A Multichannel Decision-Level Fusion Method For T Wave Alternans Detection

2017·1.1 MB·

by  Changrong Ye

REVIEWOFSCIENTIFICINSTRUMENTS88,094301(2017)
A multichannel decision-level fusion method for T wave alternans detection
ChangrongYe,1 XiaopingZeng,1,a) GuojunLi,2 ChenyuanShi,1 XinJian,1 andXichuanZhou1
1CollegeofCommunicationEngineering,ChongqingUniversity,Chongqing400044,China
2ChongqingCommunicationInstitute,Chongqing400044,China
(Received7April2017;accepted22July2017;publishedonline6September2017)
Sudden cardiac death (SCD) is one of the most prominent causes of death among patients with
cardiac diseases. Since ventricular arrhythmia is the main cause of SCD and it can be predicted
by T wave alternans (TWA), the detection of TWA in the body-surface electrocardiograph (ECG)
plays an important role in the prevention of SCD. But due to the multi-source nature of TWA, the
nonlinear propagation through thorax, and the effects of the strong noises, the information from
different channels is uncertain and competitive with each other. As a result, the single-channel
decision is one-sided while the multichannel decision is difficult to reach a consensus on. In this
paper,anovelmultichanneldecision-levelfusionmethodbasedontheDezert-SmarandacheTheory
isproposedtoaddressthisissue.Duetotheredistributionmechanismforhighlycompetitiveinfor-
mation, higher detection accuracy and robustness are achieved. It also shows promise to low-cost
instruments and portable applications by reducing demands for the synchronous sampling. Experi-
mentsontherealrecordsfromthePhysikalisch-TechnischeBundesanstaltdiagnosticECGdatabase
indicatethattheperformanceoftheproposedmethodimprovesby12%–20%comparedwiththeone-
dimensionaldecisionmethodbasedontheperiodiccomponentanalysis.PublishedbyAIPPublishing.
[http://dx.doi.org/10.1063/1.4997267]
I. INTRODUCTION a complex multi-source signal, which is usually caused by
distributed myocardial damages and arrhythmic complica-
Suddencardiacdeath(SCD)isknownforitssuddenness
tions. It suggests that the information from a single channel
andhighmortalityrate.1,2Someresearchesshowthatindevel-
isone-sidedandone-dimensional,soalltheinformationfrom
oped countries, 1 out of 1000 subjects die every year due to
differentchannelsshouldbecombinedtomakethefinaldeci-
SCD,whichisalmost20%ofalldeaths.3,4 Accordingtothe
sion. But the TWA in the body-surface ECG has inevitably
statistical results from the American Heart Association, the
been distorted during the nonlinear propagation from car-
survivalrateoftheout-of-hospitalcardiacarrestsisonly5%.5
diacmyocytestothebodysurface.Alongwiththeeffectsof
Unlesscardiopulmonaryresuscitationisperformedwithinsev-
the strong noises, the information from different channels is
eral minutes after the cardiac arrest, the chance of survival
uncertainandcompetitivewitheachother.
would be very slim.6 Along with its sudden onset and rapid
Toreachaconsensusonthefinaldecision,mostexisting
development,theriskstratificationandaccuratepredictionare
methods just get rid of partial information to reduce con-
especiallyimportantforpreventingSCD.
flict.Formostsingle-channelmethods,afixedchannelisused
The cause of most SCDs is the ventricular arrhythmia,
whiletheinformationinotherchannelsisdiscarded.Amul-
which can be predicted by T wave alternans (TWA) in the
tichannelhard-decisionstrategycalled“OR”istochooseone
body-surface electrocardiogram (ECG).7,8 The progressive
channel, which is supposed to have a higher detection accu-
increase of TWA preceding the onset of spontaneous ven-
racy than others, to make the final decision. But in essence,
triculararrhythmiashasbeenrevealedbymanyclinicalstud-
onlypartialinformationfromacertainchannelisutilized.For
ies.9,10 IthasbeendemonstratedthatTWAisoneofthemost
most multichannel methods, the information is fully used in
promising SCD predictors.11,12 As a cardiac phenomenon,
theTWAestimationbylineartransformationwhilethe“OR”
TWA refers to a periodic beat-to-beat alternating change in
strategy is performed in the decision process. Considering
the amplitude or shape of the ST-T complex in the body-
the multi-dimensional nature of TWA, these methods based
surface ECG (see Fig. 1). Technically, TWA is at the level
ontheone-dimensionalsignalmakethefinaldecisionwitha
ofseveralmicro-volts,whichishardtodiscoverbythenaked
relativelylowinformationutilizationrate.
eye. In order to detect TWA as accurate as possible, instru-
To address the challenge, a new decision-level fusion
ments with custom-designed signal processing methods are
methodbasedontheDezert-SmarandacheTheory(DSmT)is
needed.
proposedinthispaper.TheDSmTisapromisinginformation
One of the greatest challenges for the TWA detection
fusion theory that derived from the classic Dempster-Shafer
is the combination of uncertain and competitive information
theory.13 More reasonable and accurate final decisions can
from different channels to make the final decision. TWA is
be made by taking advantage of the ability of the DSmT
to combine the uncertain and even conflicting information
with decision-makingsupports. Differentfrom getting ridof
a)Electronicmail:[email protected] highlycompetitiveinformation,itutilizesthisinformationby
0034-6748/2017/88(9)/094301/11/$30.00 88,094301-1 PublishedbyAIPPublishing.
094301-2 Yeetal. Rev.Sci.Instrum.88,094301(2017)
FIG.1. The phenomenon of TWA. (a) Single channel
ECG with visible TWA (top) and alternant TWA after
removingaverageECGwaveform(bottom).(b)Super-
positionofST-Tsegments(top)andaverageTWAwave-
form (bottom). The beat-to-beat alternating shapes of
ST-TsegmentsaredefinedasTWA.Theaveragewave-
formbetweenAandBistheaverageTWAwaveform.
(ItisworthnotingthattheTWAshowninthisfigureis
muchlargerthanusualforconveniencepurpose.)
aredistributionprocessinthedecision-levelfusion.Themain methods with the decomposition algorithm such as
contribution of this study is to improve the information uti- wavelet27,28andempiricalmodedecomposition29,30werealso
lization rate to make a more reasonable decision. Due to the proposed.Forallthethreekindsofmethods,amoreimportant
channel-by-channel design, it also provides a possibility of limitationistheirsingle-channelframe.Sincetheinformation
extending the multichannel TWA detection to low-cost and fromasinglechannelisone-sidedandone-dimensional,these
portableapplications. single-channel methods always have a relatively low detec-
tionaccuracyandlessrobustdetectionperformance.Tomake
thefinaldecisioninamorecomprehensiveway,multichannel
II. RELATEDWORK schemesareneeded.
Severalmultichannelschemes31 wereproposedinrecent
Inthelastfewdecades,anumberofmethodsandschemes
years. They utilize blind source separation techniques, such
were proposed to detect TWA. From single-channel to mul-
astheprincipalcomponentanalysis(PCA)32,33 andtheperi-
tichannel schemes, these methods would be introduced as
odic component analysis (πCA),34 to concentrate the TWA
follows.
informationintooneorseveraldimensions(orcomponents).
Most single-channel methods roughly fall into three
Somemethodsusetensortoexploretherelationshipbetween
classes.14 (1) The methods in the first class are based on the
beats and channels.35,36 After the linear transformation, the
short-time Fourier transform. Most early methods, such as
consistent information is mainly concentrated into the same
thespectralmethod,15,16thecomplexdemodulationmethod,17
dimension while highly competitive information is mainly
the Poincare´ map distance method,18 the projection in 2-
transformedintodifferentones.Thiskindofmethodactually
periodicity space method,19 and Student’s t-test method,20
showssubstantialimprovementofdetectionaccuracyinsimu-
belong to this class. Although these methods have a high
lationstudies.31Butinthefinaldecisionprocess,mostofthem
sensitivity, they usually require long data (about 128 beats),
adopt a one-dimensional decision method called “OR.” This
resulting in a low temporal resolution. Since the length of
decisionmethodjustchoosesthesinglechannelordimension
some transient TWA can reach as small as seven beats, the
with the maximum detection statistic to make the final deci-
false negative rate of these methods is relatively high. (2)
sion.Sothecompetitiveinformationisstilldiscardedtoreach
Themethodsfromthesecondclassareallbasedonthesign
aconsensusonthefinaldecision.Besides,thelineartransfor-
change counting method. This class includes the Rayleigh
mationwillinevitablyintroduceerrors,whichwillbefurther
testmethod20andthecorrelationmethod.21–23Thesemethods
deliveredtothedecisionprocess.Sotheymayevenmakethem-
use a strategy based on the time-domain observation of the
selveslessrobust,especiallywhenthealternans-to-noiserate
sign changes in a beat-to-beat series. Although these meth-
(ANR)islow.Inordertoutilizethecompetitiveinformation
odshaveincreasedthetemporalresolution,theyalsobecome
from different channels or dimensions in a more reasonable
more sensitive to noises and increase the false alarm rate.
andcomprehensiveway,newmultichanneldecisionmethods
(3) The methods from the third class are nonlinear filtering
areneeded.
methods.Tworepresentativemethodsofthisclassarethemod-
ified moving average method24 and the Laplacian likelihood
ratio(LLR)method.14,25,26 Theyutilizevariousnonlinearfil-
III. METHOD
ters to identify and remove outliers in signal. This enables
themtopartiallyeliminatenoisesandusuallyhavebetterper- Thegeneralblockdiagramoftheproposedmultichannel
formance in the simulation study. But since most nonlinear decision-levelfusionmethodisshowninFig.2.Itconsistsof
criteriaaredesignedarbitrarily,theperformanceofthesemeth- fourstages:thesignalpreprocessing,thecharacteristicparam-
odsvariesfordifferentinstrumentsanddifferentclinicalset- eter extraction, the decision-level fusion, and the decision
tings.Someothermethodsthatcombinethesesingle-channel making.
094301-3 Yeetal. Rev.Sci.Instrum.88,094301(2017)
FIG.2. Generalblockdiagramoftheproposeddecision-levelfusionmethod(multi-DSmT).Theboldlinesindicatethattheircorrespondingdataflowsconsist
ofdatafrommultiplechannels.
A. Signalpreprocessing windowwillcontainW consecutivebeatsthatarestartedfrom
the[(l−1)×D+1]thbeat.Inthismethod,J=32andD=1are
Beforethedetection,ST-Tcomplexesshouldbeextracted
adoptedandthecorrespondingnumberoftheanalysiswindow
fromtherawmultichannelECGduringthesignalpreprocess- (cid:12)
willbeL=M 31.Itisworthnotingthatthehighlyoverlapped
ing stage. As summarized in Ref. 14, four steps would be
analysiswindows(smallD)areusuallyusedinthetheoretical
taken in this stage. They are the linear filtering, the baseline
analysisandthesimulationstudytoobtainabetterrepresen-
cancellation,theST-Tsegmentation,andthedatareduction.
tationoftheTWAevolutionatthecostofalargeramountof
Linear filters would be applied to the raw multichan-
computation.Inclinicalapplications,therewillbeatrade-off
nel ECG X to reject out-of-band noises. A low-pass filter
betweenthetemporalresolutionandtheamountofcomputa-
with a 100 Hz cutoff frequency and a notch filter with a
tion, usually resulting in a much larger D. Accordingly, the
50/60Hzcenterfrequencyareusedinthisscheme.Thebase-
3-wayST-TtensorYcanberearrangedasa4-waytensorZ,
linewanderisthenremovedwithacubicsplineinterpolation
whosesizeisP×J×K×Landitselementz indicatesthe
technique.37 p,j,k,l
pth sample of the jth ST-T complex in the kth channel from
TheST-Tsegmentationisconductedinthreesteps.First,
thelthanalysiswindow.
allbeatsarealignedbyRpeaksandtheirmultichannelaver-
The average energy of noises will be estimated after
agewaveformisobtained.Second,amultichanneldelineation
removingthebackgroundECGandthepotentialTWAcom-
algorithmbasedonECGslopecriteria38,39wouldbeappliedto
ponent.ThebackgroundECGcanberemovedbysubtracting
determinethelimitsoftheST-Tcomplexbasedontheaverage
theaveragewaveformas
beat waveform. Finally, the corresponding segments in each
beatsareextractedandputtogetherintoaN×M×KST-Tten- 1(cid:88)J
sorX,whereNisthenumberofsamplesoftheST-Tsegment, z(cid:48) =z − z . (1)
p,j,k,l p,j,k,l J p,j,k,l
M is the number of beats, and K is the number of channels. j=1
It is worth noting that for certain ECG record, the length of
ThepotentialTWAcomponentcanberemovedas
theST-Tsegmentisfixedanddeterminedbythedelineation
algorithm.FordifferentECGrecords,thelengthoftheST-T z(cid:48)(cid:48) =z(cid:48) −aˆ ·(−1)j, (2)
p,j,k,l p,j,k,l p,k,l
segmentmaybetotallydifferent.
Besides,toreducethenumberofsamplestobeprocessed where
(cid:40) (cid:41)
whilepreservinginformationaboutTWA,thedatareduction aˆ =median z(cid:48) ·(−1)j|J (3)
wouldbedonebyadecimationprocess.SincetheTWAwave- p,k,l p,j,k,l j=1
formismostlyconcentratedbetween0.3Hzand15Hz,40the istheestimationofthepotentialTWAwaveformbasedonthe
samplingfrequencyofthedecimatedsignalshouldbeabove modelinRefs.14,25,and26withLaplaciannoise.Thenthe
30Hz.Inthismethod,eachmodel-1fiberx (ST-Tcomplex) energyofnoisescanbeestimatedas
:mk
ofXwhosesamplingfrequencyis1kHzwouldbedecimated
byafactorofQ=32,whichmakesthesamplingfrequencyof eB = 1 (cid:88)J (cid:88)P (z(cid:48)(cid:48) )2. (4)
theoutputsignaltobe31.25Hz.Theoutputofthedatareduc- k,l JP p,j,k,l
j=1 p=1
tioncanbemarkedasP×M×K tensorYwhereP=(cid:98)N/Q(cid:99).
The element y of Y indicates the pth sample of the mth AsanalyzedinRef.14,theenergyat0.5cycles-per-beat
p,m,k
ST-Tcomplexfromthekthchannel. (cpb)ofthepowerspectrumofthebeat-to-beatserieszp:klfrom
acertainchannelandacertainanalysiswindowisregardedas
themixtureofTWAandnoises.Itsaveragevalueduringthe
B. Characteristicparameterextraction
ST-Tsegmentcanbeestimatedas
Before fusion, the relevant characteristic parameters for
eachchannelwouldbeextractedfirst.Inthismethod,theesti- 1 (cid:88)P (cid:88)J 2
mations of average energy of TWA and the noises in each eMk,lix=JP  zp,j,k,l ·(−1)j . (5)
channelarecalculated. p=1 j=1 
Duetothetransient,non-stationarynatureofTWA,each
detection must involve a limited set of neighbor beats. So a ThentheaverageenergyofTWAforacertainchannelanda
beat-by-beat sliding window analysis strategy14 is used. By certainanalysiswindowcanbecalculatedas
applyingthisstrategy,L=(cid:98)(M−J)/D(cid:99)+1analysiswindows
wloiclaltbeedcionntshtreucwtaevde,fworhmeredeMliniesatthioenn,uJmibserthoefabneaaltysstihsawtainre- eAk,l= 0, forekM,lix≤eBk,l, (6a)
eMix−eB , foreMix>eB . (6b)
dow length, and D is the shift parameter. The lth analysis k,l k,l k,l k,l
094301-4 Yeetal. Rev.Sci.Instrum.88,094301(2017)
C. Decision-levelfusion D. Decisionmaking
After the channel-by-channel characteristic parameter After the fusion process, the decision making should be
extraction, a decision-level fusion method derived from the done to decide about the presence (H ) or absence (H ) of
1 0
proportional conflict redistribution rule no. 6 (PCR6) from TWAinthemultichannelECG.
theDSmT41isperformedtofusethiscompetitiveinformation Similartothesingle-channeldecisionmakingprocess,14
from different channels in a reasonable and comprehensive thedetectionstatisticsarecalculatedas
way. eA
Within the framework of the DSmT, three main steps, Sl= elB. (11)
including the basic belief assignment (BBA) extraction, the l
fusion, and the probabilistic transformation, should be done Consideringthetransient,non-stationarynatureofTWA,the
foracompleteDSmTfusionprocess.ButintheTWAdetec- finaldetectionstatisticisobtainedby
tion,sincetheformatofthecharacteristicparametershasbeen S=max{S |L }. (12)
unifiedandthefinaldecisionwouldbemadebasedonadetec- l l=1
tionstatisticratherthanaprobability,onlythefusionprocess Finally,thedecisionmakingcanbedoneas
wcailllledbePCdoRn1e-PinCRth6ishamveethboeedn. pInrotphoeseDdS.4m1TF,rosmixtfhuesPioCnRr1ulueps SH≶0γ, (13)
H1
tothePCR6,oneincreasesontheonehand,thecomplexityof
where γ is the threshold that will be determined experimen-
therules,butontheotherhand,oneimprovestheaccuracyof
tally.
the redistribution of conflicting information. In this method,
since all experiments are conducted in a non-real-time way,
the fusion method is designed by following the PCR6 to do IV. EXPERIMENTSETTINGANDDATASET
thedecision-levelfusion.
Both simulated and real multichannel ECG records are
The main idea behind the PCR6 is redistributing the
usedtoevaluatetheperformanceoftheproposedmethod.How
conflictinginformationtohypothesestomakeamorereason-
theseECGrecordsaresimulated,recorded,andpickedoutis
ableandcomprehensivedecision.Whentheconflictbetween
shownasfollows.
channels is minor, it has similar fusion results to the clas-
sic Dempster-Shafer theory.13 When the conflict becomes
A. SimulatedmultichannelECGrecords
major, more reasonable decisions can be made by follow-
ingthePCR6.MoredetailsaboutthePCR6canbefoundin SimulatedECGrecordsandthecorrespondingsimulation
Ref.41. studyarevital.ThatisbecausetheactualpresenceofTWAina
In the TWA detection, since the problem has only two realrecordisunknownintheclinicalenvironment.Thus,since
potential hypotheses, present (H1) or not (H0), the single- most parameters (ANR, TWA dimensionality, and the wave-
channelcharacteristicparameterscanbefusedby form) are known as prior information of simulated records,
eX=(cid:89)K eX + (cid:88) (cid:81)k∈Φ1eXk,l(cid:81)k∈Φ2eYk,l(cid:80)k∈Φ1eXk,l, (7) adeMteocntitoenCpaerrlfoorsmimaunlcaet.ionapproachisappliedtoevaluatethe
l k,l (cid:80) eX +(cid:80) eY
k=1 Φ1,Φ2 k∈Φ1 k,l k∈Φ2 k,l The synthesis process of the multichannel ECG record
wheresetsΦ (cid:44)∅andΦ (cid:44)∅satisfy with a high degree of realism is shown in Fig. 3. For differ-
1 2
entsimulationsetups,thesimulatedrecordsarewithdifferent
Φ ∩Φ =∅, (8)
1 2 ANRs and different types of the TWA waveform. With the
Φ1∪Φ2={1,2,...,K}, (9) same simulation setup, the simulated records are added with
different realizations of real recorded noise. The clean ECG
and
(cid:40) A, forY=B, (10a) recordsfromthehealthypeopleinthePhysikalish-Technische
X= Bundesanstalt(PTB)diagnosticdatabase42–44areusedtosyn-
B, forY=A. (10b)
thesizethebackgroundECG.Therealrecordednoiseusedin
FIG.3. Generalblockdiagramofthesimulationsetup.
094301-5 Yeetal. Rev.Sci.Instrum.88,094301(2017)
FIG.4. General block diagram of the
TWAwaveformextraction.
synthesizingisthemuscularactivitynoisefromtheMIT-BIH whereΨ =ΨΛandΛisadiagonalmatrixthatsatisfies
TR
Noise Stress Test Database.42 More details about the noise
(cid:102) (cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32) F (cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32) (cid:103)
(cid:122) (cid:125)(cid:124) (cid:123)
record can be found in Ref. 45. It is worth noting that the diag(Λ)= 1,1,...,1,0,...,0 . (17)
muscularactivitynoiserecordalsocontainselectrodemotion
noiseinevitably,whichmeansthatitisthemostrealisticnoise With this TWA synthesis scheme, not only the dimension-
recordamongothersinthedatabase.Therealrecordednoise ality of the TWA waveform is considered but also the rel-
is first resampled from 360 Hz to 1000 Hz. With the same ative relationship between TWA in different channels is
simulationsetup,segmentsofnoisewiththesamelengthand reserved.
randomoffsetsareusedtorealizedifferentsimulatedrecords. Itisworthnotingthatthemulti-dimensionalTWAisused
SincethebackgroundECGisaninterferencethatcanbeeasily to mimic the multi-source nature of TWA and the nonlin-
removed,thenotionoftheANRiswidelyintroducedtoreflect ear propagation. The multiple sources of TWA are mainly
the level of noise in the simulation study.25,46,47 It is defined determinedbyspecificcausesandtheirpositions,whichvary
astheaveragedrelationshipbetweenthealternantwavepower frompersontoperson.Thenonlinearpropagationalsovaries
andthenoisepower, for many factors such as the health condition, the position
M(cid:80)k=K(cid:80)p=Pa2 error of the electrodes, and even the posture during record-
ANR=10log k p p,k, (14) ing. So it is hard to describe them quantitatively. However,
(cid:80)k=K(cid:80)n=N w2 withtheassumptionoflinearmixture,thesecharacteristicscan
k n n,k
be regarded as multi-dimensional dispersions. So the multi-
where a and w are the elements of the TWA wave-
p,k n,k dimensionalTWAextractedfromrealrecordsareusedinthe
form A and the noise W, respectively, in Fig. 3, and M
experiments.
is the number of beats that replicated in a simulation ECG
record.
B. RealECGrecordswithdiagnoses
TherearethreekindsofTWAusedinthesimulationstudy.
AllthesethreekindsofTWAwithdifferentdimensionality(F SincesomefeaturesintherealECGarehardtobefully
= 1, 3, 8) are simulated as in Fig. 4. The 1-D TWA is the described by the linear mixture model used in the simula-
most common setup that is used in TWA simulation studies. tionstudy,theexperimentsonrealECGrecordsarealsovery
The 3-D TWA is a result of the compromise between con- important. It is worth noting that the TWA has a transient
tentsofTWAandnoises.Becauseformostcardiacsignals,the feature, which indicates that TWA does not always exist in
3-Drepresentationaccountsfor80%–90%ofthepowerofthe real ECG records. But as a risk stratification marker of the
body-surface potentials.48,49 Besides, since only 8 leads are arrhythmiathathasbeenprospectivelydemonstratedinmore
independentinthetraditional12-leadsetup,the8-DTWAis than 7200 patients,50 the performance of detection methods
alsousedinthesimulationstudytodescribetheTWAasfully couldbeassessedstatisticallyinsomedegreebydistinguish-
aspossible. ing arrhythmia patients from health subjects. Besides, the
TheF-DTWAwaveformisestimatedasinEq.(3)channel situation in the clinical environment is much more complex
by channel, after the decomposition of PCA and the signal than simulation. When facing real ECG records, especially
reconstructionbythetruncatedinversePCA.Letthemaximum forthosefrompatients,morebiasbetweenphysicaltruthand
likelihoodestimationofthealternantwaveformestimationby simulation setups may exist, which will lead to completely
Eq.(3)beA˜.ThePCAdecompositionoftheestimatedTWA different detection results. Therefore, the detection results
waveformcanbeexpressedas on real records are also important references for the validity
S=ΨTA˜, (15) evaluation.
As an example of application to real records, the TWA
andthentheF-DTWAisreconstructedby
detection was performed on one set of real records from
A=Ψ S, (16) thePhysikalisch-TechnischeBundesanstalt(PTB)diagnostic
TR
TABLEI. Implementationdetailsforthemethods.
Method Lineartransformation One-dimensionalanalysis Multichanneldecision
Single-v3 None Laplacianlikelihoodratio(LLR) None(fixedleadv3)
Multi-OR None Laplacianlikelihoodratio(LLR) Hard-decision(OR)
Multi-πCA πCA Laplacianlikelihoodratio(LLR) Hard-decision(OR)
Multi-DSmT None Characteristicparameterextraction Decision-levelfusion
094301-6 Yeetal. Rev.Sci.Instrum.88,094301(2017)
database.42–44 This database was provided by the National of±16.384mVwith15channels,whichinclude12channels
MetrologyInstituteofGermany.Theserecordswerecollected from the conventional leads and 3 channels from the Frank
by Oeff from patients and healthy volunteers with detailed XYZleads.
clinical summaries. Each record was digitized at 1000 sam- All the real records that are used in these experiments
ples per second (Hz), with a 16 bit resolution over a range were picked out from this database as follows. To avoid the
influencefromdifferentcauses,onlyrecordsfromthemyocar-
dialinfarctionpatients(368records)andthehealthycontrols
(80records)areused.Butnotalltheserecordsaresuitablefor
TWAdetection.Someofthem(20records)havetoofewbeats,
someofthem(9records)havestronginterference,suchasarti-
ficial impulses from implantable cardioverter defibrillators,
huge beat-to-beat variability, consecutive anomalous beats,
andelectrodedetaching,andsomeothers(27records)arejust
toonoisytoaccomplishthedelineation.Iftheserecordsappear
in clinical trails, re-recording is the most common approach
todealwiththissituation.Inthisexperiment,alltheserecords
willbediscardedandtheremaining392recordsareclassified
intotwogroups.
1. Myocardial infarction group: This is the experimental
groupthatiscomposedof316recordswith“myocardial
infarction”inaffiliateddiagnosis.
2. Healthy control group: This is the control group that
is composed of 72 records with “healthy control” in
affiliateddiagnosis.Alltheserecordsarecollectedfrom
healthy volunteers who have never had a heart-related
disorderordisease.
V. EXPERIMENTRESULTS
Totally four schemes were performed and compared in
theseexperiments.TheyarethestandardsinglechannelLLR
schemewithleadv3(single-v3),theLLRwith“OR”strategy
(multi-OR),themultichannelschemebasedonπCAproposed
inRef.34(multi-πCA),andtheproposedmultichannelmethod
inthispaper(multi-DSmT).Themaindifferencesamongthese
methodsareshowninTableI.Theresultsoftheseexperiments
areshownasfollows.
A. Simulationstudy
In the simulation study, the detection performances of
different methods were evaluated and compared by detec-
tion rates with different ANRs. In a detection problem, the
detectionperformanceisusuallyjointlyevaluatedbythetrue
TABLEII. TWAdetectionresultsoftheexperimentsonthesimulatedECGs
withdifferenttypesofTWA(1-D/3-D/8-D).
TWA
Parameter Method 1-D 3-D 8-D
Equivalent Single-v3 −17.49 −15.81 −15.78
minimumANR Multi-OR −18.19 −18.16 −18.28
R(dB) Multi-πCA −21.88 −20.85 −20.61
Multi-DSmT −22.89 −22.73 −22.79
MaximumPD vs.single-v3 71.64 82.28 82.64
FIG.5. DetectionresultsPD(top)andcorrespondingimprovementbetween improvementof vs.multi-OR 68.44 67.28 66.52
the multi-DSmT and other three methods (bottom) of experiments on multi-DSmT(%) vs.multi-πCA 15.38 32.94 37.18
simulatedrecordswith(a)1-D,(b)3-D,and(c)8-DTWA.
094301-7 Yeetal. Rev.Sci.Instrum.88,094301(2017)
positiverate(TPR,i.e.,detectionrateP )andthefalsepositive
D
rate(FPR,i.e.,falsealarmrateP ).Inthissimulationstudy,
FA
theTPR/FPR,alsocalledsensitivity/specificity,isdefinedas
theproportionofrecordswithpositivedetectionresultswhile
all the tested records are with/without TWA. To compare
the performance in a more intuitive way, the threshold that
makes the FPR P = 0.05 is first calculated, and then the
FA
detectionrateiscalculatedwiththisthreshold.Foreachsim-
ulationsetup(specificANRandspecifictypeofTWA),5000
recordsweresimulated.Thedurationofeachrecordis33beats
(M =33).
The resulting detection rates with different ANRs are
shown in Fig. 5 (top) and the differences between the multi-
DSmT and the other three methods are shown in Fig. 5
(bottom). The equivalent minimum ANR and the maximum
P improvement of the multi-DSmT are also calculated and
D
shown in Table II. The equivalent minimum ANR is defined
as
R=r− ∫−a∞(PD(ξ)−PFA)dξ, (18)
1−P
FA
where P (ξ) is the detection rate when the ANR is ξ and r
D
istheANRthatisbigenoughtomakeP (r)=1.According
D
tothisdefinition,alowerRwouldindicateabetterdetection
performance.
To compare detection results of the records simulated
with specific simulation setup, the receiver operating char-
(cid:12)
acteristic (ROC) curves (ANR = 20 dB) are calculated and
shown in Fig. 6. The ROC curve is drawn by linking points
[P (γ),P (γ)] where the threshold γ varies from 0 to +∞.
FA D
The ROC curve can be further evaluated by the maximum
Youden’sJstatistic(J )andtheareaundercurves(AUC),
max
whicharealsocalculatedandshowninTableIII.IntheTWA
detectionproblem,J meansthemaximumpossiblediffer-
max
ence between P and P with certain threshold γ. Besides,
D FA
thehighAUCindicatesthelowsensitivitytothethresholdγ,
whichwillbeagreathelptothedeterminationofthethreshold
γinclinicaltrails.
As the TWA information from different dimensions
becomesmorecompetitive(TWAfrom1-Dto8-D),thediffer-
encesofdetectionperformanceofthemethodsbecomemore
evident.Whentherecordsaresimulatedwiththe1-DTWA, (cid:12)
FIG.6. ROCcurvesofdetectionresultsonsimulatedrecords(ANR= 20
mostinformationisconsistentandcanbeexpressedintoone
dB)with(a)1-D,(b)3-D,and(c)8-DTWA.
dimensionbythelineartransformation.Sothedetectionper-
formance of the multi-DSmT and the multi-πCA is almost
the same [see Figs. 5(a) and 6(a)]. When the 8-D TWA is proposedmulti-DSmTshowsmoreaccurateandmorerobust
used, the information from different channels become more performance.
competitive with each other. By utilizing the highly com- The slope of each detection curve in Fig. 5 reflects the
petitive part of the information rather than discarding it, the robustnesstonoise.Itcanbeobservedthatthemulti-πCAis
(cid:12)
TABLEIII. FeatureparametersofROCcurvesofsimulationdetectionresultswithANR= 20DB.
MaximumYouden’sJstatistics(%) AreaundercurvesAUC(%)
Methods 1-DTWA 3-DTWA 8-DTWA 1-DTWA 3-DTWA 8-DTWA
Single-LLR 35.46 24.76 23.98 73.85 65.85 65.45
Multi-OR 48.74 47.88 49.00 81.18 80.80 81.54
Multi-πCA 80.36 69.22 65.56 96.52 92.31 90.60
Multi-DSmT 84.94 83.58 83.86 97.65 97.35 97.38
094301-8 Yeetal. Rev.Sci.Instrum.88,094301(2017)
FIG.7. ROC curves (top) and corre-
spondingYouden’sJstatistic(bottom)
ofdetectionresultsonrealrecordsfrom
thePTBdatabase.(a)12channelsand
(b)15channelsare,respectively,used
intheseexperiments.
TABLEIV. TWAdetectionresultsofrealECGrecordsfromthePTBdatabase.
Detectionresultsa ROCcurves(%)
InvolvedECGlead(s) Methods Healthycontrol Myocardialinfarction Jmax AUC S95
Leadv3 Single-LLR (3.02±2.10)×10−2 (4.86±6.60)×10−2 23.25 65.16 11.01
Standardleads Multi-OR (7.49±4.05)×10−2 (9.70±8.29)×10−2 17.95 61.35 10.00
(12channels) Multi-πCA (1.23±0.49)×10−1 (1.55±1.34)×10−1 18.49 60.73 10.63
Multi-DSmT (1.55±1.11)×10−4 (2.59±7.61)×10−4 31.48 67.98 15.63
Standardleads+ Multi-OR (7.94±4.09)×10−2 (1.06±1.10)×10−1 21.34 62.75 11.33
FrankXYZleads Multi-πCA (1.44±0.59)×10−1 (1.76±1.38)×10−1 14.84 58.36 11.33
(15channels) Multi-DSmT (1.59±1.10)×10−4 (2.55±6.43)×10−4 35.63 70.40 18.23
aExpressedasmean±onestandarddeviation.
moresensitivetonoisethanthemulti-DSmT.Thatisbecause is too small and the threshold γ is mainly determined by no
thelineartransformationisdeterminedbystatisticalparame- more than 4 records (5% of 72), which is more likely to be
ters,whoseerrorswillincreasewhennoisesbecomestronger. influencedbyoutliers.
The output TWA components may be harmed by the biased As the extra channels are used (from 12 channels to 15
linear transformation. These errors will be delivered to the channels)intheexperiments,itcanbeobservedthatthemulti-
followinganalysisanddecisionprocess,resultinginrelatively DSmT gets better performance while the multi-πCA gets
lowrobustnesstonoises. worse.Thatisbecausetheextrachannelsmaketheinforma-
tionmorecompetitive.Somoreinformationwillbediscarded
B. Experimentsonrealrecords by multi-πCA, resulting in a lower information utilization
and a lower detection accuracy. On the contrary, the multi-
Forrealrecords,theirANRsandtheTWAineachchan-
DSmTgetsbetterdetectionperformancebyutilizingtheextra
nelaredifferentandunknown,sothedetectionresultsareonly
information.
evaluatedbytheROCcurve,whichhasbeenshowninFig.7
(top). The corresponding Youden’s J statistics are shown in
Fig.7(bottom).Thesamefourdetectionmethodsasevaluated
VI. DISCUSSION
inthesimulationstudywereperformedonthetwogroupsof
therealECGrecords.Furthermore,thedetectionresults,the According to the experimental results, detection accu-
J , and the AUC of ROC curves are also calculated and racyiscloselyrelatedtohowhighlycompetitiveinformation
max
shown in Table IV. In clinical trails, the low FPR P usu- is dealt with. Due to the effect of the noises and the multi-
FA
ally has a higher priority than the TPR P , so a parameter dimensionalnatureofTWA,uncertainandcompetitiveinfor-
D
calledS proposedinRef.25isalsocalculatedandshownin mationisinevitable.Toreachaconsensusonthefinaldecision,
95
TableIV.Itisworthnotingthattheaccuracyandthereliability most existing methods discard partial information to reduce
of S obtained in these experiments are relatively low. That conflict, resulting in the loss of important information. By
95
isbecausethenumberofrecordsinthehealthycontrolgroup utilizing this competitive information in a more reasonable
094301-9 Yeetal. Rev.Sci.Instrum.88,094301(2017)
and comprehensive way, the proposed method can achieve The proposed method is far from perfect and further
more accurate detection results and more robust detection work is needed. According to the clinical experience and
performance. the experiments on real records, we found that the TWA
The proposed decision-level fusion method cannot be distribution among channels is not completely random. For
directlyappliedafterthelineartransformationssuchasπCA. the single-channel method, some channels (from v1 to v3)
Thatisbecausethelineartransformationisaimedatimprov- have a higher detection accuracy than the other channels. It
ing the ANR of a certain dimension at the cost of ANR suggests that the detection results from different channels
deteriorationinotherdimensions,whichwillmaketheinfor- have different confidence, and equal treatment to them in
mation between dimensions more competitive. When one- the fusion process is not fitting. Thus a weighted decision-
dimensional decision method such as hard-decision “OR” levelfusionmethodsuchastheDSmTwithanalytichierarchy
method is applied, it will improve the performance greatly process (DSmT-APH)52 may be able to further improve the
by just choosing a certain dimension with higher ANR. But detection performance. How to measure the weight coeffi-
whentheproposeddecision-levelfusionmethodisappliedto cientsfordifferentchannelswillbethefocusinthefollowing
makethefinaldecision,theANRsinallchannelsarerequired researches.
tobeashighaspossible.Sothedirectcombinationofthelin-
ear transformation and the proposed method will result in a
VII. CONCLUSION
verylowdetectionaccuracy.
It is worth noting that the performance of multi-πCA is A novel multichannel decision-level fusion method for
much worse than it is in the simulation study. There are two TWA detection was proposed. It was compared to single-
possible explanations for this strange result. First, the real channelandmultichannelmethodsinboththesimulationstudy
recordsusedintheexperimentsarelimited.Theycannotrepre- and the experiments with real ECG records. The simulation
sentallsituationsinclinicaltrails.MorerealECGrecordsmay studyshowedthattheproposedmethodcouldutilizethecom-
be needed to get the more accurate assessment of the detec- petitiveinformationfromdifferentchannelsanddimensionsin
tionperformance.Second,itmaybecausedbytheerrorsfrom amorereasonableandcomprehensiveway.Bytakingallchan-
thelineartransformation,whichrequireslinearmixtureofall nelsintoconsiderationinthedecisionprocess,theinformation
sources and each component should be stationary. However, utilizationisimproved.Withthehigherinformationutilization
theTWAinthebody-surfaceECGisanon-stationarysignal rate,theproposedmethodshowedahigherdetectionaccuracy
andhasbeendistortedbyanonlinearpropagationthroughthe and stronger robustness to noises. The results of the experi-
thorax. These differences may become more evident in the mentswithrealECGrecordsshowedthattheproposedmethod
experiments with real records and deteriorate the detection also showed higher accuracy in distinguishing patients with
performance. myocardialinfarctionfromhealthypeoplethroughtheTWA
Somedisadvantagesoftheproposedmethodshouldalso detection. Since the proposed method is designed to detect
be noted. Since the single-channel analysis results are non- TWAchannel-by-channel,italsoreducesthedemandsonthe
linearlyfused,themostobviousdisadvantageisthatnoTWA samplingprocessoftheECGrecorder.
estimation has been done in the proposed method. If the
globalTWAamplitudeorwaveformisrequired,theadditional
ACKNOWLEDGMENTS
methodforTWAestimationisneeded.
Anotherdisadvantageistheincreasedcomputation.Com- This work was supported in part by the National Natu-
paredwiththehard-decision“OR”method,theredistribution ral Science Foundation of China (Grant Nos. 61671452 and
processforcompetitiveinformationwillbringextracomputa- 61471073) and Natural Science Foundation of Chongqing
tion.However,sincethespeedofECGbeatsisrelativelyslow, (GrantNos.Cstc2014pt-sy40003,Cstc2015jcyjBX0078,and
real-time TWA detection by the multi-DSmT can be easily Cstc2016jcyjA0556).
achievedbyageneral-purposecomputerbasedontheanalysis
windowschemeusedinthisstudy(W =32,D=1).Inprac- 1C. M. Albert, C. U. Chae, F. Grodstein, L. M. Rose, K. M. Rexrode,
ticalapplications,ifthecomputingpowerisverylimited,the J. N. Ruskin, M. J. Stampfer, and J. E. Manson, “Prospective study of
suddencardiacdeathamongwomenintheUnitedStates,”Circulation107,
calculationcanbereducedbyusingalargershiftparameterD
2096–2101(2003).
oftheslidinganalysiswindowatthecostofalowertemporal 2T.W.SmithandM.E.Cain,“Suddencardiacdeath:Epidemiologicand
resolution. financial worldwide perspective,” J. Interventional Card. Electrophysiol.
To further improve the situation, the implementation 17,199–203(2006).
3D.L.HoyertandJ.Xu,“Nationalvitalstatisticsreports,”inCentersfor
code has been optimized for the TWA detection. Since the
DiseaseControlandPrevention(DHHS,2012),Vol.21.
number of hypotheses and input channels are fixed and 4Z. J. Zheng, J. B. Croft, W. H. Giles, C. Ayala, K. J. Greenlund,
known before fusion in the TWA detection, the addressing N.L.Keenan,L.Neff,W.A.Wattigney,andGeorgeMensah,“State-specific
indices are identical in each fusion. Based on this fact, all mortalityfromsuddencardiacdeath–UnitedStates,1999,”Morb.Mortal.
Wkly.Rep.56,123(2002).
indices can be calculated and stored once and for all before
5D. Mozaffarian, E. J. Benjamin, A. S. Go, D. K. Arnett, M. J. Blaha,
fusion. So the computation amount would be reduced at the M.Cushman,S.R.Das,S.D.Ferranti,J.P.Despre´s,andH.J.Fullerton,
cost of more random access memory (RAM) usage. Com- “Heartdiseaseandstrokestatistics—2016update,”Circulation133,e38
pared with the general implementation method proposed in (2015).
6R.O.Cummins,M.S.Eisenberg,A.P.Hallstrom,andP.E.Litwin,“Survival
Ref. 51, this customized method reduces the computation
ofout-of-hospitalcardiacarrestwithearlyinitiationofcardiopulmonary
dramatically. resuscitation,”Am.J.Emerg.Med.3,114–119(1985).
094301-10 Yeetal. Rev.Sci.Instrum.88,094301(2017)
7R. M. John, U. B. Tedrow, B. A. Koplan, C. M. Albert, L. M. Epstein, 28V. Nannaparaju and S. Narasimman, “Detection of T-wave alternans
M.O.Sweeney,A.L.Miller,G.F.Michaud,andW.G.Stevenson,“Ven- in ECGs by wavelet analysis,” Procedia Mater. Sci. 10, 307–313
triculararrhythmiasandsuddencardiacdeath,”TheLancet380,1520–1529 (2015).
(2012). 29M.A.Hasan,V.S.Chauhan,andS.Krishnan,“Beat-to-beatT-wavealter-
8F.J.Gimeno-Blanes,M.Blanco-Velasco,O´.Barquero-Pe´rez,A.Garc´ıa- nansdetectionusingtheensembleempiricalmodedecompositionmethod,”
Alberola, and J. L. Rojo-A´lvarez, “Sudden cardiac risk stratification Comput.Biol.Med.77,1–8(2016).
with electrocardiographic indices-a review on computational process- 30M.Blanco-Velasco,R.Goya-Esteban,F.Cruz-Rolda´n,A.Garc´ıa-Alberola,
ing, technology transfer, and scientific evidence,” Front. Physiol. 7, 82 and J. L. Rojo-A´lvarez, “Benchmarking of a T-wave alternans detec-
(2016). tionmethodbasedonempiricalmodedecomposition,”Comput.Methods
9V.Shusterman,A.Goldberg,andB.London,“UpsurgeinT-wavealternans ProgramsBiomed.145,147–155(2017).
andnonalternatingrepolarizationinstabilityprecedesspontaneousinitiation 31P.Laguna,J.P.M.Corte´s,andE.Pueyo,“Techniquesforventricularrepo-
ofventriculartachyarrhythmiasinhumans,”Circulation113,2880–2887 larizationinstabilityassessmentfromtheECG,”Proc.IEEE104,392–415
(2006). (2016).
10R.K.Sandhu,O.Costantini,J.E.Cummings,S.Poelzing,D.S.Rosenbaum, 32V. Monasterio, P. Laguna, and J. P. Mart´ınez, “Multilead estimation
andK.J.Quan,“IntracardiacalternanscomparedtosurfaceT-wavealter- of T-wave alternans in the ECG using principal component analysis,”
nansasapredictorofventriculararrhythmiasinhumans,”HeartRhythm5, in 2008 16th European Signal Processing Conference (IEEE, 2008),
1003–1008(2008). pp.1–5.
11D. M. Bloomfield, J. T. Bigger, R. C. Steinman, P. B. Namerow, 33V.Monasterio,P.Laguna,andJ.P.Mart´ınez,“MultileadanalysisofT-wave
M.K.Parides,A.B.Curtis,E.S.Kaufman,J.M.Davidenko,T.S.Shinn, alternans in the ECG using principal component analysis,” IEEE Trans.
andJ.M.Fontaine,“MicrovoltT-wavealternansandtheriskofdeathorsus- Biomed.Eng.56,1880–1890(2009).
tainedventriculararrhythmiasinpatientswithleftventriculardysfunction,” 34V. Monasterio, G. D. Clifford, P. Laguna, and J. P. Mart´ınez, “A
J.Am.Coll.Cardiol.47,456–463(2006). multilead scheme based on periodic component analysis for T-wave
12T.Chow,S.Saghir,C.Bartone,M.Goebel,J.Schneider,T.Booth,andP. alternans analysis in the ECG,” Ann. Biomed. Eng. 38, 2532–2541
S.Chan,“UsefulnessofmicrovoltT-wavealternansonpredictingoutcome (2010).
inpatientswithischemiccardiomyopathywithandwithoutdefibrillators,” 35G.Goovaerts,C.Varon,B.Vandenberk,R.Willems,andS.VanHuffel,
Am.J.Cardiol.100,598–604(2007).
“Tensor-baseddetectionofTwavealternansinmultileadECGsignals,”
13G.Shafer,“Amathematicaltheoryofevidence,”Technometrics20,106
inComputinginCardiologyConference(CinC),2014(IEEE,2014),pp.
(1978).
185–188.
14J.P.Mart´ınezandS.Olmos,“MethodologicalprinciplesofTwavealternans 36G. Goovaerts, B. Vandenberk, R. Willems, and S. Van Huffel, “Tensor-
analysis:Aunifiedframework,”IEEETrans.Biomed.Eng.52,599–613
based detection of T wave alternans using ECG,” in 2015 37th Annual
(2005).
InternationalConferenceoftheIEEEEngineeringinMedicineandBiology
15J.M.Smith,E.A.Clancy,C.R.Valeri,J.N.Ruskin,andR.J.Cohen,
Society(EMBC)(IEEE,2015),pp.6991–6994.
“Electricalalternansandcardiacelectricalinstability,”Circulation77,110– 37R. Jane, P. Laguna, N. V. Thakor, and P. Caminal, “Adaptive baseline
121(1988).
wanderremovalintheECG:Comparativeanalysiswithcubicsplinetech-
16D. S. Rosenbaum, L. E. Jackson, J. M. Smith, H. Garan, J. N. Ruskin,
nique,”inProceedingsofComputersinCardiology1992(IEEE,1992),
and R. J. Cohen, “Electrical alternans and vulnerability to ventricular
pp.143–146.
arrhythmias,”N.Engl.J.Med.330,235–241(1994). 38J.PanandW.J.Tompkins,“Areal-timeQRSdetectionalgorithm,”IEEE
17B.D.Nearing,A.H.Huang,R.L.Verrieretal.,“Dynamictrackingof
Trans.Biomed.Eng.32,230–236(1985).
cardiacvulnerabilitybycomplexdemodulationoftheTwave,”Science
39P.Laguna,R.Jane`,andP.Caminal,“Automaticdetectionofwavebound-
252,437–440(1991).
18P.StrumilloandJ.Ruta,“Poincare´mappingfordetectingabnormaldynam- ariesinmultileadECGsignals:ValidationwiththeCSEdatabase,”Comput.
Biomed.Res.27,45–60(1994).
ics of cardiac repolarization,” IEEE Eng. Med. Biol. Mag. 21, 62–65
40B. D. Hearing, P. H. Stone, and R. L. Verrier, “Frequency response
(2002).
19T.Srikanth,D.Lin,N.Kanaan,andH.Gu,“Estimationoflowlevelalternans characteristics required for detection of T-wave alternans during ambu-
latory ECG monitoring,” Ann. Noninvasive Electrocardiol. 1, 103–112
usingperiodicitytransform-simulationandeuropeanst/tdatabaseresults,”
(1996).
inProceedingsoftheSecondJoint24thAnnualConferenceandtheAnnual
41F. Smarandache and J. Dezert, Advances and Applications of DSmT for
FallMeetingoftheBiomedicalEngineeringSocietyEMBS/BMESConfer-
InformationFusion (CollectedWorks)(AmericanResearch Press,2004-
ence,2002,EngineeringinMedicineandBiology,2002(IEEE,2002),Vol.
2015),Vol.1-4.
2,pp.1407–1408.
20T. Srikanth, D. Lin, N. Kanaan, and H. Gu, “Presence of T wave alter- 42A.L.Goldberger,L.A.Amaral,L.Glass,J.M.Hausdorff,P.C.Ivanov,
R.G.Mark,J.E.Mietus,G.B.Moody,C.K.Peng,andH.E.Stanley,
nans in the statistical context-a new approach to low amplitude alter-
“Physiobank,physiotoolkit,andphysionet:Componentsofanewresearch
nansmeasurement,”inComputersinCardiology,2002(IEEE,2002),pp.
resource for complex physiologic signals,” Circulation 101, e215–e220
681–684.
21L.Burattini,W.Zareba,J.Couderc,E.Titlebaum,andA.Moss,“Com- (2000).
puter detection of non-stationary T wave alternans using a new cor- 43R. Bousseljot, D. Kreiseler, and A. Schnabel, “Nutzung der EKG-
relation method,” in Computers in Cardiology, 1997 (IEEE, 1997), signaldatenbank CARDIODAT der PTB u¨ber das internet,” Biomed.
pp.657–660. Tech./Biomed.Eng.40,317–318(1995).
22L.Burattini,“ElectrocardiographicT-wavealternansdetectionandsignif- 44Seehttps://www.physionet.org/physiobank/database/ptbdb/forPhysioNet,
icance,”Ph.D.thesis,DepartmentofElectricalEngineering,Universityof ThePTBdiagnosticECGdatabase.
Rochester,1998. 45G.B.Moody,W.K.Muldrow,andR.G.Mark,“ANoisestresstestfor
23L.Burattini,W.Zareba,andA.J.Moss,“Correlationmethodfordetec- arrhythmiadetectors,”Comput.Cardiol.11,381–384(1984).
tionoftransientT-wavealternansindigitalholterECGrecordings,”Ann. 46M.Orini,B.Hanson,V.Monasterio,J.P.Martinez,M.Hayward,P.Taggart,
NoninvasiveElectrocardiol.4,416–424(1999). and P. Lambiase, “Comparative evaluation of methodologies for T-wave
24B. D. Nearing and R. L. Verrier, “Modified moving average analysis of alternansmappinginelectrograms,”IEEETrans.Biomed.Eng.61,308–316
T-wave alternans to predict ventricular fibrillation with high accuracy,” (2014).
J.Appl.Physiol.92,541–549(2002). 47M.Blanco-Velasco,F.Cruz-Roldan,J.I.Godino-Llorente,andK.E.Barner,
25J.P.Mart´ınezandS.Olmos,“ArobustTwavealternansdetectorbasedon “Nonlineartrendestimationoftheventricularrepolarizationsegmentfor
theGLRTforLaplaciannoisedistribution,”inComputersinCardiology, T-wave alternans detection,” IEEE Trans. Biomed. Eng. 57, 2402–2412
2002(IEEE,2002),pp.677–680. (2010).
26J. P. Mart´ınez and S. Olmos, “Detection of T wave alternans in non- 48P.E.Mcsharry,G.D.Clifford,L.Tarassenko,andL.A.Smith,“Adynami-
stationarynoise:AGLRTapproach,”inComputersinCardiology,2003 calmodelforgeneratingsyntheticelectrocardiogramsignals,”IEEETrans.
(IEEE,2003),pp.161–164. Biomed.Eng.50,289–294(2003).
27M.Boix,B.Canto´,D.Cuesta,andP.Mico´,“Usingthewavelettransformfor 49R.Pardolesi,Bioelectromagnetism:PrinciplesandApplicationsofBioelec-
T-wavealternansdetection,”Math.Comput.Modell.50,738–742(2009). tricandBiomagneticFields.PartI(OxfordUniversityPress,2002),p.550.