Fuzzy Soft System and Arrhythmia Classification

13 Pages·2015·2.89 MB·English

Hindawi Publishing Corporation
Chinese Journal of Mathematics
Volume 2014, Article ID 164781, 12 pages
http://dx.doi.org/10.1155/2014/164781
Research Article
Fuzzy Soft System and Arrhythmia Classification
PankajSrivastava,1NeerajaSharma,1andC.S.Aparna2
1DepartmentofMathematics,MotilalNehruNationalInstituteofTechnology,Allahabad,UttarPradesh211004,India
2DepartmentofAppliedMechanics,MotilalNehruNationalInstituteofTechnology,Allahabad,UttarPradesh211004,India
CorrespondenceshouldbeaddressedtoNeerajaSharma;[email protected]
Received11October2013;Accepted12November2013;Published18February2014
AcademicEditors:S.DengandS.N.U.A.Kirmani
Copyright©2014PankajSrivastavaetal. This is an open access article distributed under the Creative Commons Attribution
License,whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperly
cited.
Anarrhythmiaisanirregularitywiththespeedorrhythmoftheheartbeat.Duringanarrhythmia,theheartcanbeattoofast,too
slow,orwithanirregularrhythm.Mostarrhythmiasareharmless,butsomecanbeseriousorevenlifethreatening.Thepresent
paper deals with the classification scheme of arrhythmia commonly occurring in human beings of Southeast Asian countries.
Medicalknowledgeusedinpracticehasbeencloselystudiedformodellinguserfriendlyreferralsystemtosharpenarrhythmia
diagnosisbyexpertsandthissystemistestedwithsatisfactoryfactorwhichismeasuredwithdegreeofmatchcriterionunderthe
domainofconsideredinputsandcomputedoutput.
1.Introduction stimulator. In the late 1960s, a major breakthrough in our
understandingofcardiacarrhythmiascamewhenareliable
In Charaka and Sushruta Samhitas there is a description recordingof the electrogramof the Bundle of His and pro-
of five types of heart disease, namely, Vatika, Paittika, grammedelectricalstimulationoftheheartbecameavailable
Kaphaj, Tridoshaj, and Krimij that are caused due to Vata, forclinicaluse.Thebackgroundforthesedevelopmentscame
Pitta,Kapha,tripledoshas,andworms,respectively.Hridrog fromtheworkofpioneerssuchasHecht,Latour,Puech,and
Prakarana deals with the treatment for above-mentioned Giraudwho,inthe1940sto1950s,showedthatintracardiac
heart diseases. It appears that many kinds of heart related catheterscouldbeusedtorecordelectricalactivityinsidethe
diseases like arrhythmia have been included under Vat- heartandtomapcardiacactivation[3].
inducedinflammationandrespiratorydiseaseontheground There has been extensive work on techniques of clas-
of similarity of symptoms. According to Ayurved, when sification of arrhythmia based on databases that may not
PranvayuandSamanvayualongwithAvlambakkaphaget berelevantforpresent-dayclinicaldiagnosticsystems. This
disturbedduetofaultydiet(richinsalt,bitter,andpungent), is due to limitation in types of arrhythmia considered in
excessivesmoking,andprolongedalcoholconsumption,the them. The present papaer tries to overcome this limitation.
cardiac rhythm may be slow or fast [1]. Although ancient Mahmoodabadi,etal.suggestedthatNeuralNetworkscan-
Chinese pulse theory laid the foundation for the study of not respond correctly to unpredictable and abrupt changes
arrhythmiasandclinicalelectrophysiologyinthe5thcentury encounteredinpatientsbecauseofvaryingshapesofarrhyth-
BC, the most significant breakthrough in the identification mias.Incontrast,theapplicationoffuzzytoolsisfirmlytied
and treatment of cardiac arrhythmias first occurred in the tohumanjudgment;thereforethestudyofhumanbehaviour
20th century. Hippocrates stated in his Aphorisms (Section towards a problem is very important to achieve reasonable
II,number41):thosewhoaresubjecttofrequentandsevere results[4].
fainting attacks without obvious cause die suddenly. This Inthefieldofmedicine,BellmanandZadeh[5]proposed
might be the first description of sudden cardiac death [2]. application of fuzzy tools. In 1973, Zadeh [6] introduced a
In1958,FurmanandRobinsonshowedthattheheartcould numberofprocedurestodesignanddevelopfuzzyalgorithm
be stimulated by connecting an intracardiac catheter to a fortheanalysisofcomplexsystemsanditsdecisionprocesses.
2 ChineseJournalofMathematics
Zong and Jiang [7] presented a fuzzy reasoning approach The algorithm proposed helps us in designing the fol-
for ECG beat rhythm detection and classification. They lowing information system. There are three steps as in
usedlinguisticvariablestorepresentbeatfeaturesandfuzzy Algorithm1.
conditional statements perform reasoning. De Chazal et al.
[8] proposed method for the automatic processing of the
2.1. Input Parameters. The ten input factors are ventricular
electrocardiogramfortheclassificationofheartbeatsinwhich
rate (VR), PR interval (PRI), QRS duration (QRSd), R-R
allocationofdetectedheartbeatstooneofthefivebeatclasses
interval, atrial rate (AR), P-P interval (P-P), P-QRS ratio
recommended by ANSI/AAMI (American National Stan-
dardsInstitute/AssociationfortheAdvancementofMedical (P:QRS),RI2:RI1ratio,PI2:PI1ratio,andTwave.
(a)Ventricularrate(VR)iscategorizedinfourdifferent
Instrumentation) EC57:1998 standard, that is, normal beat,
fuzzysetswiththeirmembershipfunctionsshowninFigure1
ventricularectopicbeat(VEB),supraventricularectopicbeat,
asfollows:
fusion of a normal and a VEB, or unknown beat type was
manuallyperformedondataobtainedfromthe44nonpace-
makerrecordingsoftheMIT-BIHarrhythmiadatabase.Yeh (1)slow(S):<40bpm,
etal.[9]proposedfuzzylogicmethodtoanalyseECGsignals
fordeterminingtheheartbeatcasewhichcanaccuratelyclas- (2)normal(N):40to100bpm,
sify and distinguish both normal heartbeats and abnormal
heartbeats; Mahmoodabadi et al. [4] selected ECG features (3)high(H):100to150bpm,
whicharecomparedmedicallyacceptednormalcasesusing
thefuzzyclassifier,andarrhythmiaswillbedetectedaccord- (4)veryhigh(VH):>150bpm,
ingly.Theinferencesectionofafuzzyclassifierimplemented
expertdesignedfuzzyrules.SadiqandKhan[10]presented
1 𝑥≤55
anautomatedapproachtobeatrecognitionoffourdifferent {{{{
beattypesinECGs,namely,normalbeats,ventricularectopic (60−𝑥)
beats, supraventricular ectopic beats, and fusion beats with (1) 𝜇Slow(𝑥)={{{{ 5 55<𝑥<60
thehelpoffeaturevectortodifferentiatebetweenthedifferent {0 𝑥≥60
beats containing morphological features and beat intervals
fsPoc.rhSeremiavcaehstfoabvreaactaa.nrRddieacAce.naStnlryai,vlyaisnsitsasvaoanftd[1c1ho,ym1p2pe]u,rttteihnnegsisorynisstkepmraospsdeoesssseimgdneebndyt {{{{{{{{{0(𝑥, −55) 5𝑥5≤<5𝑥5<or6𝑥0≥105
5
on MATLAB Software gives the person the ratio of the (2) 𝜇 (𝑥)=
rnioskrmaanldlymoraywirtehcodmiemt oerndwiwthhedtrhuegrtpreerastomnenhta,sretsopelicvteivelilfye. Normal {{{{{{{{{1(1,05−𝑥) 60≤𝑥≤100
100<𝑥<105
Srivastavaetal.[13]proposedasoftcomputingclassification
{ 5
criterion to design and develop user friendly diagnostic
system for Hepatitis B and the clinical data of the patients (1)
adnesdigtnhethoepdiniaiognnsosotifcmsyesdteicmal.Sexripvearsttsavhaaveteabl.ee[1n5]uptirloizpeodsetdo {{{{{{{{{0(𝑥, −100) 1𝑥0≤01<0𝑥0<or1𝑥05≥160
softcomputingdiagnosticsystemfordiabetesthatsharpens 5
(3) 𝜇 (𝑥)=
tshtreatdeigaigesnotsoticcopnrtorocelstshaesirwsuelglaarslegvueidl.eRsepcaetnietnlyt,sStroiveavstoalvvae High {{{{{{{{{1(1,60−𝑥) 105≤𝑥≤155
andSharma[16]proposedasoftcomputingdecisionmaking 155<𝑥<160
{ 5
model to handle real life complex problems related with
medicalsciences.
0, 𝑥≤155
{{{{
(𝑥−155)
2.MaterialsandMethod (4) 𝜇VeryHigh(𝑥)={{{{ 5 155<𝑥<160
Theproposedsoftcomputingsystemisdesignedbymaking {1, 𝑥≥160.
use of facts related to Sugeno approach of fuzzy inference.
The system is applied to real and fresh data collected from
hospitals in and around Allahabad district (U.P., India).
(b) PR interval (PRI) which represents atrial depolar-
The categorization of arrhythmia is done by making use of
ization is categorized in three different fuzzy sets shown in
availabledataandspecificfeaturesfromECGappropriateto
Figure2withtheirmembershipfunctionsasfollows:
dotheclassificationaredecidedupon.Theinputparameters
ofthesystemareframedonthebasisoftenfactorsresponsible
forarrhythmiaandoutputisthetypeofarrhythmiaclassifica- (1)narrow(Na):<120ms,
tion.Theaccuracyoftheinferenceisobtainedbycomparing
itwiththeresultsprovidedbyexpertcardiologists. (2)normal(N):120–200ms,
ChineseJournalofMathematics 3
STEP1:AlgorithmforFuzzificationMechanism
(1)Input—FuzzySystemwithsuitable“𝑛”parameters
𝐴𝑖,𝑖=1,2,...,𝑛
(2)𝑖←1
While𝑖≤𝑛do
(1)Categorizein𝑛𝑖fuzzysets𝑋𝑗inlinguisticvariables,𝑗=1,2,...,𝑛𝑖
while𝑗≤𝑛𝑖 do
(1)Designsuitablemembershipfunction𝜇𝑋𝑗
endwhile
endwhile
STEP2:AlgorithmforFuzzyRuleBaseandDefuzzificationMechanism
(1)Input—“𝑛𝑖”linguisticvariables𝑋𝑗,𝑖=1,2,...,𝑛and𝑗=1,2,...,𝑛𝑖
(2)Input—“𝑚”outputparameter𝑌𝑘,𝑘=1,2,...,𝑚
(3)Develop“𝑟”If-ThenFuzzyRules𝑅𝑝inconsultationwithmedicalexperts,𝑝=1,2,...,𝑟
(4)Input—FuzzyRuleBase𝑅𝑝
(5)Input—Valuesofparameters𝐴𝑖
(6)𝑝←1
while𝑝≤𝑟 do
(1)Calculatefiringstrength𝑤𝑝 =AND𝐴𝑖,𝑖=1,2,...,𝑛
(2)𝑍𝑝= 𝑝thrule’sconsequentfuzzyset.
endwhile
𝑧 𝑤
(7)FinalOutputofthefuzzysystem𝑍=∑𝑟 𝑝 𝑝
𝑝=1 𝑤
𝑝
(8)EvaluatedDiagnosis(ED)=Finaloutput
STEP3:AlgorithmforSatisfactoryFactorMechanism
(1)Input—EvaluatedDiagnosis(ED),ObservedDiagnosis(OD)
(2)Input—“𝑛”inputparameter𝐴𝑖,𝑖=1,2,...,𝑛andoutputresult𝑍
(3)𝑖←1
(4)DM𝑇=1
while𝑖≤𝑛 do
(1)CalculateDM(𝐴𝑖)=2𝜇𝐴𝑗 −1
(2)DM𝑇=DM𝑇ANDDM(𝐴𝑖)
endwhile
((65))CEvaalcluualateteSDatMisf𝑂ac=toDryMF(a𝑍ct)o=r2(S𝜇F𝑍)−=1󵄨󵄨󵄨󵄨DM𝑇−DM𝑂󵄨󵄨󵄨󵄨
Algorithm1
Slow Normal High Very high Narrow Normal Broad
1 1
hip 0.8 hip 0.8
mbers 0.6 mbers 0.6
me me
Degree of 00..24 Degree of 00..24
0 0
20 40 60 80 100 120 140 160 180 200 100 150 200 250
VR PRI
Figure1:Ventricularrate. Figure2:PRinterval.
4 ChineseJournalofMathematics
(3)broad(B):>200ms, 1 Narrow Normal Broad
{{{{1(120−𝑥) 𝑥≤115 ership 0.8
(1) 𝜇Narrow(𝑥)={{{{ 5 115<𝑥<120 memb 0.6
{0 𝑥≥120 of 0.4
e
e
{{{{{{{{{0(𝑥−115) 1𝑥1≤51<1𝑥5<or1𝑥20≥205 Degr 0.20
(2) 𝜇 (𝑥)= 5 (2)
Normal {{{{{{{{{1(2,05−𝑥) 120≤𝑥≤200 20 40 60 Q8R0Sd 100 120 140
200<𝑥<205
Figure3:QRSduration.
{ 5
0, 𝑥≤200
{{{(𝑥−200) 1 Short Normal Wide
(3) 𝜇Broad(𝑥)={{{1, 5 2𝑥0≥02<0𝑥5.<205 hip 0.8
{ ers
mb 0.6
e
m
(c)QRSduration(QRSd)iscategorizedinthreedifferent of 0.4
e
fuzzy sets having their membership functions shown in egre 0.2
Figure3asfollows: D
0
(1)narrow(Na):<60ms,
0.2 0.4 0.6 0.8 1 1.2 1.4
(2)normal(N):60–100ms, R-R
(3)broad(B):>100ms, Figure4:R-Rinterval.
1 𝑥≤55
{{{{ (3)wide(W):>1sec,
(60−𝑥)
(1) 𝜇Narrow(𝑥)={{{{{0 5 5𝑥5≥<6𝑥0<60 (1) 𝜇Short(𝑥)={{{{{{1(0.06.0−5𝑥) 𝑥0.5≤50<.5𝑥5<0.6
(2) 𝜇Normal(𝑥)={{{{{{{{{{{{{{{{{{{01((𝑥1,0−5555−5𝑥)) 156𝑥0500≤<≤<5𝑥𝑥5𝑥<≤o<61r100𝑥005≥105 (3) (2) 𝜇Normal(𝑥)={{{{{{{{{{{{{{{001((𝑥1,.0−05.00−5.5𝑥5))𝑥≥𝑥001...0560≤.506≤0<<.𝑥5𝑥𝑥5≤<<o1r.010𝑥..0605≥1.05 (4)
{ 0.05
0, 𝑥≤100
(3) 𝜇Broad(𝑥)={{{{{{{{(𝑥−5100) 100<𝑥<105 (3) 𝜇Wide(𝑥)={{{{{{0(𝑥, −0.015.00) 𝑥1.0≤01<.0𝑥0<1.05
{1, 𝑥≥105. 1, 𝑥≥1.05.
{
(e)Atrialrate(AR)whichistheAtrialrhythmcalculated
(d) R-R interval (RR) is categorized in three different
byPwavesiscategorizedinsixdifferentfuzzysetsshownin
fuzzysetswiththeirmembershipfunctionsshowninFigure4
Figure5asfollows:
asfollows:
(1)slow(S):<60bpm,
(1)short(S)<0.60:sec,
(2)normal(N):60–100bpm,
(2)normal(N):0.6–1sec, (3)littlebithigh(LH):100–150bpm,
ChineseJournalofMathematics 5
(f)P-Pinterval(PP)iscategorizedinthreedifferentfuzzy
1 SlowNormalLittle high High Very high Extremely high
sets with their membership functions shown in Figure6 as
hip 0.8 follows:
mbers 0.6 (1)short(S):<0.60sec,
e
m
(2)normal(N):0.6–1sec,
of 0.4
egree 0.2 (3)wide(W):>1sec,
D
1 𝑥≤0.55
0 {{{(0.6−𝑥)
50 100 150 200 250 300 350 400 450 500 (1) 𝜇Short(𝑥)={{{ 0.05 0.55<𝑥<0.6
0 𝑥≥0.6
AR {
Figure5:Atrialrate. {{{{{{{0(𝑥−0.55) 𝑥0.5≤50<.5𝑥5<or0𝑥.6≥1.05
(4)high(H):150–250bpm, (2) 𝜇Normal(𝑥)={{{{{{{1(1,.005.0−5𝑥) 0.6≤𝑥≤1.00 (6)
(5)veryhigh(VH):250–350bpm, 1.00<𝑥<1.05
{ 0.05
(6)extremelyhigh(EH):>350bpm,
0, 𝑥≤1.00
{{{(𝑥−1.00)
{{{1(60−𝑥) 𝑥≤50 (3) 𝜇Wide(𝑥)={{{ 0.05 1.00<𝑥<1.05
(1) 𝜇S(𝑥)={{{ 10 50<𝑥<60 {1, 𝑥≥1.05.
0 𝑥≥60
{
(g) P-QRS ratio (P:QRS) shows the ratio of P wave
{{{{{{{0(𝑥−50) 5𝑥0≤<5𝑥0<or6𝑥0≥110 tfoollQowRiSngwathvreeeindoiffneerecnatrdfiuazczycysceltes. wItitihs cthateeigromrizeemdbienrshthipe
(2) 𝜇N(𝑥)={{{{{{{1(1,1100−𝑥) 16000≤<𝑥𝑥≤<110100 func(t1i)onloswsh(oLw):n<i1n, Figure7:
{ 10
(2)desirable(D):=1,
{{{{{{{0(𝑥−105) 1𝑥0≤51<0𝑥5<or1𝑥10≥155 (3)high(H):>1,
(3) 𝜇LH(𝑥)={{{{{{{1(1,555−𝑥) 115100<≤𝑥𝑥<≤115550 {{{{{{{{11−2(𝑥+6 2)2 𝑥−2≤<−𝑥2≤1
{ 5 (1)𝜇 (𝑥)=
{{{{{{{0(𝑥−150) 1𝑥5≤01<5𝑥0<or1𝑥60≥250 (5) Low {{{{{{{{{20(, 𝑥−6 4)2 14<<𝑥𝑥≤4
(4) 𝜇H(𝑥)={{{{{{{{1(2,501100−𝑥) 214600<≤𝑥𝑥<≤225400 {{{{{{{{02(𝑥+6 2)2 𝑥−2≤<−𝑥2≤1 (7)
(2)𝜇 (𝑥)=
{{{{{{{0(𝑥−245) 𝑥24≤52<4𝑥5<or2𝑥50≥355 High {{{{{{{{1−2(𝑥−6 4)2 1<𝑥≤4
(5) 𝜇 (𝑥)= 5 {1, 4<𝑥.
VH {{{{{{{1(3,55−𝑥) 250≤𝑥≤350
350<𝑥<355
{ 5 (h) RI2:RI1 ratio is the ratio of two successive R-R
intervals.Itiscategorizedinthefollowingthreefuzzyfactors
{{{0(𝑥, −350) 𝑥≤350 withtheirmembershipfunctionsshowninFigure8:
(6) 𝜇EH(𝑥)={{{ 5 350<𝑥<360 (1)low(L):<1,
1, 𝑥≥360.
{ (2)desirable(D):=1,
6 ChineseJournalofMathematics
1 Short Normal Wide 1 Low Desirable High
hip 0.8 hip 0.8
ers ers
mb 0.6 mb 0.6
e e
m m
of 0.4 of 0.4
e e
e e
egr 0.2 egr 0.2
D D
0 0
0.2 0.4 0.6 0.8 1 1.2 1.4 −3 −2 −1 0 1 2 3 4 5
P-P RI2: RI1
Figure6:P-Pinterval. Figure8:RI2:RI1ratio.
Low Desirable High
1 Low Desirable High
1
embership 00..68 mbership 00..68
m e
Degree of 00..24 egree of m 00..24
D
0
0
−3 −2 −1 0 1 2 3 4 5 −3 −2 −1 0 1 2 3 4 5
P : QRS
PI2: PI1
Figure7:P:QRSratio. Figure9:PI2:PI1ratio.
(3)high(H):>1,
(3)high(H):¿1,
1 𝑥≤−2
(1)𝜇Low(𝑥)={{{{{{{{{{{{{{{{{120(,−𝑥2−6(𝑥4)+622)2 −142<<<𝑥𝑥𝑥≤≤41 (1)𝜇Low(𝑥)={{{{{{{{{{{{{{{{112(−𝑥2−6(𝑥4)+622)2 𝑥−12<≤<𝑥−𝑥2≤≤41
{0, 4<𝑥
(8)
0 𝑥≤−2 (9)
(2)𝜇High(𝑥)={{{{{{{{{{{{{{{{{211(,−𝑥2+6(𝑥2)−624)2 −142<<<𝑥𝑥.𝑥≤≤41 (2)𝜇High(𝑥)={{{{{{{{{{{{{{{{021(−𝑥2+6(𝑥2)−624)2 𝑥−12<≤<𝑥−𝑥2≤≤41
{1, 4<𝑥.
(i)PI2:PI1ratioistheratiooftwosuccessiveP-Pintervals.
It is categorized in following three fuzzy factors with their (j) T wave is categorized in three fuzzy sets shown in
membershipfunctionsshowninFigure9: Figure10withtheirmembershipfunctionsasfollows:
(1)low(L):<1, (1)negative(N):<0,
(2)desirable(D):=1, (2)isolated(I):=0,
ChineseJournalofMathematics 7
1 Negative Isolated Positive 1.00 N ST AT AF AFb VT SB 1B 2B1 2B2 3B PAC PVC
hip 0.8
ers
mb 0.6
e
m 0.50
of 0.4
e
e
egr 0.2
D
0.00
0
0 1 2 3 4 5 6 7 8 9 10 11 12
−4 −3 −2 −1 0 1 2 3 4 Figure11:Typesofarrhythmia.
T wave
Figure10:Twave.
This firing strength is further used in finding the final
(3)positive(P):>0, conclusionoftheproposedsystemusingthedefuzzification
ofweightedaverageofallruleoutputs𝑍𝑖,𝑖=1,...,16.
1 𝑥≤−3 The final output of the system is calculated by
{{{{{{{{1−2(𝑥+6 3)2 −3<𝑥≤0 ∑1𝑖=60I(n𝑍o𝑖𝑤rd𝑖/e𝑤rt𝑖)o.knowtowhatextentourresultissatisfiedby
(1)𝜇Negative(𝑥)={{{{{{{{2(𝑥−6 3)2 0<𝑥≤3 gMivaetTcnheinnapclgauostersistahanrmdeodtobisscceourmsvseepdduotbeuetslpoautwitsstf,oawcstehoomrwyafktahecetuoesrffe[eo1c7ft]Di.veengreesesooff
{0, 3<𝑥 theproposedsystem.
(10)
0 𝑥≤−3
{{{{{{{{2(𝑥+6 3)2 −3<𝑥≤0 2.4.CaseStudy
(2)𝜇 (𝑥)= Case1. TheECGrecordoftheconcernedpatientismanually
Positive {{{{{{{{1−2(𝑥−6 3)2 0<𝑥≤3 calcVulRate=da1s10foblplomw,s.PRI = 90ms, QRSd = 100ms, AR =
{1, 3<𝑥. 410bpm, R-R interval = 0.46sec, P-P interval = 0.15sec,
P:QRS = 2, RI2 : RI1 = 0.7, PI2 : PI1 = 0.9 and T wave is
positive.
2.2. Output Parameter. The abnormalities in rhythm of the
heart contribute to a number of arrhythmia of which we Themembershipfunctionsdesignedforinputparameters
have taken thirteen types as outputs for the classification are used to fuzzify the crisp inputs which are transformed
of arrhythmia. These are as follows: Normal (N), Sinus into fuzzy outputs by making use of the constructed fuzzy
Tachycardia (ST), Atrial Tachycardia (AT), Atrial Flutter IF-THENrulesandfinallydefuzzifiedbyusingtheweighted
(AF),AtrialFibrillation(AFb),VentricularTachycardia(VT), averagefunctiondefinedabove.
Sinus Bradycardia (SB), First AV Block (1st B), Second AV ThedefuzzificationisshowninFigure12whichshowsthe
Block Type 1 (2nd B1), Second AV Block Type 2 (2nd B2), output that is, Arrhythmia = 4, which stands for the Atrial
ThirdAVBlock(3rdB),PrematureAtrialContraction(PAC), Fibrillation (AFb). This diagnosis matches the observed
and Premature Ventricular Contraction (PAC). Spikes are diagnosisbymedicalexperts.
usedtorepresenttheseoutputsasgiveninFigure11. Inordertomeasuresatisfactoryfactor,valuesofDegree
ofMatchofinputparametersarecomputedandtotalDegree
2.3. Fuzzy Inference System. Evaluation of ECG signals for ofMatchofinputsDM𝑇isgivenbelow:
arrhythmiadetectionconsistsofthedeterminationofseveral
characteristicsofthesignal.Inordertoclassifydifferenttypes DM𝑇 =min{1,1,1,1,1,1,0.778,0.595,0.533,0.778}
ofarrhythmiafiftyfiverulesareconstructedwiththehelpof
(12)
medicalexperts.TheyaregiveninTable1.
=0.533.
Theoutput𝑍𝑖,thatis,conclusionpartofaruleisweighted
by the firing strength 𝑤𝑖 of the rule which is calculated by
usingANDoperationoneachantecedent𝐴𝑗,where𝑗isthe
numberofinputsusedineachrule𝑖asfollows: Degree of Match of output DM𝑂 is 1; hence our satis-
factory factor is 𝐷 = |DM𝑇 − DM𝑂| = |0.533 − 1| = 0.467
whichliesbetween0and1andneartozero,thatmeetslevel
𝑤𝑖 =AND{𝐴𝑗}, 𝑖=1,...,16. (11) ofsatisfaction.
8 ChineseJournalofMathematics
a
mial
hythormSB1B1B2B12B12B12B2VT3B3B3B3B3B3B3B3BPACPACPACPACPACPACPACPACPACPACPACPACAFbAFbSTSTSTSTATATAFAFAFAF
rN
r
A
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RI:RI21DesirablDesirablDesirablDesirablHighHighHighHigh—LowLowHighHighLowLowHighHighLowLowHighHighLowLowHighHighLowLowHighHighLowHighDesirablDesirablDesirablDesirabl——DesirablDesirablDesirablDesirabl
R-RNormalWideWideNormalNormalWideWideWideShortWideWideWideWideWideWideWideWideNormalNormalNormalNormalWideWideWideWideShortShortShortShortShortShortShortShortShortShort——NormalNormalShortShort
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Table1: P-PNormalWideNormalNormalNormalNormalNormalNormal—NormalNormalNormalNormalShortShortShortShortNormalNormalNormalNormalWideWideWideWideShortShortShortShort——ShortShortShortShortShortShortShortShortShortShort
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ARNormalSlowNormalNormalNormalNormalNormalNormal—NormalNormalNormalNormalLittlehighLittlehighLittlehighLittlehigh————————————xtremelyhixtremelyhiLittlehighHighVeryhighxtremelyhiHighVeryhighVeryhighxtremelyhiVeryhighxtremelyhi
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Sdmalmalmalmalmaladmaladadadadadadadadadadmalmalmalmalmalmalmalmalmalmalmalmalmalmalmalmalmalmalmalmalmalmalmalmal
QRNorNorNorNorNorBroNorBroBroBroBroBroBroBroBroBroBroNorNorNorNorNorNorNorNorNorNorNorNorNorNorNorNorNorNorNorNorNorNorNorNor
PRINormalNormalBroadBroadBroadNormalBroadNormal—————————NormalNormalNormaNormalNormalNormalNormalNormalNormalNormalNormalNormal——NormalNormalNormalNormalNarrowNarrow————
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VRNormalSlowSlowNormalNormalNormalSlowSlowHighSlowSlowSlowSlowSlowSlowSlowSlow————————————VeryhigVeryhigHighVeryhigVeryhigVeryhigVeryhigVeryhigNormalNormalHighHigh
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ChineseJournalofMathematics 9
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10 ChineseJournalofMathematics
VR = 110 PRI = 90 QRSd = 100 AR = 410 P-P = 0.15 P : QRS = 2 R-R = 0.46 RI2: RI1=0.7 PI2: PI1=0.9 T wave = 0 Arrhythmia = 4
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Figure12:Designedinformationreferralsystem.
Case2. TheECGrecordoftheconcernedpatientismanually Values of Degree of Match of input parameters are
calculatedasfollows. computedandtotalDegreeofMatchofinputsDM𝑇isgiven
VR = 114bpm, PRI = 120ms, QRSd = 296ms, AR = below:
20bpm,R-Rinterval=0.52sec,P-Pinterval=0.5sec,P:QRS
=0,RI2 :RI1=1.2PI2 :PI1=1andTwaveisnegative. DM𝑇 =min{1,1,1,1,1,1,0.564,0.653,0.5,0.778} (14)
Implementing these features, the Arrhythmia output is =0.5.
8.59;thatis,heartbeatisSecondAVBlockType2(2ndB2).
Here,theobserveddiagnosisbymedicalexpertisVentricular DegreeofMatchofoutputDM𝑂is−1;thus𝐷=|DM𝑇−
Tachycardia(VT). 𝐷𝑀𝑂| = |0.5 − (−1)| = 1.5 which does not meet level of
Values of Degree of Match of input parameters are satisfaction.
computedandtotalDegreeofMatchofinputsDM𝑇isgiven
below: Case4. TheECGrecordofthepatientisasfollows.
VR = 104.89bpm, PRI = 164ms, QRSd = 94ms, AR =
DM𝑇 =min{1,1,1,1,1,1,0.778,0.564,0.5,0.778} 107.14bpm,R-Rinterval=0.572sec,P-Pinterval=0.56sec,
=0.5. (13) P:QRS=1,RI2 :RI1=1.2,PI2 :PI1=1,andTwaveispositive.
Implementingthesefeatures,theArrhythmiaoutputis9;
DegreeofMatchofoutputDM𝑂is−1;thus𝐷=|DM𝑇− that is, heart beat is Second AV Block Type. The evaluated
DM𝑂|=|0.5−(−1)|=1.5whichdoesnotliebetweenzeroand diagnosisisverifiedbymedicalexpert.
one;thereforelevelofsatisfactionisnotgood. Thesatisfactoryfactoris |DM𝑇 −DM𝑂|=|0.022−1|=
0.978.
Case3. TheECGrecordofthepatient,asfollows.
VR=40bpm,PRI=120ms,QRSd=150ms,AR=91bpm, Case5. TheECGrecordofthepatientisasfollows.
R-R interval = 1.5sec, P-P interval= 0.66sec, P:QRS= 1.2, VR = 132bpm, QRSd = 80ms, R-R interval = 0.457sec,
RI2 :RI1=1.5,PI2 :PI1=1,andTwaveispositive. P:QRS=1.6,RI2 :RI1=1.4andT,waveispositive.
Implementing these features, the Arrhythmia output is Implementing these features, the Arrhythmia output is
9.77; that is, heart beat is Third AV Block (3B). Here, the 1; that is, heart beat is Sinus Tachycardia. The observed
observed diagnosis by medical expert is the same, that is, diagnosisbymedicalexpertisAtrialFlutter.
ThirdAVBlock(3B). Thesatisfactoryfactoris|DM𝑇−DM𝑂|=|0.63+1|=1.63.