Vortical Features for Myocardial Rotation Assessment in Hypertrophic Cardiomyopathy using Cardiac Tagged Magnetic Resonance

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JID:MEDIMA [m5G;March15,2018;18:55]

Highlights

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ContentslistsavailableatScienceDirect

Medical

Image

Analysis

journalhomepage:www.elsevier.com/locate/media

Graphical

Abstract

MedicalImageAnalysisxxx(2018)xxx–xxx

Vortical features for myocardial rotation assessment in hypertrophic cardiomyopathy using cardiac tagged magnetic resonance

SantiagoSanz-Estébaneza,∗_,_Lucilio_{Cordero-Grande}b_,_Teresa_Sevillac_,

AnaRevilla-Orodeac_,_Rodrigo_de_Luis-Garcíaa_,_Marcos_{Martín-Fernández}a_,

CarlosAlberola-Lópeza

a_Laboratorio_de_Procesado_de_Imagen,_Department_of_Teoría_de_la_Señal_y ComunicacioneseIngenieríaTelemática,ETSIT,UniversidaddeValladolid,Campus MiguelDelibess.n.,Valladolid40011,Spain

b_Centre_for_the_Developing_Brain_and_Department_of_Biomedical_Engineering,_Division ofImagingScienceandBiomedicalEngineering,King’sCollegeLondon,StThomas’ Hospital,LondonSE17EH,U.K

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MedicalImageAnalysisxxx(2018)xxx–xxx

ContentslistsavailableatScienceDirect

Medical

Image

Analysis

journalhomepage:www.elsevier.com/locate/media

Vortical

features

for

myocardial

rotation

assessment

in

hypertrophic

cardiomyopathy

using

cardiac

tagged

magnetic

resonance

Santiago

Sanz-Estébanez

a,∗

_,

_Lucilio

_{Cordero-Grande}

b

_,

_Teresa

_Sevilla

c

_,

_Ana

_{Revilla-Orodea}

c

_,

Q1

Rodrigo

de

Luis-García

a

_,

_Marcos

_{Martín-Fernández}

a

_,

_Carlos

_{Alberola-López}

a

a_Laboratorio_de_Procesado_de_Imagen,_Department_of_Teoría_de_la_Señal_y_{Comunicaciones}_e_Ingeniería_Telemática,_ETSIT,_Universidad_de_Valladolid,_Campus MiguelDelibess.n.,Valladolid40011,Spain

b_Centre_for_the_Developing_Brain_and_Department_of_Biomedical_Engineering,_Division_of_Imaging_Science_and_Biomedical_Engineering,_King’s_College London,StThomas’Hospital,LondonSE17EH,U.K

c_Unidad_de_Imagen_Cardiaca,_Hospital_Clínico_{Universitario}_de_Valladolid,_CIBER_de_enfermedades_{cardiovasculares}_(CIBERCV),_Valladolid_47005,_Spain

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received6June2017 Revised10January2018 Accepted14March2018 Availableonlinexxx

Keywords: Myocardialrotation Taggedmagneticresonance Vorticalfeatures

Hypertrophiccardiomyopathy

a

b

s

t

r

a

c

t

Leftventricularrotationalmotionisafeatureofnormalanddiseasedcardiacfunction.However,classical torsionandtwistmeasuresrelyonthedefinitionofarotationalaxiswhichmaynotexist.Thispaper re-viewsglobalandlocalrotationdescriptorsofmyocardialmotionandintroducesnewcurl-based(vortical) featuresbuiltfromtensorialmagnitudes,intendedtoprovidebettercomprehensionaboutfibrotictissue characteristicsmechanical properties.Fifty-sixcardiomyopathypatientsand twenty-twohealthy volun-teershavebeenstudiedusingtaggedmagneticresonancebymeansofharmonicphaseanalysis.Rotation descriptorsarebuilt,withnoassumptionaboutaregulargeometricalmodel,fromdifferentapproaches. Theextractedvorticalfeatureshavebeentestedbymeansofasequentialcardiomyopathyclassification procedure;theyhaveprovenuseful fortheregionalcharacterizationoftheleftventricular functionby showinggreatseparabilitynot onlybetweenpathologic andhealthypatients butalso, andspecifically, betweenheterogeneousphenotypeswithincardiomyopathies.

1. Introduction

1

Hypertrophic cardiomyopathy (HCM) (Maron et al., 2014) is 2

a relatively common heart muscle disease with a heteroge-3

neousphenotypicexpressionthatoccasionallyoverlapswithother 4

pathologiesthatalsopresentleftventricularhypertrophy. Differen-5

tiatingtheunderlyingetiology oftheventricularhypertrophy isa 6

frequentclinicalproblemwithrelevantimplicationssinceeach eti-7

ologyneedsaspeciﬁcmanagement andpresentsadifferent prog-8

nosis.HCMischaracterizedbyahypertrophiedandnondilatedleft 9

ventricle(LV)(Baron,2008),oftenwithanasymmetricalwall thick-10

ness distribution. HCMoccurs inthe presence ofmyocyte hyper-11

trophy andinterstitial and replacement ﬁbrosis, which causethe 12

walls of the ventricles to thicken (Maron et al., 1992) and a re-13

duction on the cavity volume is usually observed. This thicken-14

∗ _{Corresponding}_author.

E-mail addresses: [email protected] (S. Sanz-Estébanez),

[email protected] (L. Cordero-Grande), [email protected] (R. de Luis-García), [email protected] (M. Martín-Fernández), [email protected] (C. Alberola-López).

URL:http://www.lpi.tel.uva.es/ssanest(S.Sanz-Estébanez)

ingmayblockbloodﬂowoutoftheventricle.Therefore,themain 15 features of a HCM heart summarize in increased LV mass and 16 thickenedwalls,especiallyintheinterventricularseptum(Urbano- 17

Moral etal., 2014). Theseabnormalities lead toalteredforces re- 18 vealingasigniﬁcant reductionin thediagonalcomponents ofthe 19 strain(Saltijeraletal.,2010).Previousstudieshaveshownthatre- 20 gionalLV dysfunctions predate over themorphologic changes re- 21 latedwiththephenotypicexpressionofhypertrophyandobstruc- 22

tion(Dhillonetal.,2014). 23

As previously stated, etiological factors are of great impor- 24 tanceinthecardiovascular diseasedetection(Maronetal.,2006). 25 Globalindices,suchasthegloballongitudinalstrain(Shimonetal., 26

2000), havebeen employed for cardiovascular disease identifica- 27 tion, reporting noticeable prognostic value; however, local mea- 28 surementscould providemore insight to the behavior offibrotic 29 tissue (Piella etal., 2010). Inthis direction, it hasbeen hypothe- 30 sizedthatthepresenceofgreatermyocardialtwistmaybeassoci- 31 atedwithagreaterdegreeofmyocardialfibrosisinHCMpatients. 32 Consequently,assessmentofLVrotationmechanicsasacharacter- 33 isticofcardiac functionmayhelp differentiatethepresenceoffi- 34 brosis(Young andCowan, 2012). Consistently withthese studies, 35 weadheretotheappropriatenessoflocalanalysesandtheirclini- 36

https://doi.org/10.1016/j.media.2018.03.005

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calvalueonthebasis thatmostheartdiseasestypically affect lo-37

calizedregions of the myocardium. In addition,local studies can 38

beusedtoimprovecardiacanalytics,whichmayhelppredictthe 39

effectsofspeciﬁccardiovasculardiseasesonthetissue. 40

Rotation parameters have recentlygained increasing attention 41

dueto their simplicityandease ofquantiﬁcation;they constitute 42

interesting measures ofcardiac performance which provide addi-43

tionalinformation on myocardial mechanics as a complement of 44

standard pump function indices (Rüssel et al., 2009a). However, 45

most of the rotation parameters described in the literature im-46

plicitlyrequirean accuratedescription ofan axisofrotation.The 47

center of mass given by myocardial boundaries is widely used 48

assuch; however, the heart can translate during the cardiac cy-49

cle,whichcommonlyresultsinmisalignmentsofthecenteralong 50

subsequentframes, incurringinestimationerrors. Hence,non bi-51

asedcalculation methods,whichcompensatecentroidmotion,are 52

mandatory forthe use of LV torsionas a measure of myocardial 53

dysfunctionquantiﬁcation(Senguptaetal., 2008). Still, additional 54

drawbackshavebeenreported;Young etal.(1994)statethat, for 55

HCM,theaxisofrotationisshiftedfromtheLVcenterofmass to-56

wards theinferoseptal region. In addition,for HCM patients, due 57

totheircharacteristicasymmetricalwallthicknessdistribution, ac-58

curatecentroidestimationcouldbecomeanextremelychallenging 59

task. 60

Imagingtechniquesprovideessentialinformationforthestudy 61

ofthesepathologies;severalmodalitieshavebeenproposedinan 62

effortto measureadvanced cardiac mechanics in the LV: speckle 63

tracking echocardiography (Helle-Valle et al., 2005; Bansala and

64

Kasliwalb, 2013), Cine Displacement Encoded (DENSE) Magnetic 65

Resonance Imaging (MRI) (Zhong et al., 2010) or traditional cine 66

Steady State Free Precession (SSFP) MRI, combined with feature 67

trackingtechniques,(Heermannetal.,2014),tomentionafew. Nev-68

ertheless,myocardialtissue tagging withcardiovascular magnetic 69

resonanceiscurrentlythegoldstandardforassessingregional my-70

ocardialfunction (Shehataetal.,2009).Ifitisnot widelyusedin 71

thedaily practiceis becauseit istime consuming, butto date is 72

anaccuratemethodtomeasureregionalcontractility(Jeungetal.,

73

2012).MR-Tagging(Ibrahim,2011) isusuallyperformedbyspatial 74

magnetizationmodulation(SPAMM)(AxelandDougherty,1989)or 75

avariant ofthistechnique. SPAMMis groundedon theability of 76

alteringthemagnetization ofthetissue (withinthelimitationsof 77

relaxationtimesinMR) eveninthepresenceofmotion.The tag-78

gingprocedureisbasedonthesuperpositionofaspatial modula-79

tionovertheappliedgradientswhichmaybesubsequentlytracked 80

throughoutthecardiaccycle,fromwhichthecardiacfunctioncan 81

beassessed. 82

Harmonic Phase (HARP) based methods (Osman et al., 2000) 83

arewidely used asamotion estimationtechniquein MR-Tagging 84

(MR-T).Thesemethodsarecapableofreconstructingdisplacement 85

ﬁelds accurately, grounded on the assumption of constant local 86

phase, which turns out to be more reliable than the constant 87

pixelbrightnessassumption.Thisapproachisbasedontheuseof 88

SPAMMtagpatterns,which modulatethe underlyingimage, pro-89

ducingasetofspectralpeaksintheFourierdomain.Eachofthese 90

spectralpeakscarry informationaboutaparticular componentof 91

tissuemotion,andthisinformationcan be extractedusingphase 92

demodulationmethods,obtainingtensorialdescriptorsof deforma-93

tionand,forourcase,rotationestimations. 94

Curlisadifferentialoperatorthatdescribestheinﬁnitesimal ro-95

tationofa vector ﬁeld. Its directiondetermines the axisof rota-96

tionwhileitsmagnitudeshowstheamountofrotation.Theterm 97

vortex is commonlyassociated to a localized increased value on 98

themagnitudeofthegivencurlvector(thispropertywillbe here-99

afterreferred toasvorticity).The localrotation measured bythe 100

curloperatorshouldnotbeconfusedwiththebulkangular veloc-101

Table1

Demographicdataofthepathologicandhealthypatientsinthestudy(mean± std).

Patients HCM SLVH HealthyVol.

Numberofcases 39 17 22 Age 58± 16.3 69.8± 10.5 49.2± 21.8 Sex(M/F) 27/12 12/5 14/8 EjectionFraction(%) 70.4±5.4 69.7± 6.1 63.6± 6.5 DiastolicLVvolume(ml) 140.6±22.8 131±50.3 150.3±31.5 SystolicLVvolume(ml) 42± 9 41.8 ±22.4 53.8± 13.9 Wallthickening(%) 78.4±20.1 79.8± 18.6 89.6± 16.9

ityvectorobservedwithinthemyocardialtissuewithrespecttoa 102

ﬁxedcardiacaxis. 103

Numerous 4D phase-contrast MRI (Köhler et al., 2013) stud- 104 ies havemade useof thecurl operator. Flow vortical patternsin 105 the heart chambers, the aorta, the carotid sinus and pulmonary 106 circulation are physiological, but can also be related to certain 107 pathologies including aortic aneurysms, pulmonary hypertension 108 andcongenitalheartdefects.Vorticalpatternsoftenoccurbecause 109 of morphological alterations, vessel widenings or after stenosis 110 (von Spiczaketal.,2015).Thesestructuresmayalterthepressure 111 andshearforcesonthewallsandtriggerprocessesleadingtocell 112

death. 113

Itisourunderstandingthatcurlcanalsoquantifythelocalro- 114 tationwithinthemuscle.Consequently,inthispaperweintroduce 115 a novel local rotation descriptor based on robust tensorial mea- 116 surements that relates the presence of increased vorticity values 117 with the hypertrophic tissue in the heart. Rotation is estimated 118 withoutinfluenceofglobalmyocardialparameters,such asaxisof 119 rotationorcavityradius,allowingaregionalcomparativestudyin 120 patientswithLVhypertrophyofdifferentetiologies;HCMandSec- 121 ondary forms of LV Hypertrophy (SLVH), as well ashealthy sub- 122 jects.Tothebestofourknowledge,thisisthefirststudythatre- 123 lateslocalvorticesinmyocardialtissuewiththepresenceoffibro- 124

sis. 125

2. Materials and methods 126

2.1. Materials 127

Forthevalidationoftheproposedapproach,ourstudyisaret- 128 rospectiveanalysisbasedonadatabaseofpatientswhounderwent 129 the ordinary clinical protocol according to their symptoms; the 130 databaseconsistedin 78individualswho were affectedby either 131 primary HCMorSLVH (hypertensiveheart disease,aorticstenosis 132 orathlete heartdisease)orwere healthyvolunteers. Thenumber 133 ofpathologic patientswas56; 39ofthem, withages from30to 134 86, were diagnosed asprimary HCM. These patientsshowed hy- 135 pertrophy,predominantlyintheseptalregionoftheLV.Following 136 thesame protocol,17patientswere diagnosed ofSLVHaccording 137 to chronic pressure overload. The differential diagnosis between 138 primaryHCM andSLVHwasbasedonpreviousechocardiopraphic 139 studiesandclinical andfamilialrecords.Aboutthehealthyvolun- 140 teers,22wereincludedinthestudywithagesbetween16and84; 141 thesesubjectsunderwenttheMRI protocolbecauseofaprevious 142 suspicion of cardiac pathology but all of them turned out to be 143

healthy. 144

All subjectssigned the ordinary informed consentfor theMR 145 sessionandagreedinwritingtosharetheresultingimagesforre- 146 search purposes. Personaldata were treatedaccording tocurrent 147 legislation.Demographicdataofbothcontrolsandcases,thelatter 148 indexedbypathologytype,aregiveninTable1. 149 We have acquired short axis (SA) and long axis (LA) MR-T 150 datasetsforeachpatient, fromapexto base,usingaMRComple- 151 mentary SPAMM(C-SPAMM) SENSitivity Encoding (SENSE) Turbo 152

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S.Sanz-Estébanezetal./MedicalImageAnalysisxxx(2018)xxx–xxx 3

Fig.1. Exampleimagesofthesequencesacquiredforthestudy.MR-CineSA,MR-CineLA,MR-TaggingSAandMR-TaggingLA,fromlefttoright.

Table2

DetailsonthesequencesofMRimagesusedinthepaper.p:ReconstructedPixelResolution(mm).s:SliceThickness(mm).Np:Numberofpixelsfordimension.Nt: NumberofTemporalPhases.Ns:Numberofslices.TR:RepetitionTime(ms).TE:EchoTime(ms).α:FlipAngle(degrees).

Parameters p s Np Nt Ns TR TE α

MR-TSA 1.21-1.32 10 256–432 16–25 10–15 2.798-6.154 1.046-3.575 7–25 MR-CSA 0.96-1.18 8–10 240–320 30 10–15 2.902-3.918 1.454-2.222 45 MR-TLA 1.21-1.34 10 240–340 15–27 1–3 2.903-4.507 1.097-2.897 10–45 MR-CLA 0.98-1.25 8–10 256–448 30 1–3 2.858-3.529 1.251-2.132 45

Field Echo sequence on a Philips Achieva 3T scanner. Regarding 153

the tagging parameters, we validate the method for a ﬁxed tag 154

spacing of k i = 1/

λ

, with

λ

=7mm using two different

=[

π

/4;3

π

/4]forthestripe

di-156

rections. 157

Additionally, we have also acquired a balanced SSFP SA MR-158

Cine(MR-C)sequenceatthesamespatiallocationforeachpatient; 159

snapshotsoftheacquiredsequencesare showninFig.1.The my-160

ocardium has beensegmentedin theend-diastolic (ED) phaseof 161

the MR-C sequence by two cardiologists. Cine segmentations are 162

usedtoalignthetaggingorientationstoacommonreference sys-163

tem to correct for patient motion.The ED segmentation is used 164

to deﬁne a region of interest (ROI) in which to compute mean-165

ingfulmeasurements.Resolutiondetailsaboutthesesequencesare 166

includedinTable2. 167

2.2. Methods

168

2.2.1. Preprocessing

169

Wehaveimplemented apreprocessingpipelineinorderto(a) 170

propagatetheROIinMR-CfromEDtotheend-systolic(ES)phase 171

—in which subsequent calculations will be carried out— and (b) 172

aligntheMR-CandMR-TsequencesatES.Thesetwostepsare: 173

• Registration The MR-C sequence is processed by means of a 174

groupwiseelasticregistrationprocedure(Cordero-Grandeetal.,

175

2013a)inordertopropagatetheEDsegmentationstowardsES 176

phase. The transformation is achieved by B-spline based Free 177

Form Deformations (FFD) (Rueckert et al., 2006). A gradient-178

descent optimization scheme is performed where the sumof 179

thesquareddifferencesofimageintensitiesisusedas registra-180

tion metric. A smoothness penalty term has also been intro-181

ducedto constrain the spline-based FFDtransformation to be 182

smooth. 183

• AlignmentAnaﬃne registrationmethodisperformedtoalign 184

MR-T and MR-C images at ES phase. The MR-T sequence has 185

beendetaggedbymeansofahomomorphicﬁlteringprocedure 186

(Makrametal.,2015)priortothealignmentprocess. 187

2.2.2. Motion estimation

188

3D HARP motion reconstruction using the C-SPAMM tech-189

nique requires a minimum of 3 linearly independent wave vec-190

tors (Osmanet al., 2000). We haveextended theaforementioned 191

HARPmethodologyforthecomputationofthedeformation gradi- 192 enttensorusingSAandLAimagesontheintersectionoftheslices 193 asshowninFig.2.ForpointsonwhichLA axisimageswere not 194 available,2D motion hasbeenreconstructed. The motionestima- 195 tiontechniqueisbasedontheextractionofthelocalphaseofthe 196 gridpatternaccordingtothemethodpresentedinCordero-Grande 197

etal.(2011,2016).AwindowedFourierTransform(WFT)isapplied 198 to the image at ES phase. The WFT provides a representation of 199 theimagespectruminthesurroundingsofeachpixeloftheorig- 200 inalimage,soHARPbandpassfilteringtechniquescanbedirectly 201 appliedon thespatially localizedspectrum oftheimage. Toade- 202 quatelyretrievetheshapeofthespectral peaks,wehaveresorted 203 toananisotropicfilteringapproachcombiningGaussianband-pass 204 andall-pass filters asproposed in Sanz-Estébanez et al.(2016a). 205 Finally,eachoftheimagephase

ϕ

_i(x )(twoforeachplane)canbe 206 extractedinthespatialdomainfromtheinverseWFToftheafore- 207

mentionedﬁlteredspectrum. 208

As mentioned before, we have extended the HARPmethodol- 209 ogy by allowing the estimation of motion under the application 210 of a set of four wave vectors. Therefore, 3D deformation gradi- 211 ent tensor can be robustly recovered at the intersection points 212 ofbothaxes, byapplyingthemethodology presentedinCordero- 213

Grandeetal.(2016).Thematerialdeformationgradienttensor F (x ) 214 canbe estimatedfromthe gradientofthe phaseimage asstated 215

inOsmanetal.(2000)as: 216

K=

∂ϕ

Fromthisestimatedtensor,themaincardiacfunctioncharacter- 225 isticscanbeobtainedthroughtheLagrangianstraintensor,deﬁned 226

as: 227

The spatial resolution of the reconstructed tensors depends on 228

thewidthoftheHARPband passﬁlter(ParthasarathyandPrince,

229

2003;2004);theHARPmethodisupperlimitedbyhalfofthetag 230

spacing(smalldeformation assumption). However, WHARP meth-231

ods(Sanz-Estébanezetal.,2016a;Cordero-Grandeetal.,2016) try 232

toaccommodatethebandpassﬁltertothelocalfrequencyofthe 233

signalinordertoapproachtothemaximumachievableresolution. 234

Therefore,effectiveHARPresolution willvary dynamically, allow-235

inglargedeformations,asthoseobservedatES,beingcapturedat 236

amaximalscaleof1.5timeshalfthetagspacing. 237

These tensors have been calculated atES, where the greatest 238

deformationalongthecardiaccycletakesplace. 239

2.2.3. Rotation parameters

240

Inaddition tothickeningandshortening,themyocardium also 241

undergoes a wringing motion during systolic phases due to the 242

obliquely oriented subendocardial and subepicardial myoﬁbers. 243

Manydescriptorshavebeenproposedtomeasurethismotionthat 244

relyoneitherglobalinformationderivedfromsimpliﬁed anatomi-245

calmodelsorontensorialstrainanddeformationmagnitudesbuilt 246

fromlocalmotionestimates. 247

Measures based on global information. It is well known that the 248

LVapexgloballyrotatesanticlockwiseata relativelyconstantrate 249

throughoutsystole.Onthecontrary,thebase,initiallyrotating an-250

ticlockwise,reverses directionproviding a net clockwiserotation 251

atESphase. Theresulting differenceofthese twomotions is de-252

ﬁned as twist, deﬁned to be positive by convention (Young and

253

Cowan,2012). 254

Thereiscurrentlyalackofstandardizationformethodsusedto 255

characterizetheglobalLV twisting motion.Thesedescriptorsrely 256

ongeometricalmodels oftheheart fortorsionandtwist calcula-257

tion.Consequently,both a well-deﬁnedﬁxed axisofrotation and 258

regularmyocardial radiiover thewhole heartare mandatory.For 259

example,torsion has been traditionally calculated as relative ro-260

tationindegrees(Lorenzetal., 2000), rotationper length in de-261

grees/mm,torsionalshear angle,alsoin degrees(Buchalteretal.,

262

1990), and longitudinal-circumferential shear strain (dimension-263

less)(Fung,1965).Traditionalrotationindicesareobtainedby vec-264

torial product between position vectors at ES u _ESand ED u _ED 265

phasesas: 266

sin

(

β

compensation,specially forcentroidmotion correction. Twist per 269 unit lengthisalsowidespread, sincetorsionisrelatively constant 270 in the longitudinaldirection (Young and Cowan,2012). Nonethe- 271 less, thismeasuredoesnotscale appropriately betweenhearts of 272 differentsizesandwehavenotobservedasigniﬁcantcomplemen- 273 taryvaluewithrespecttothetwist. 274 The torsional shear angle is a measure of the change in an- 275 gle between line segments which are initially aligned with the 276 anatomical axes of the LV. Many studies have used the formula 277 given by Aelen etal. (1997). However, it hasbeen demonstrated 278 thatitusuallyoverestimatesdeformation(Rüsseletal.,2009b),so 279 wehaveresortedtoanunbiasedalternativeformulabasedoncir- 280

cumferentialdisplacements: 281

T =

(

β

apex r apex −

β

base r base

)

D , (5)

where D is the distance between selected segments.1 _However, ₂₈₂

HCMcharacteristicendocardialirregularitiesmayhindertheaccu- 283 rateestimationofboth themyocardialradiusandtheaxis,which 284

arecrucialinthisformulation. 285

Tensorial descriptors. Anotherimportantgroupofrotationdescrip- 286 tors focus on the properties of the tissue that provide localized 287 characterization of the motionby tensorial analysis.As stated in 288 solidmechanics(Fung,1965),the3D strainstateatanypointina 289 bodycan befullyrepresentedbythreediagonalstrainsandthree 290 shear strains. From them, the longitudinal-circumferential shear 291 (E _lc)isausefulmeasurecloselyrelatedtotorsion.Accordingtothis 292 analysis, local torsion measures can be deﬁned, i.e., the 3D local 293

torsionshearcanbegivenby: 294

sin

(

θ

_lc

)

=√ 2 E lc 1 +2 E cc

1 +2 E ll

, (6)

where E _ccand E _llrepresent the circumferential and longitudi- 295 nal strains, respectively; these components can be obtained by 296 straightforward operations on the Cartesian components in (3). 297 Nevertheless,shear strainsareseveralmagnitudes lower thandi- 298 agonalstrains,sofactorsotherthaninotropicstatemaygreatlyaf- 299 fectitsestimation(Petitjeanetal.,2005). 300 Angular variation between two states of stress in the plane 301 inCartesian coordinates can beexpressed by a singleangle

φ

as 302

1_Rotation_parameter_β _has_been_pixelwise_estimated;_therefore,_rotation mea-suresexpressedon(5)arereferredtothemedianoftherotationdistributionon basalandapicalsegments.

(8)

Fig.3. ExamplesofvorticityvectormodulusatESfrom(9)inbasalandapicalslices,leftandrightrespectively.Thearrowsshowtheextractedcardiacdisplacementﬁeld whilethecolourrepresentstheintensityofvorticity(unitless).SomeoutliersareobservedneartheboundariesduetothediﬃcultyofHARPmethodsintrackingmaterial pointsinthepresenceofgreatintensitychanges.Scalesaresettobestaccomodatetherangeofvaluesonthegivencardiacplane,sincemyocardialrotationvariesin modulusanddirectionalongthecardiacaxis.

statedinFung(1965): 303

tan

(

2

φ

)

=

_ε

2

ε

xy

xx −

ε

yy , (7)

where

ε

representstheCauchy’s straintensor (

ε

) directly related 304

withthe stresstensor bythe Lamé parameters(Fung,1965). Par-305

ticularvaluesof

φ

showangularvariationofstressprincipal direc-306

tionsbetweenbothstates(ESandEDphases). 307

Additionally,in Cordero-Grandeetal.(2013b) a novelrotation 308

parameter hasbeenproposed builtfromthe (longitudinal) trans-309

formationthatsuffersalocalcoordinateatEDthroughtimeinthe 310

LR planeasgivenbythematerialdeformationgradienttensor F . 311

α

LRl ₌_arctan

₍

₋_F

lr /F ll

)

. (8)

Ourworkellaborates onvorticalpatternswidelyemployed for 312

theidentiﬁcationofabnormalﬂowpatterns.Nonetheless,theterm 313

vortex bearsdifferent interpretations asdeﬁned inthe literature. 314

Formostﬂowstudiesperformedinclinicalpractice,theterm vor-315

tex denotes rotating motion, where stream or pathlines tend to 316

curl back onthemselves (Markl etal., 2011). Inﬂuid dynamics,a 317

vortexisaregioninaﬂuidinwhichtheﬂowisrotatingaroundan 318

axisline,whichmaybestraightorcurved.Moreexplanatorynotes 319

on the theoretical deﬁnitionof the term vortex can be found in 320

Stalderetal.(2010).Inthispaper,thetermvortexwillbeusedin 321

thesolid mechanics contextasalocalabnormallyincreased rota-322

tioncomponent. Inordertoﬁndevidenceofperturbations within 323

themyocardialtissue,materialvorticalpatternscanthenbe asso-324

ciated to increased valuesof an dynamicrotation parameter ex-325

tractedfromthedeformationgradienttensor. 326

Thecurlofagivendeformationﬁeld u describeslocalspinning 327

vectors(seeFig.3)andcanbecalculatedas: 328

ω

(

t

)

)

=1

2

∇

×u

(

t

)

= 1 2

⎛

⎜

⎝

_F

zy −F yz F xz −F zx F yx −F xy

(9)

where F _abrepresents a component of the material deformation 329

gradient tensor in Cartesian coordinates. Hereinafter, vortical pa-330

rameterswillbeexpressedinCartesiancoordinatesasopposedto 331

thecylindricalcoordinatesfromthestraintensorusedin(6). 332

In this paper we hypothesize that local increasing of vortic- 333 ity values (in modulus) arises within myocardial segments with 334 fibrosis-relatedperturbations.Nonetheless,highvorticityvalues,ir- 335 respectiveofthefibrosisdegree,arepronetoappearinmyocardial 336 boundaries,givingrisetomultipleoutliersinrotationestimation. 337 Thesevorticitymeasuresareinsensitivetothedefinitionofthe 338 rotationaxis,although3D deformationsare neededforits proper 339 reconstruction.WhenLAinformationisnotavailable,onlythelon- 340 gitudinalcomponent(

ω

z )ofthevorticityvectorcanbeestimated. 341 In addition, if the cardiac axis is not planned properly, vorticity 342 parameters will be estimated with a systematic error related to 343 theangularerroroftheaxis.However,asitiscommoninclinical 344 practice,wewillassume thatthemainaxisofrotationwilllie on 345 theLAplanes(i.e.,willbenormaltotheSAimageplanes).Hence, 346 the

ω

z componentofthevorticityvectorprovidesclinicalcompli- 347 anceasitisalignedwiththewringingmotionofmyocardialﬁbers. 348 Thus,aphaseincrementduetotheaforementionedlocalrotation 349

canbeextractedbyintegration: 350

t ES

t ED

ω

ω

z

(

₂t ES

)

(

t ES −t ED

)

.

(10)

This parameter will be referred to as local rotation ϑ. Therefore, 351 twistmotionwillbeapproximatedas 352

Twist

ϑ

=

|

ϑ

base−

ϑ

apex

|

(11)

Forcomparative purposes,wewillalsoestimate ϑand

β

rota- 353 tiondistributionswithtwootherdifferentmethodologies.First,we 354 willanalysethecapabilitiesoftheelasticregistrationalgorithmde- 355 scribedinSection2.2.1appliedtoMR-Ctodetectrotationfromthe 356 estimateddeformationﬁelds.Second,wehaveemployed anatlas- 357 based approach that consists of a spheroidal model (Young and 358

Axel, 1992) ﬁtted at ED and that deforms due to the forces ex- 359 ertedfromastripetrackingprocedure(Young etal., 1995) onthe 360 MR-Tsequencethroughoutthecardiaccycle.Deformationsarefor- 361 mulatedfromcontinuousparameterfunctionswhich,in addition, 362 include parameterized twisting and rotation axis deformation as 363 givenin Park et al. (1996)and, therefore,can be applied to any 364

shape. 365

2.2.4. Classiﬁcation 366

We have resorted to a classiﬁcation method (Sanz- 367

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Fig.4. Pipelineforthefeatureselectionandclassiﬁcationstages.

to classify heterogeneous groups of ventricular hypertrophy (and 371

controls) from myocardial functional descriptors. The proposed 372

classiﬁcation method is grounded on the idea that populations 373

overlap strongly irrespective of the speciﬁc features selected for 374

classiﬁcation ifthe problemis addressed through a singlestage. 375

Our purpose is to classify a sample into one of three classes, 376

namely,control, primaryHCMandsecondaryhypertrophy(SLVH). 377

Sincesecondaryhypertrophypatientshavesubtledifferenceswith 378

respecttotheother twoclasses,wehaveresortedto atwo-stage 379

classiﬁcation procedure. Thus, we have divided the classiﬁcation 380

process in three stages and performed a feature selection step 381

for each stage independently, following a sequential methodol-382

ogythat adapts to the characteristics of the population at every 383

stage. Different machine learning methods (both supervised and 384

unsupervised)havebeenimplementedforeachstageandalltheir 385

possiblecombinationshavebeentested. 386

Mechanicaldescriptorsextractedfromtheaforementioned ten-387

sorsarean essentialpartoftheclassiﬁcation procedure.Wehave 388

considered different groups of features. First, the components of 389

the strain tensor in the cylindrical coordinate system {R , C , L } 390

are accounted for. We also use twist and torsion features (see 391

Table 3) built from the aforementioned rotation parameters as 392

extracted from the MR-T and MR-C sequences, as well as using 393

thespheroidalmodelwehavepreviouslyreferredto.Additionally, 394

since some rotation-related componentshave opposite directions 395

inapexandbase,weconsiderthelocationofthezerocrossingfor 396

thesecomponentsaswell. 397

For the feature extraction step, we have previously se- 398 lected for each feature the mostrepresentative cardiac segments 399 (Cerqueira,2002)withinclinicalpractice.Fortwistandtorsionde- 400 scriptors,wehaveconsidered septalsegments,whereas fortenso- 401 rialparameters,mid-ventricularorbasalsegments havebeencho- 402 sen.InTable3weshow thesegments involvedinthecalculation 403 ofeachofthe features;then theoverall featureis,forrobustness 404 purposes, the median of the distribution within those segments, 405 which will be the input to the classifier. For the twist parame- 406 ters the feature extracted is the difference between medians on 407 apical andbasal septalsegments.Ontheother hand,forthezero 408 crossingparameter,thefeaturerepresentstheheightofthecardiac 409 axisatwhichthegivenrotationparameter,estimatedslicebyslice, 410 changesitssign.Noticethatthefeatureextractionstepisgrounded 411 onclinicalknowledge,i.e.,itisnotdata-driven. 412 As reflected in Fig. 4, after feature extraction we carry out a 413 normalizationstageinordertodiminishtheinfluenceofpossible 414 outliers. A sigmoidal function, withits scale factorset according 415 toTheodoridis andKoutroumbas(1999),isusedtothisend. Data 416 aremappedontheinterval(0,1)byimposingageneralizedlogistic 417 function;outlierswilltendtoappearateitherofthetwoextremes, 418 whilemaintaininga linearrelationfortherestofthe data.Then, 419 normalizedfeaturesarearrangedinvectorswithdifferentnumber 420

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Table3

Cardiacsegmentsinvolvedduringthefeatureextractionstageforeachoneofthemotiondescriptorsemployedintheclassificationprocedure.Foreachrow,onlyonefeature willbeextracted,summarizingallthesegmentsindicatedbelow.Theextractedfeatureswillbetheinputtothefeatureselectionstep,fromwhichthefinal(survivor)feature vector(from2to5components)willarise.Thenumberwithinbracesindicatestheequationthatdefinestheparameter.

Segment 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Err(3) √ √ √ √ √ √

Ecc(3) √ √ √ √ √ √

Ell(3) √ √ √ √ √ √

Elc(3) √ √ √ √ √ √

||ω||(9) √ √ √ √ √ √ √ √ √ √ √ √

Twistϑ(11) √ √ √

Twistβ(4) √ √ √

Twistφ(7) √ √ √

T(5) √ √ √ √ √ √ √ √ √ √

αLRl₍₈₎ √ √ √ √ √

θlc(6) √ √ √ √

ωzzerocross.(9) √ √ √ √ √ √ √ √ √ √ √ √ √ √ √ √ βzerocross.(4) √ √ √ √ √ √ √ √ √ √ √ √ √ √ √ √

ofcomponents(2through5).Allpossiblecombinationsoffeatures 421

indicatedinTable3havebeentested. 422

Featureselectionandclassiﬁcationperformanceassessmenthas 423

beencarriedoutinasimilarbutsequentialmanner.Forboth,data 424

samples have been randomized and a Leave-10-out method has 425

been applied; the proportions of control/primary/secondary have 426

been keptunaltered alongtrials. Speciﬁcally,forfeature selection 427

intheﬁrstclassiﬁcationstage,weclassifythesamplesincontrols 428

andprimariesandcalculatetheaccuracy;thefeaturesetwiththe 429

highestﬁgureisselectedforthisstage.Inparallel,andforthe sec-430

ond stage, controlsand secondaries are classiﬁed on one branch 431

(left branch) andprimariesand secondarieson theother branch. 432

In thiscase, features are selectedwith the criterion of maximiz-433

ing the sensitivitytosecondaries soasto avoidbias towardsthe 434

groupswithlargersamplesize,speciallybetweenHCM andSLVH. 435

Thisprocedure hasbeenlabelledin Fig.4as K-fold Feature Selec-

436

tion .Asforﬁndingclassiﬁcation performance,asimilarcross vali-437

dationprocedurehasbeencarriedout(labelledinFig.4as Leave-

438

10-out Classiﬁcation ) onnewrandomizations.Theclassiﬁerstested 439

havebeenFuzzyc-Means(FCM)(Bezdec,1981)andSupportVector 440

Machines (Cortes and Vapnik,1995) both withquadratic (SVMq) 441

andGaussian(SVMg)kernels(Vertetal.,2004). 442

In order to assess the performance of a given feature in the 443

classiﬁcation procedure we have measured its surviving percent 444

rate. This parameter shows the membership probability of the 445

givenfeature tothe featurevector extractedfromthefeature se-446

lectionstep;inotherwords,itisthefrequencythatthefeatureis 447

employedwithinanyofthestagesoftheclassiﬁcationalongtrials. 448

3. Results

449

3.1. Rotation analysis

450

Torsionis knownto be dependent onLV shape,with reduced 451

twistinmoresphericallyshapedheartsandincreasedtorsionwith 452

concentrichypertrophyduetoanincreasedleverarmfor myocar-453

dial ﬁbers.InHCM, torsionhasbeenreportedtoincrease despite 454

reduced circumferential and longitudinal shortening (Young and

455

Cowan, 2012). These ﬁndings, together with others described in 456

Section1,canbeobservedintheresultsincludedinTable4,where 457

the mean and standard deviation of the twist and torsion dis-458

tributions derived from the aforementioned rotation features are 459

shown. 460

In Fig. 5 we show snapshots of mid-ventricular slices of the 461

local rotationextractedby means ofthevorticalapproach as de-462

scribedin(10)foraHCMandaSLVHcaseaswellasforahealthy 463

volunteer.Ingeneral,septalsegmentsforHCMhaveshownhigher 464

vorticity,speciallywhencomparedtolateralsegments,whereasfor 465

Table4

TwistandtorsionparametersextractedfromtheMR-Tsequence(mean ±std)for segmentsinTable3foreachpopulation.Thenumberwithinbracesindicatesthe equationthatdeﬁnestheparameter.

Populations HCM SLVH Control

Twistϑ(11) 10.46±2.11 9.23±2.28 7.33±2.08 Twistβ(4) 13.53±2.50 13.80±3.37 9.87±2.81 Twistφ(7) 2.73±0.53 2.71±0.64 1.25±0.072 T(5) 7.26±1.14 6.85±1.90 4.63±1.68 Elc(3) 0.02±0.003 0.022±0.01 0.011±0.006

θlc(6) 7.94±1.66 7.22±1.81 3.18±0.39

αLRl₍₈₎ _1.83_±_1.57 _2.08_±_1.98 _2.82_±_1.79

secondarycases thisbehavior canbe observed inanyofthe car- 466 diacsegments.Inhealthyvolunteerstheextractedvaluesarelower 467 comparedtoHCMpatientsindependentlyofthecardiacsegment. 468 In Fig. 6, we show color codes of the mean ± standard 469 deviation (respectively, inner and outer rings within each seg- 470 ment) of the rotation parameters over the 17-segment model 471 (Cerqueira,2002),estimatedfromboththevorticalapproachgiven 472 in(10) and thetraditional approach by (4) forthe resulting dis- 473 tributionofthedeformationvector ﬁeld.Additionally,andforthe 474 sakeofcomparison,rotationparametersextractedwiththeelastic 475 registrationprocedure overMR-Candfromthedeformablemodel 476 havebeenincludedaswell inthesecond andthird rows,respec- 477

tively. 478

Studentt-tests2 _have _been _performed _to _highlight _differences ₄₇₉

onthemeanofthevorticitymodulusandtheaforementionedro- 480 tationdistributionsoneachofthe17cardiacsegments.Eachpop- 481 ulationofthestudyhasbeencomparedwiththeothertwo,sepa- 482 ratelyforeachrotationparameter;thenumericalresultsareshown 483 inTable5andgraphicallyinFig.7bull’seyedisplay.Itisnotice- 484 able that the vorticalapproach seems to show larger differences 485 betweenpopulations compared to the traditional approach. Sep- 486 tal segments seem to bear higher discriminating capability, spe- 487 ciallywhentwistismeasured bythevorticalapproach.Addition- 488 ally,wehaveperformed(two-way)ANOVAtestsovertheϑdistri- 489 butionsextractedfromMR-CandMR-Tsequencesaswellasusing 490 the deformable model (over MR-T) for each population and car- 491 diacsegment. Signiﬁcant differences(p <10−3₎ _have _been_found ₄₉₂

inthevastmajorityofthecomparisons.ϑand

β

distributionswere 493 notcomparedsincethemeasuredparametersdonotrepresentthe 494 samecomponentofthephysiologicalrotationmotion. 495

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Fig.5. Snapshotsonvortical-basedrotationmeasurementωzfrom(9)forHCM,SLVHandahealthyvolunteerovermid-ventricularslices(fromlefttoright).

Fig.6. RegionalstudyoftheaforementionedvorticalrotationparametersobtainedfromtheMR-CandMR-Tsequences,aswellasusingthedeformablemodeloverthe latter,forthedifferentpopulations.Traditionalrotationisalsodepictedinthelastrow.Foreachcardiacsegmenttwocolorsaredepicted,theinnershowingmean+stdand theouterformean−std.

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Table5

p-valuesforthecomparisonsbetweendistributions(H,SandCstandforHCM,SLVHcasesandcontrols,respectively)ofthegivenrotationparametersindexedbynumber ofsegment.Whenunspeciﬁed,MR-Tistheimagesource.SigniﬁcancelevelafterBonferronicorrectionis0.017.

Differencesonϑdistributions Differencesonβdistributions DifferencesonϑCINEdistributions DifferencesonϑMODELdistributions

Seg. H.vsS. C.vsS. H.vsC. H.vsS. C.vsS. H.vsC. H.vsS. C.vsS. H.vsC. H.vsS. C.vsS. H.vsC.

1 0.078 0.001 ≤10−6 _0.91 _0.01 _0.001 _0.20 _0.008 _≤₁₀−6 _0.19 _0.033 _≤₁₀−6 2 0.022 ≤10−6 _≤₁₀−6 _0.97 _2.49_·₁₀−6 _≤₁₀−6 _0.47 _≤₁₀−6 _≤₁₀−6 _0.12 _≤₁₀−6 _≤₁₀−6 3 0.065 ≤10−6 _≤₁₀−6 _0.65 _5.82_·₁₀−5 _≤₁₀−6 _0.10 _0.002 _≤₁₀−6 _0.24 _≤₁₀−6 _≤₁₀−6 4 0.33 ≤10−6 _≤₁₀−6 _0.71 _1.77_·₁₀−6 _≤₁₀−6 _0.66 _≤₁₀−6 _≤₁₀−6 _0.093 _8.23_·₁₀−5 _≤₁₀−6 5 0.52 ≤10−6 _≤₁₀−6 _0.31 _5.48_·₁₀−6 _≤₁₀−6 _0.090 _0.002 _≤₁₀−6 _0.073 _6.88_·₁₀−5 _≤₁₀−6 6 0.092 ≤10−6 _≤₁₀−6 _0.23 _8.04_·₁₀−5 _3.05_·₁₀−5 _0.057 _1.17_·₁₀−4 _≤₁₀−6 _0.55 _0.0095 _≤₁₀−6 7 0.64 0.002 3.12·10−5 _0.78 _0.26 _0.21 _0.18 _0.022 _3.29_·₁₀−5 _0.055 _0.0037 _≤₁₀−6 8 0.011 7.32·10−5 _≤₁₀−6 _0.16 _0.008 _3.03_·₁₀−6 _0.042 _0.098 _6.34_·₁₀−5 _0.038 _0.002 _≤₁₀−6 9 0.049 0.17 0.002 0.27 0.41 0.028 0.09 0.010 4.29·10−4 _0.013 _0.051 _6.81_·₁₀−5 10 0.12 0.27 0.044 0.29 0.89 0.20 0.53 0.016 3.52·10−5 _0.34 _0.046 _2.25_·₁₀−4 11 0.018 6.88·10−6 _≤₁₀−6 _0.58 _5.79_·₁₀−4 _1.37_·₁₀−6 _0.25 _0.037 _1.98_·₁₀−5 _0.091 _0.047 _0.12 12 0.006 8.21·10−6 _≤₁₀−6 _0.94 _0.004 _6.94_·₁₀−5 _0.26 _0.18 _1.34_·₁₀−4 _0.65 _0.059 _0.064 13 0.10 0.092 0.002 0.57 0.085 0.002 0.040 0.092 2.69·10−4 _0.021 _0.0068 _≤₁₀−6 14 0.79 0.068 5.38·10−5 _0.54 _0.017 _0.001 _0.055 _0.003 _≤₁₀−6 _0.032 _0.0082 _≤₁₀−6 15 0.18 0.061 0.003 0.56 0.58 0.24 0.018 0.019 ≤10−6 _0.76 _0.019 _2.16_·₁₀−5 16 0.46 0.045 ≤10−6 _0.25 _0.019 _0.001 _0.18 _0.38 _0.018 _0.083 _0.025 _≤₁₀−6 17 0.87 0.86 0.22 0.73 0.88 0.82 0.14 0.17 0.27 0.81 0.17 3.76·10−4

Fig.7. p-valuebull’s-eyeplotsfromintra-segmentcomparisonsbetweenprimaryHCMandSLVHpatientsforϑdistributionsobtainedwithdifferentmethodologies,aswell astraditionalrotationβdistribution.Scaleisdeﬁnedas−log10(p-value).

3.2. Classiﬁcation analysis

496

Wehaveassessedthesurvivalrateofthefeatureselectionstage 497

of the classiﬁer (recall Fig. 4). Results are shown in Table 6 for 498

thefeaturesdescribedinTable3;featuresobtainedfromboththe 499

MR-Celasticregistrationaswellasfromthespheroidaldeformable 500

modelhavealsobeenincluded.Additionally,wehavealsoincluded 501

conventional indices of cardiac motion used in clinical practice, 502

suchaswallthickening(WT)overmid-ventricularslices(seeDong

503

etal.,1994; Prasadetal.,2010 formoredetails),ejection fraction 504

(EF) and LV volume, with the latter both at ED (EDLVV) andES 505

phases(ESLVV). 506

The mostrepeated conﬁguration of the classiﬁer consisted of 507

FCM for stages 1 and 2.2 and SVMg for stage 2.1. The best ac-508

curacy ﬁgures were obtained when using diagonal strain ten-509

sor components on stage 1, whereas for stages 2.1 and 2.2, the 510

best feature vectorsturned out to be [E _ll, TwistϑTAG , Twist

φ

] and

511

[E _ll,E cc ,Twist

ϑ

_TAG,

||

ω

||

],respectively.Ifwe takeinto accountnot 512

onlythebestclassiﬁerbutwealsorankperformanceandanalyze 513

the ﬁrst, say,ten results,the composition of theselected feature 514

vectorsshowssome degreeofvariabilitywhichseemsvery much 515 inaccordancewiththeresultsinTable6. 516 In terms of end-to-end performance, the obtained accuracy 517 (86%)seemscomparableinclassificationfigures withotherproce- 518 dures(see Gopalakrishnan etal., 2014; Puyol-Antón et al., 2017) 519 although, in these cases, no SLVH are analyzed, so comparisons 520 havetobemadecautiously.Indisaggregatedterms,thesequential 521 classifierhasobtainedsensitivityfigureshigherthan70%foreach 522 group(specifically,81%forcontrol,72%forsecondaryhypertrophy 523 patientsand95%forprimary HCMpatients).Itisworthmention- 524 ingthatnoprimaryisclassifiedascontrolandviceversa;therefore, 525 the pipeline proposed seems a proper screening tool. Secondary 526 patientsperformanceisclearlylowerascomparedwithbothcon- 527 trolsandprimaryHCMpatients, possiblyduetoasmallersample 528 sizeaswellasthesubtledifferencestheyshow. 529 Finally, in order to assess the relative strength of the differ- 530 entmeasuresinclassification performance,wehaverun theclas- 531 sificationpipeline withdifferentfeaturessubsets. Inparticular, in 532

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Table6

Survivingpercentrateofthefeaturesemployedintheclassiﬁcationprocedure(see notationinFig.4).Stage2.2isdevisedtoSLVH-to-HCMsensitivity,whilestage2.1 referstoSLVH-to-Controlsensitivity.

Features Stage2.2 Stage2.1 Stage1

Err 7 38 35

Ecc 54 24 60

Ell 49 50 37

Elc 22 11 6

||ω|| 43 25 19

TwistϑTAG 42 32 27

TwistϑCINE 7 2 13

TwistϑMODEL 15 8 7

TwistβTAG 19 16 16

TwistβCINE 8 5 4

TwistβMODEL 12 3 0

Twistφ 18 20 24

T 8 13 18

θlc 3 0 1

αLRl ₇ ₉ ₁₀

ωzzerocross.TAG 21 13 4 ωzzerocross.CINE 2 5 2 ωzzerocross.MODEL 12 3 0 βzerocross.TAG 14 1 3 βzerocross.CINE 0 2 1 βzerocross.MODEL 3 1 0

WT 0 8 10

EF 0 6 3

EDLVV 0 0 1

ESLVV 0 2 0

clinicalindices) andwithMR-Tfeatures only. Fromthe latter,we 535

have also shown classiﬁcation performance obtained discarding 536

traditionalandvorticalrotationfeatures,respectively. 537

4. Discussion

538

Therelationshipbetweenmyocardialﬁbrosisandlocal mechan-539

ics is important for the diagnosis and treatment of cardiomy-540

opathies(Karamitsos andNeubauer,2011). Thispapershowsthat 541

LVrotationisessentialforpropermyocardialfunction.Inourcase, 542

mostofthemeasurementsshowninTable4indicatethatLV rota-543

tioncanbe considered asa markerforcardiacdisease identiﬁca-544

tionandmightbehelpfulforcardiomyopathyunderstanding,thus 545

providingcomplementary informationtostandard pumpfunction 546

indices. 547

The diagonal components of the strain tensor (E cc , E _lland 548

E _rr), deﬁned in (3), have provided the highest separability be-549

tween pathologicandhealthy groups (cardiomyopathyscreening) 550

asshowninTable6;ourresultsareinaccordancewiththis ﬁnd-551

ing(Saltijeraletal.,2010).Twistparameters seemtobealso valu-552

ablein thisstep, showinghigher survival ratethan shear strains 553

andtorsionparameters.Forthereﬁnementstepforcontrols/SLVH 554

(stage2.1inFig.4) the E cc componentinmid-ventricularareasis 555

the mostdiscriminative. Amongst the rotation-based parameters, 556

vorticitymodulus

||

ω

||

andtwistϑTAG remainthemost

discrimina-557

tivefeatures. 558

In parallel, for the classiﬁer stage 2.2, lower ﬁgures on the 559

globalperformanceareobtained.Besides,theselectedfeature vec-560

torpresentedonemorecomponentandtwocurl-derivedentries;it 561 consistedofacombinationoftwodiagonalstrain parameters,the 562 vorticitymodulus(9)andthetwistextractedfromthevorticalap- 563 proach(10).Extendingtheanalysistomore(thanone)high-ranked 564 features vectors, we observea greater degreeof heterogeneityas 565 well as the frequent presence of

ω

z (9). Consequently, the pro- 566 posedcurl-derivedparameters(9)–(11)haveturnedouttobepar- 567 ticularly useful for the discrimination of primary and secondary 568 casesasreflectedbysensitivityfiguresextractedfromTable7. 569 To the best of our knowledge, thisis the first study in HCM 570 patientsthatrelatesvorticityincardiacdeformationfieldswithlo- 571 cal myocardialmechanics andits abnormalities; our results sug- 572 gest that vorticity mayhelp deepen onthe underlying character- 573 isticsbehindprimary andsecondary casesofLVhypertrophy.For 574 these parameters, neither the length nor the centerof the heart 575 are needed, so no bias is introduced in their estimation; as we 576 havedescribedabove,vorticityisdirectly relatedto thedeforma- 577 tion gradient tensor and, consequently, it can be estimatedfrom 578 thesameinformationusedinthestraintensor(3)analysis.Inad- 579 dition, they show higher survival rates than techniques that use 580 fixedLVaxisandcenterrepresentations,givingrisetoamorereli- 581

ableparameter. 582

The color-coded results shown in Fig. 6 reveal that patients 583 withboth formsof ventricular hypertrophy presentgreater rota- 584 tion distributionsascompared withcontrolsovermostsegments 585 both forvortical(10)andtraditional (4)rotations.As forprimary 586 HCMpatients, thereisaclearincreasedrotation(in modulus)for 587 allsegments,buthighvorticityareasaremainlylocatedonseptal 588 segments. SLVHpatientsshowed asomewhat differentpatternin 589 mid-ventricular andbasal regions ofthe heart, presentinghigher 590 valuesthan controls;those valuesare not focused on septalseg- 591 ments but a slight bias to lateral segments may exist. Other re- 592 gionalanalyses havealsobeenperformedby meansof automatic 593 LVsegmentation(Baietal.,2016;Liangetal., 2015).However,the 594 presence of hypertrophic tissue and other pathologies may bias 595 theﬁnal parcellationofthe cardiacsegments.Forthisreason, we 596 havemadeuseofthe17-segmentmodelasaconsistentandwell- 597 established model formotion analysis(Smiseth etal., 2016). The 598 usefulness of the vortical parameters has also been reﬂected by 599 theimprovementshowninTable7withrespecttotraditionalro- 600 tationparameters andtheminordegradation withrespectto the 601 full-feature optionwhencurl-derivedparameters are usediniso- 602

lation. 603

OurresultsalsoindicateahigherperformanceofMR-Tformo- 604 tion estimation withrespect toMR-C; however,it is well-known 605 that HARPprocedures havesome diﬃcultiesin correctlyestimat- 606 ing the phase in the vicinity of boundaries. In those areas, elas- 607 ticregistration procedures over MR-Cis usually more robust.For 608 thisreason,acoordinatedprocedurethatweighsbothinformation 609 sources according to position may potentially provide better ﬁg- 610

ures. 611

Additionally,vorticalmeasures werecomparedwhenextracted 612 bothfromtheHARPmethodandbydeformingaspheroidalmodel 613 previously ﬁt.Similar vorticityvalueswere obtainedalthoughthe 614 extracted vortical patterns from the spheroidal model showed 615

Table7

Confusionmatricesforclassiﬁcationperformancewithdifferentfeaturesubsets.Matriceshavebeennormalizedwithrespecttothetotalnumberofpatients. Eachcolumnrepresentstheinstancesinapredictedclasswhilerowsrepresenttheinstancesinanactualclass.

FullFeatureSet MR-Taggingonly Vorticalonly Traditionalonly

C S H C S H C S H C S H

C 0.236 0.064 0 0.243 0.057 0 0.24 0.06 0 0.234 0.066 0 S 0.023 0.145 0.032 0.038 0.144 0.018 0.021 0.141 0.038 0.038 0.127 0.035 H 0 0.017 0.483 0 0.025 0.475 0 0.022 0.478 0 0.023 0.477

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higher spatial smoothness dueto the regularized functions used 616

todeﬁnethedeformation,therebyreducingitsusefulnessfor clas-617

siﬁcation(seeTable6). 618

Finally, conventional global indices in HCM diagnosis (see 619

Table 1) have also been tested in the classiﬁer. Neither of them 620

presented a very representative survival rate (even in stage 1), 621

hence, their inﬂuence on ﬁnal performance does not seem rele-622

vant. 623

5. Conclusions and future lines

624

In thispaperwe haverelatedanomalies onlocalvortical pat-625

terns with the presence of ﬁbrotic tissue by means of an im-626

age processing pipeline and a two-stage sequential classiﬁcation 627

method.Localrotationparametersareestimatedbymeansofa ro-628

bustmotionandtensoranalysissothat potential biasesofglobal 629

analysesareavoided. 630

Local rotation wassigniﬁcantlyincreased inprimary HCM pa-631

tients,speciallyintheseptum,comparedtocontrolsandsecondary 632

cases;inthelatter,vorticalabnormalitiesmayshowaslighttrend 633

to lateral segments and with values less pronounced than pri-634

maries. Theseﬁndings may provideimportantinformation in hy-635

pertrophic diseases to establish a differential diagnostic between 636

thesetwoclasses. 637

Classiﬁcation ﬁgures, although collateral in the paper, are 638

promising;clearly,discrimination betweenprimary HCMand sec-639

ondarycasesismorechallengingthanbetweenHCMandcontrols. 640

Therefore,ﬁgures relatedtothe formerproblemhavebeenlower 641

thanthoserelatedtothelatter.Alargercohortmayletusincrease 642

this number in the near future. Classiﬁcation of SLVH cases has 643

proven tobe achallengingtaskbutﬁgures,despite notbeing re-644

markable, are likely to improve when equalizing the number of 645

subjectsinthestudyorbyintroducingfeatures thattake into ac-646

countthepositionofvorticalpeaks. 647

Acknowledgments

648

This work was partially supported by the Spanish Ministerio 649

de Ciencia e Innovación under Research Grant TEC2013-44194-P, 650

theEuropeanRegionalDevelopmentFund(ERDF-FEDER)under Re-651

searchGrantTEC2014-57428-RandtheSpanishJuntadeCastillay 652

LeónunderGrantVA069U16. 653

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