosetheseedvoxel.Although,mostofthetime,thehighestintensity
voxelcorrespondstothetumour,itispossiblethatinsomecasesthiswillnotbetrue—a
manualassignmentmayberequired.Forthechoiceofthethresholdvalue,oneshould
confirmthattheseedvalueminusthethresholdcorrespondstotheminimumintensity
valueofthetumourvoxels;henceonlyvoxelsbelongingtothetumourwillbeincluded
inthegrowingregion.Experimentsusingourdatasetshowedthatalowerboundof
thresholddefinedbythemeanminusthreetimesthestandarddeviationofallbodyvoxels
providedgoodresults.
Oftentimes,the3Dregiongrowingalgorithmwasunabletosegmentthetumourex‐
clusively,especiallyforheterogenoustumourswithawiderangeofvoxels’intensities.
Instead,otherbodytissueswereincludedinthegrowingregion.Hence,inordertoseg‐
mentonlythetumour,theHoshen‐Kopelmanalgorithmwasapplied[63]toretrievethe
largestconnectedcomponent.Aschematicofthemethodologyusedforbreasttumour
segmentationisshowninFigure2.
Figure2.Simplifiedschematicsoftheprocessingstepstoobtainthemaskofthebreasttumours.
2.4.DielectricPropertiesEstimation
Weperformedthedielectricpropertiesestimationbyassigningthevoxelintensities
ofthedifferenttissuesofthebreast(fat,fibroglandular,skin,muscle,andtumour),inthe
T1‐wDixon‐Iimage,tothecorrespondingdielectricpropertiesreportedintheliterature
viapiecewise‐linearmapping[21,64,65].
Relativepermittivityandconductivitycurvesofsingle‐poleDebyemodelhavebeen
described[21,64,65]foreachtissuetypeofthebreast(fat,fibroglandular,tumour,skin,
andmuscle).Inaddition,wefurtherseparatedthefatandfibroglandulartissuesintosix
categorieswiththecorrespondingdielectricpropertycurve:fibroglandular‐low,fibro‐
glandular‐medium,fibroglandular‐high,fat‐low,fat‐medium,andfat‐high.Toobtainan
appropriatemappingbetweenthevoxelintensitiesandthecorrespondingdielectric
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properties,wefittedatwo‐componentGaussianMixtureModeltothehistogramofthe
pre‐processedimages,adaptedfrom[21].Thehistogramcontainsthecontributionoffat
andfibroglandulartissuesasdefinedinEquation(4),forfat,andEquation(5),forfibro‐
glandulartissue,bytheGaussianMixtureModelmethod,
𝛾 𝜇,𝛿(4)
𝛾 𝜇,𝛿, (5)
where𝜇and𝛿representthemeanandvarianceofeachdistribution.Theremaining
parametersaredefinedinTable1.Skinalsohasspecificdielectriccurvesreportedinthe
literature[64,65].
Table1.Linearpiecewisemappingbetweenthevoxelintensitiesandthecorrespondingdielectric
propertycurveforthehistogramofanexamwherethecontributionofthegaussiancurvesoffat
andfibroglandulartissueareseparated.
DielectricPropertyCurvesVoxelIntensity
Minimum0
Fibroglandular_low𝜇 𝜎
Fibroglandular_median𝜇
Fibroglandular_high𝜇 𝜎
Fat_low𝜇 𝜎
Fat_median𝜇
Fat_high𝜇 𝜎
MaximumMaximumintensityoftheimage
WhenahistogramdoesnotshowsufficientseparationbetweentheGaussiancurves
correspondingtothecontributionsofthefatandfibroglandulartissues,weusedthepa‐
rametersinTable2,whereδisauser‐definedpositivescalar[21].Inourwork,wedefine
𝛿asinEquation(6),
𝛿𝐹𝑎𝑡_𝑙𝑜𝑤 𝐹𝑖𝑏𝑟𝑜𝑔𝑙𝑎𝑛𝑑𝑢𝑙𝑎𝑟_ℎ𝑖𝑔ℎ
2(6)
Table2.Linearpiecewisemappingbetweenthevoxelintensitiesandthecorrespondingdielectric
propertycurveforahistogramofanexamwherethefattissueispredominantoverthefibroglan‐
dulartissueandthecontributionsofthegaussiancurvesoffatandfibroglandulartissuesarenot
clearlyseparated.
DielectricPropertyCurvesVoxelIntensity
Minimum0
Fibroglandular_low2𝜇
𝑀
Fibroglandular_median𝜇
Fibroglandular_high𝑀 𝜇
𝜎
𝛿
Fat_low𝜇 𝜎
Fat_median𝜇
Fat_high𝜇 𝜎
MaximumMaximumintensityoftheimage
Foreachsegmentedtissuetype,theminimumandthemaximumvalueoftheinten‐
sityvoxelsoftheMRIexamareassociatedwiththelower‐andupper‐boundcurveofeach
tissue,respectively.Ateachfrequency,theremainingvoxelsarelinearlymappedtoa
valuebetweenthecurvesofthattissueusingapiecewiselinearinterpolation.
Table3containssingle‐poleDebyeparameters(permittivityathighfrequency—𝜀,
thedifferencebetweenstaticpermittivityandpermittivityathighfrequency— ∆𝜀 ,
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relaxationtime—𝜏,andstaticconductivity—𝜎)ofthedielectriccurvesforeachtissuetype
[64,65].Asreportedin[64,65],Debyeparametersareonlyvalidforfrequenciesbetween
3and10GHz.Weassumedthatthebreast/chestwallboundarywascomposedofmuscle.
Table3.Single‐poleDebyeparametersforthedielectricpropertycurvesforeachtissuetype[64].
𝜺∆𝜺𝝉𝒑𝒔𝝈𝒔𝑺/𝒎
Minimum2.3090.09213.000.005
Fibroglandular_low12.9924.4013.000.397
Fibroglandular_median13.8135.5513.000.738
Fibroglandular_high14.2040.4913.000.824
Fat_low2.8481.10413.000.005
Fat_median3.1161.59213.000.050
Fat_high3.9873.54513.000.080
Maximum23.2046.0513.001.306
Skin15.9323.8313.000.831
Muscle21.6633.2413.000.886
AccordingtoLazebniketal.[15],thedielectricpropertiesofbenigntissuesaresimilar
tothepropertiesoflower‐adipose‐contentnormalbreasttissues,hence,weusedthesame
linearinterpolationobtainedfromthewholeimagetoestimatethedielectricpropertiesof
benigntissues.Regardingmalignantbreasttumours,the1‐poleCole‐Coleparametersof
thedielectricpropertycurvesarereported[15].Twocurveslimitingthelower‐andupper‐
boundswereobtainedfromparametersofthe25thand75thpercentilescurves,respec‐
tively.The1‐poleCole‐Coleparametersarevalidforafrequencyrangefrom0.5–20GHz.
Inordertocomparethedielectricpropertiesoftumourstootherbreasttissues,we
convertedthe1‐poleCole‐ColemodeltotheDebyemodel.Fromthereporteddielectric
propertycurves,wegeneratedaDebyemodelfittedtothedatapointsandextractedthe
Debyeparametersformalignanttumours.ThefittedparametersaredetailedinTable4.
Table4.FittedDebyeparametersforthedielectricpropertycurvesofmalignantbreasttumours.
Percentile𝜺∆𝜺𝝉𝒑𝒔𝝈𝒔𝑺/𝒎
25th12.933.913.01.38
75th 14.647.213.01.60
Figure3representsthebehaviourofthedielectricproperties(relativepermittivity
andconductivity)asafunctionoffrequencyfornon‐tumoroustissuetypes.Figure4rep‐
resentsthedielectricpropertiesofmalignanttumourtissuesfordifferentfrequencies.
2.5.CreationofBreastRegionModels
WederivedanthropomorphicbreastcomputationalmodelsfromMRIexams.Such
modelsaretheresultoftheapplicationoftheproposedpre‐processingandsegmentation
pipelines,detailedabove.Thesemodelsincludeskin,fat,fibroglandular,andmuscletissues,
aswellasbenignandmalignanttumours,segmentedfromtheMRimages.Microwave‐
frequencypropertiesofbreasttissuesat3,6,and9GHzarealsoavailableinourmodels.
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(a)
(b)
Figure3.Relativepermittivity(a)andeffectiveconductivity(b)curvesofnon‐tumoroustissues
adaptedfrom[64,65]forthefrequencyrangeof3–10GHz.
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(a)
(b)
Figure4.Relativepermittivity(a)andeffectiveconductivity(b)curvesobtainedfromthefittedDe‐
byeparametersshowninTable4.
3.Results
Thissectionshowstheresultsofthedevelopedsegmentationpipelineappliedto
breastMRIexamsforbreasttissuesegmentationandtheestimationofthedielectricprop‐
ertiesofthesegmentedtissuesfromMRIexams.Inthispaper,wedepictedtheresultsof
thestepspreviouslydescribedfortwoexams(onewithabenigntumourandtheother
withanextremelyheterogeneousmalignanttumour).Bothmodelsincludethedielectric
propertiesestimatedfor6GHz.Additionally,therepositorycontainsmorebreastmodels,
includingbenignandmalignanttumours,withtheestimateddielectricpropertiesalsofor
3GHzand9GHz.
3.1.Pre‐ProcessingPipeline
3.1.1.Registration
ThetransverseSUB‐DCE‐fl3Dsequenceusedfortumoursegmentationwasinitially
registeredtothecoronalT1‐wDixonsequence.Figure5showstheresultingimagesofthe
alignmentofthetwoimagesinT1‐wDixonspatialreference.
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(a)(b)
Figure5.ResultingimagesfromtheregistrationofthetransverseSUB‐DCE‐fl3Dimage(moving
image)tothecoronalT1‐wDixon‐Wimage(staticimage),inabreastexamwitha(a)benignand
(b)amalignanttumour.
3.1.2.BiasFieldCorrection
ThecorrectionofthebiasfieldisacommonsteptoT1‐wDixon‐I,T1‐wDixon‐W,
andT1‐wDixon‐Fimages,aswellasSUB‐DCE‐fl3Dimages.Figure6illustrates(a,d)the
originalT1‐wDixon‐Iimages,(b,e)thebiasfieldpresentineachimage,and(c,f)thecor‐
rectedimages,foranexamwithabenigntumour(top)andamalignanttumour(bottom).
(a)(b)(c)
(d)(e)(f)
Figure6.BiasfieldcorrectionperformedonabreastMRIexamwithabenigntumour(top)andamalignanttumour
(bottom).Figures(a,d)showoneslicefromeachexambeforetheapplicationofthebiasfieldcorrectionfilter.Figures(b,e)
showtheinhomogeneitybetweenthevoxelintensities.Redregionsrepresentareaswheretheinhomogeneitybetween
voxelintensitiesislarger.Figures(c,f)showthesameslicesaftercorrectionofthebiasfield.
3.1.3.ImageFiltering
Theapplicationofamedianfiltertothepre‐processedimage,withatumourlarger
than1cm,smoothstheedges,facilitatingthebreasttumoursegmentationprocess.Figure
7depictstheapplicationofamedianfilterforedgesmoothing.
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(a)(b)
Figure7.Medianfilterforedgesmoothing:(a)imagepre‐filteringand(b)imagepost‐filtering.
3.2.ImageSegmentation
3.2.1.BreastRegion
Step1:Fatmask+removaloforgansinsidethethoraciccavity
Figure8showsarepresentationofthenumberofvoxelswithanintensityhigherthan
themeanintensityoftheT1‐wDixon‐Wimagecountedatthecentreofthebody,starting
outsidethepatient’sbody,andfinishingatthepatient’sspine.Thecoordinatesofthester‐
numcorrespondtotheouter‐mosthighlightedvoxel.Thecoordinatesofthecentreofthe
bodyareselected,andthenwesweepthecoordinatealongthecoronalplane.Thecoordi‐
nateforthecoronalplanethatindicatesthefirststernumvoxelisidentifiedinFigure8by
adarkbluecircle.
(a)(b)
Figure8.Thenumberofvoxelswithintensityhigherthanthemeanintensityoftheinputimage
(T1‐wDixon‐Wimage)wascountedtodetectthecoordinatesofthesternumin(a)theexamwith
thebenigntumour,andin(b)theexamwiththemalignanttumour.
Figure9showstheresultoftheregiongrowingalgorithmappliedtotheT1‐wDixon‐
Fimages.Forbothexams,theregiongrowingalgorithmseparatesthefattissueofthe
breastregionfromthefattissueinthethoraciccavity,andthewatershedtransformfrom
markerswasnotnecessary.
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(a)(b)
Figure9.Outputoftheregiongrowingalgorithmappliedto(a)theexamwiththebenigntumour
andto(b)theexamwiththemalignanttumour.
Step2:Skin+Fibroglandular+Fatmask
InFigure10,wedepicttheseveralstepsfollowedtoobtainabreastmaskwithfat,
skin,andfibroglandulartissuesdescribedinStep2fortheexamwiththemalignanttu‐
mour.Figure10arepresentsthefatmaskresultingfromStep1.Afterdilatingthefatmask
obtainedfromregiongrowing(Figure10b)andwhitingouttheanteriorsideofthebody
(Figure10c),wemultipliedtheresultingmaskandtheT1‐wDixon‐Wimage(Figure10d).
Afterthresholding,weobtainamaskofthebreastregion(Figure10e).
(a)(b)
(c)(d)
(e)
Figure10.Step‐by‐stepimagesobtainedinStep2.(a)Maskrepresentingthefattissueobtainedfrom
theregiongrowingalgorithm.(b)Maskobtainedfromregiongrowing,dilatedbyastructuring
elementofradius3,toincludetheskin.(c)Dilatedmaskwiththeanteriorregionofthebodywhited
out.(d)Imageobtainedbymultiplyingtheimagein(c)andtheoriginalT1‐wDixon‐Wimage.(e)
Resultingmaskafterthresholdingtheimagerepresentedin(d).
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Figure11showsthebreastmaskobtainedafterconcludingStep2fortheexamwith
thebenigntumour.
Figure11.MaskobtainedafterStep2ofourmethodologyfortheexamwiththebenigntumour.
Step3:Maskevaluation
Fortheexamwiththebenigntumour,themean‐squarederrorvaluebetweenthe
originalmaskanditsflippedimage,is4.8%.Fortheexamwiththemalignanttumour,the
mean‐squarederrorvalueis11.1%.AsobservedinFigure11,themaskfortheexamwith
thebenigntumouriscomplete,andthemaskfortheexamwiththemalignanttumour
(Figure10e)hasaholewherethetumourinvadesthepectoralismuscle.
Step4:Maskforanexamwithaninvasivetumour(optional)
Tocompletethemaskfortheexamwiththemalignanttumour,themethoddescribed
inStep4wasfollowed.Figure12ashowsthesuperimpositionofthemaskobtainedfrom
Step2anditsflippedimage.Figure12bcorrespondstothebinarisedT1‐wDixon‐Iimage
usingthemeanvoxelsintensityasthreshold.Figure12ccorrespondstotheresultingout‐
putofStep4.
(a)(b)(c)
Figure12.(a)SuperimpositionoftheoriginalmaskfromStep2anditsflippedimage.(b)BinarisedT1‐wDixon‐Iimage
usingthemeanvoxelsintensityasthreshold.(c)Resultingmaskoftheintersectionof(a,b),aftertheapplicationofSim‐
pleITK’sBinaryFillholeImageFilter.
Step5:Segmentationofskinandbreast/chestwallboundary
Figure13shows,indetail,thestepsfollowedtoobtaintheskinandbreast/chestwall
boundariesfortheexamwiththemalignanttumour.Afterscanningthevoxelsinthe
breastcontour(Figure13a),weobtaineda1‐voxel‐thickskincontour(Figure13b).An
artefactcorrespondingtothebreast/chestwallboundaryappearsinFigure13bsincepart
oftheskinintheoriginalT1‐wDixon‐Wimagewasnotvisible.The1‐voxel‐thickchest
wallboundarycontourisshowninFigure13c.Thefinalskincontour,representedinFig‐
ure13d,correspondstothelargestconnectedcomponentofthesubtractionbetweenFig‐
ure13a,c.Thefinalcontourofthebreast/chestwallboundary,inFigure13e,corresponds
tothesubtractionbetweenFigure13a,d.
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(a)(b)
(c)(d)
(e)
Figure13.(a)Contourofthebreastmask.(b)Skincontour(1‐voxel‐thick)afterscanningthevoxelsof
thecontourbreastmaskfromlefttoright,toptobottomandrighttoleft.(c)Breast/chestwallboundary
contour(1‐voxel‐thick)obtainedaftersubtractingthecontourrepresentedin(b)fromthecontourrep‐
resentedin(a).Final(d)skinand(e)breast/chestwallboundarycontoursobtainedafterStep5.
Theskinandbreast/chestwallboundariesobtainedafterfollowingStep5arepre‐
sentedinFigure14,fortheexamwiththemalignanttumour.
(a)(b)
Figure14.(a)Skincontourobtainedfortheexamwiththemalignanttumour,andcorresponding
(b)breast/chestwallboundaryobtainedafterfollowingStep5.
InFigure15,theskinandbreast/chestwallboundariesobtainedafterfollowingStep
5arepresentedfortheexamwiththebenigntumour.
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(a)(b)
Figure15.(a)Skincontourfortheexamwiththebenigntumour,andthecorresponding(b)
breast/chestwallboundaryobtainedafterfollowingStep5.
Step6:Skinevaluation
Figure16showstheoutputofStep6fortheexamswiththebenignandthemalignant
tumours.
(a)(b)
Figure16.Skinmaskobtainedafterstep6for(a)theexamwiththebenigntumour,andfor(b)the
examwiththemalignanttumour.
Figure17showsthefinallabelmapobtainedfromthesegmentationpipeline,aspre‐
viouslydescribed.Thelabelsforeachcomponentareasfollows:0forthebackground,1
fortheforeground(includingfatandfibroglandulartissues),−2fortheskinand−1forthe
chest/breastwallboundary.
(a)(b)
Figure17.Labelmapobtainedfromtheprocessingpipeline.Backgroundislabelledas0,fore‐
ground,whichincludesfatandfibroglandulartissues,arelabelledas1,theskinislabelledas−2
andthebreast/chestwallboundaryislabelledas−1.Labelmapsfor(a)theexamwiththebenign
tumour,andfor(b)theexamwiththemalignanttumour.
3.2.2.TumourSegmentation
Figure18showsthelocationoftheseedmarkedwitharedcrossfor(a)thebenign
tumourand(b)themalignanttumour,whichisthestartingpointofthe3Dregiongrow‐
ingalgorithms.Thechoiceoftheseedwasautomaticfor(a)andmanualfor(b).
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(a)(b)
Figure18.Locationofthe3Dregiongrowingalgorithmseedmarkedwitharedcrossin(a)theexam
withthebenigntumourand(b)theexamwiththemalignanttumour.
Figure19illustratestheoutputoftheregiongrowingalgorithmfortheexamwith
thebenigntumour,inthethreeanatomicalplanes.
(a)(b)(c)
(d)(e)(f)
Figure19.Outputoftheregiongrowingalgorithmfortheexamwiththebenigntumour:(a–c)correspondtotransverse,
coronal,andsagittalplanesofthepre‐processedSUB‐DCE‐fl3Dimagefortumoursegmentation,respectively;(d–f),illus‐
tratethesuperimpositionofthetumourmask(yellow)tothepre‐processedSUB‐DCE‐fl3Dimageinthetransverse,coro‐
nal,andsagittalplanes.
Figure20illustratestheoutputoftheregiongrowingalgorithmfortheexamwith
themalignanttumour,inthethreeanatomicalplanes.
(a)(b)(c)
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(d)(e)(f)
Figure20.Outputoftheregiongrowingalgorithmfortheexamwiththemalignanttumour:(a–c)correspondtotrans‐
verse,coronal,andsagittalplanesofthepre‐processedSUB‐DCE‐fl3Dimagefortumoursegmentation,respectively;(d–
f)illustratethesuperimpositionofthetumourmask(yellow)tothepre‐processedSUB‐DCE‐fl3Dimageinthetransverse,
coronal,andsagittalplanes.
Figure21illustratestheoutputoftheHoshen‐Kopelmanalgorithmplusmanualcor‐
rectionofthetumourmask,inthethreeanatomicalplanes.Hoshen‐Kopelmanisolates
tumoursbyremovingregionsthatdonotbelongtothetumourtissue.However,forex‐
tremelyheterogenouscasessuchastheonepresentedinthispaper,theHoshen‐Kopel‐
manalgorithmwasnotenoughtoisolatethetumoursincenearbybloodvesselsarepre‐
sentincontiguousregions;therefore,manualcorrectionwasrequiredtoobtainabinary
maskofthetumour.
(a)(b)(c)
Figure21.OutputoftheHoshen‐Kopelmanalgorithmplusmanualcorrectionofthetumourmask:(a–c)correspondto
transverse,coronal,andsagittalplanes.
Thefinallabelmaps,includingthetumoursegmentationareshowninFigure22.
Tumourlabelcorrespondsto−3.
(a)(b)
Figure22.Finallabelmapfor(a)theexamwiththebenigntumourandfor(b)theexamwiththemalignanttumour.
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3.3.DielectricProperties
Thehistogramsofthebreastdataofthefatandfibroglandulartissues(labelledas1
inthelabelmaps)forbothexamsarerepresentedinFigure23.Forthebenigntumour,it
ispossibletoseparatefatandfibroglandulartissuesthroughthehistogram(Figure23a)
usingparametersdescribedinTable1.Thevoxelintensitiescorrespondingtofatandfi‐
broglandulartissuescanbeseparatedinthehistogramoftheexamwiththemalignant
tumour(Figure23b)usingparametersdescribedinTable2.Table5includesalistofthe
parametersextractedfromtheGaussianMixtureModelusedtoobtainthepiecewise‐lin‐
earmappingcurvebetweentheMRIvoxelintensityandthedielectricproperties.
(a)(b)
Figure23.HistogramofMRIvoxelintensitiesfor(a)theexamwiththebenigntumourandfor(b)theexamwiththe
malignanttumour.
Table5.ParametersoftheGaussianMixtureModelfortheexamwiththebenigntumourandtheexamwiththemalignant
tumour(roundedtothenearestunit).
ExamwiththeBenignTumourExamwiththeMalignantTumour
VoxelIntensity
EquationsVoxelIntensityVoxelIntensity
EquationsVoxelIntensity
Minimum0000
Fibroglandular_low𝜇
𝜎
552𝜇
𝑀
104
Fibroglandular_median𝜇
80𝜇
115
Fibroglandular_high𝜇
𝜎
104𝑀
𝜇
𝜎
𝛿127
Fat_low𝜇
𝜎
113𝜇
𝛿
134
Fat_median𝜇
129𝜇
143
Fat_high𝜇
𝜎
144𝜇
𝛿
152
MaximumMaximumintensityof
theimage221Maximumintensityof
theimage255
Anexampleofapiecewise‐linearmapbetweentherelativepermittivity/effective
conductivityatthefrequency6GHzandtheMRIvoxelintensityfortheexamwiththe
benigntumourisrepresentedinFigure24.
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(a)(b)
Figure24.Exampleofthepiecewiselinearmappingobtainedat6GHz(a)oftherelativepermittivity
and(b)effectiveconductivityfortheexamwiththebenigntumour.
Figures25and26showthedielectricpropertymapsfortherelativepermittivityand
effectiveconductivity(S/m)at6GHzfortheexamswiththebenignandmalignanttu‐
mours,respectively.Wewouldliketonotethedifferentcolourscalesinbothfigures;for
thebenigntumour,therelativepermittivityandconductivityvaluesvarybetween0and
60.3,and0and7.37(S/m),respectively;forthemalignanttumour,therelativepermittivity
andconductivityvaluesvarybetween0and60.3,and0and7.82(S/m),respectively.
(a)(b)
Figure25.Mapofthedielectricpropertiesfortheexamwiththebenigntumour:(a)relativepermittivityat6GHzand(b)
effectiveconductivity(S/m)at6GHz.
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(a)(b)
Figure26.Mapofthedielectricpropertiesfortheexamwiththemalignanttumour:(a)relativepermittivityat6GHzand
(b)effectiveconductivity(S/m)at6GHz.
3.4.BreastRegionModelsRepository
TherepositoryisavailablefordownloadinGitHub(https://github.com/acpeli‐
cano/breast_models_repository,createdon27October2021).Initially,itonlyincluded
twobreastmodels,asportrayedinthispaper:oneofabenigninfra‐centimetrictumourof
roundedshape;andtheotherofamalignantinvasivetumourofirregularshape,with
approximately8cmalongitsmajoraxis,andextremelyheterogenousregardingvoxels
intensities.Themodelsincludethedielectricpropertiesofthebreasttissuesestimatedat
frequenciesof3,6,and9GHz.Modelsfromthefulldatasetcollectedfrompatients,as
describedinSection2.1,willbeaddedastheprocessingofeachiscompleted.
4.DiscussionandConclusions
Wepresentedanimageprocessingpipelinetosegmenthealthybreasttissuesand
tumoursinspiredbytheavailableliterature.Mostmodelsforthebreastregionarebased
onclusteringalgorithmsortheidentificationofair/breastandbreast/chestwallbounda‐
ries.However,thefattissueinsidethethoraciccavity,withnoclearseparationfromother
tissuesinsidethebreast,hindersthecorrectidentificationofthebreastregion.Addition‐
ally,theidentificationofthebreast/chestwallboundaryisespeciallydifficultinthepres‐
enceofaheterogeneousmalignanttumourthatisinvadingthepectoralismuscle,asisthe
casepresentedinthispaper.
Theproposedsegmentationpipelinecanseparatethefattissuesinthebreastand
insidethethoraciccavitybyapplyingtheregiongrowingalgorithm.Inaddition,wesug‐
gestedusingthewatershedtransformfrommarkerswhentheregiongrowingalgorithm
failstoprovideagoodseparationbetweenbothfattissues.Ifthereisnopriorknowledge
ofwhetheraninvasivetumourispresentintheMRIimage,andtoaccountforthearea
whereitinvadesthepectoralismuscle,weproposedamethodthatautomaticallyevalu‐
atesthebreastmaskafterregiongrowing/watershedtransformandfillsthatarea.
Wedevelopedasemi‐automaticsegmentationpipelineparticularlyrobustwhenseg‐
mentingbreasttumourswithavaryinglevelofheterogeneityregardingvoxelintensity.
Theproposedpipelineisflexiblesinceitdoesnotoperateundertheassumptionthat,gen‐
erally,biologicaltissuesarewellseparatedwithinagrayscaleimage.Forthetumourseg‐
mentationpipeline,weuseda3Dregiongrowingalgorithm.Althoughnotfullyauto‐
matic,itsuggestsusingthehighestintensitypointinaslicecontainingthetumourasthe
seedpointandusing,asthelowerthreshold,themeanminusthreetimesthestandard
deviationofallbodyvoxelsintensityvalues.Thismethodologyprovidedbetterresults
Sensors2021,21,826525of27
whencomparedtowidelyusedsegmentationmethods,suchasK‐means.TheHoshen‐
Kopelmanalgorithmeliminatedvoxelsincludedinthegrowingregionofthetumourthat
didnotbelongtothattissue.Forthemalignanttumourpresentedinthispaper,wealso
performedmanualcorrectionofthetumourmask.
Weestimatedthedielectricpropertiesforthemalignanttumourtissuefromthere‐
portedDebyeparameters.Forthebenigntumourtissue,literaturereportsthatthedielec‐
tricpropertiesofthesetissuesaresimilartothepropertiesoflower‐adipose‐contentnor‐
malbreasttissues;hence,weestimatedthedielectricpropertiesusinginterpolationbe‐
tweenthecurvesofhealthybreasttissues.
Inthispaper,wepresentedtworealisticbreastmodelswhereskin,muscle,fat,fibro‐
glandular,andtumourtissues(malignantandbenign)areidentified.Inaddition,the
modelsinourpaperincludethedielectricpropertiescalculatedforthefrequencyof6
GHz.Anatomicallyrealisticbreastandtumour(benignandmalignant)models,portray‐
ingtherealisticshapesofthesetissues,areavailabletoallwithestimateddielectricprop‐
ertiesforfrequenciesof3,6,and9GHzinapublicrepository.
AuthorContributions:Conceptualization,R.C.C.andE.P.;methodology,A.C.P.,M.C.T.G.and
D.M.G.;validation,A.C.P.,M.C.T.G.andD.M.G.;formalanalysis,A.C.P.,M.C.T.G.,R.C.C.andE.P.;
investigation,A.C.P.,M.C.T.G.andD.M.G.;resources,T.C.andM.L.O.;datacuration,A.C.P.and
M.C.T.G.;writing—originaldraftpreparation,A.C.P.andM.C.T.G.;writing—reviewandediting,
allauthors;supervision,R.C.C.,E.P.,N.A.M.A.;projectadministration,R.C.C.;fundingacquisition,
R.C.C.,E.P.Allauthorshavereadandagreedtothepublishedversionofthemanuscript.
Funding:ThisresearchwasfundedbyFundaçãoparaaCiênciaeTecnologia(FCT)underthefel‐
lowshipUI/BD/150762/2020and2021.07228.BD(grantawardedonthe21October2021),FCT/MET
(PIDDAC)undertheStrategicProgramUIDB/00645/2020andUIDP/00645/2020,andunderCon‐
tractsno.PTDC/FIS‐MAC/28146/2017(LISBOA‐01‐0145‐FEDER‐028146),UIDB/00618/2020,and
UIDP/00618/2020.
InstitutionalReviewBoardStatement:ThestudywasapprovedbytheComissãodeÉticaparaaSaúde
ofHospitaldaLuz(referencesCES/44/2019/ME(19/09/2019)andCES/34/2020/ME(6November2020)).
InformedConsentStatement:Informedconsentwasobtainedfromallsubjectsinvolvedinthestudy.
DataAvailabilityStatement:Anatomicallyrealisticbreastandtumour(benignandmalignant)
modelswiththeestimateddielectricpropertiesatfrequenciesof3,6and9GHzareavailableonline
athttps://github.com/acpelicano/breast_models_repository(createdon27October2021).
ConflictsofInterest:Theauthorsdeclarenoconflictofinterest.
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