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MultiǦstepPredictionofPathologicalTremor WithAdaptiveNeuroFuzzyInferenceSystem (ANFIS)

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SivanagarajaTatinatiandKalyanaC.Veluvolu SchoolofElectronicsEngineering,CollegeofITEngineering,KyungpookNational University,Daegu,SouthKorea

AbstractǦ In this paper, to overcome the inevitable phase delay due to preǦfiltering techniques and electromechanical delay in the procedure of pathological tremor compensation, a machine learning technique based on fuzzy logic and neural networks (adaptive neuro fuzzy inference system (ANFIS)) is employed. Experimental evaluation on tremor data is performed with data acquired from eight patients. ResultsshowthatANFISprovidesgoodperformanceincomparisonwithexistingmethods.

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I.Introduction

Pathologicaltremorisdefinedasaninvoluntaryandapproximatelyrhythmicoscillationsofabodypart[1]. Pathologicalisoneoftheseriousdisablingformsoftremorsandoftenaccompanieswithaging.Although pathological tremor is not a lifeǦthreatening disorder, but it hampers the ability of individual to perform dailylivingactivitieslikedrinkingwaterwithaglass,unlockthedoorwithakeyetc.Further,theinability duetotremorleadstosocialembarrassment[1].Tocompensatethefunctionaldisability(tremor)thereby to improve the quality of life, several pharmaceutical and surgical therapies are developed. The methods havetheirlimitationsandsideeffects.So,aneffectivetreatmentthatcancompensatetremoraccuratelyyet tobedeveloped.

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Over the last decade, considerable research has been focussed on developing active pathological tremor compensation techniques in realǦtime [3], [4], [6], [7]. One such approach is compensating pathological tremorbystimulatingtherelevantmusclegroupswithappropriateelectricpulsesthrufunctionalelectrical stimulator(FES)[3].Forexample,considerhandsupinationǦpronationmusclegroup,iftremorisduetothe supinationmusclegroupnecessaryelectricpulseswillbeprovidedtopronationmusclegrouptocounteract theinvoluntarymovement,andviceversa.Tocompensatethetremor,awearabledevicenamedasWOTAS (wearableorthosisfortremorassessmentandsuppression)wasdevelopedbyusingafeedbackcontrolled FES. The efficacy of the wearabledevicesdepends ontheaccurate andzeroǦphasedelayfiltering oftremulous motionfromthewholemotion.InthetremorcompensationprocedurewithFES,adelayofapproximately 80mswasidentified.Themajorsourceforthedelayiselectromechanicaldelay(EMD),definedasthedelay betweentheonsetofactivationofmuscleandthedetectionofmovement[2].Asaresultofseveralstudies, theEMDwas identifiedinthe range of50Ǧ60ms [2]. The othersource fordelayis thepreǦfiltering stage whichisusedtoseparatethevoluntarymotionandtremulousmotionfromthewholesensedmotion[7]. Onawhole,alatencyof80mswasinevitableintheprocedureandthisdelayadverselyaffectsthetremor compensationaccuracy. Toovercomethephasedelaylimitation,multiǦsteppredictionwithharmonicmethodandAutoregressive methodwasproposedin[4].Thedevelopedmethodsyieldaccuratepredictionwithperiodicsignals.Owing to the quasiǦperiodic nature of the tremor signals, prediction accuracy with the above methods is rather limited. To further enhance the prediction capabilities, in this work, we employed a machine learning technique,adaptiveneurofuzzyinferencesystem(ANFIS).ANFIShasbeenrecentlypopularasaneffective method for time series prediction, function estimation, system identification and classification problems.

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ThegoallofANFISistofindamod delormappingthatwillc correctlyasso ociatetheinp puts(initialvvalues)with thetargeet(predictedvalues).Theefuzzy infereencesystem (FIS) is a kn nowledge representation w whereeach fuzzy ru ule describes a local behaaviour of the system. Th he network sstructure thaat implemen nts FIS and employs hybridÇŚlearn ning rules to train is callled ANFIS. T The paper is organized ass follows: In section II, tremord datacollection n,delayinth heprocedureandthemetthodemployeedarediscusssed.Inthelaatersection resultsob btainedwithANFISarepresented.Theelastsection npresentstheeconclusionss.

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II.Method ds

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In this ssection, we first discusss about the collection of pathological tremor daata. Later th he detailed descriptiionregarding gthedelayasssociatedint tremorcompeensationproccedureandaabriefdescrip ptionabout ANFISarrepresented.

 Fig. 1: Subject #1, A Action tremor (a) Parkin nsons patientt tremor wh hile executing g voluntary alternating Zoomedportiionofthewh holemotion( (0–5s);(c) pronationandsupinaationmovemeentsoftheleefthand;(b)Z hewholemottion FFTofth

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A.Patho ologicalTre emordata

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Tremor is acquired w with a portaable Motus ssystem comp prises a gyrosscope placed d on the patiient’s wrist withouto objectingfreeeflowofany ymotion[8].A Allthesubjectssignthei  nformedcon nsentformsapprovedby the Ethiics Committee of local hospital. Th he sampling rate employed is 100 deg/sec. Thee collected patholog gical tremor d data set conttains posturaal tremor, paarkinsonian tremor t and eessential trem mor. In this work forr analysis, fou ur subjects’ aaction tremor (tremulouss motion colllected while performing aa voluntary motion)andfoursub bjectsposturaaltremorareemployed.F Foranillustraation,actiontremorcollecctedfroma parkinso onian patient while volun ntarily perform ming pronatiion and supiination moveement with leeft hand as shownin nFig.1.FFTo ofthesignali  salsoshowninFig.1(c).

B B.Latencyi inTremorC CompensattionProced dureWithF FES

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ThephassedelayinweearabledevicceswithFESi isduetothetwosources:preǦfilteringstageandEM MD.InpreǦ filtering stage, to fiilter the treemulous mottion from w whole sensed d motion, a Butterworth h lowǦpass filter/ButtterworthbandǦpassfilterrwasemployyed.Fromthephaseresponse,aaveraagedelayof3 300mswas identified dforfifthord derButterwo orthlowǦpasssfilter,whereeaswithfifth horderbutteerworthband dǦpassfilter withpassband2Ǧ20Hzadelayo of20mswasi identified[7]].Inthepressenceofeitheerdelaysthe eprediction accuracyywasadverseelyeffected.E EMD,ingeneeraladelayoff80§20msexxistsbetween npeakmusclleforceand theappaarentpeak in nEMG[2].In n[2], adelay y of 40Ǧ60msswas identifi fiedbetween surfaceEMG G andforce acquired dformtheflexxionandexteensionmuscllegroupinfo orearm.

 Fig.2:D Delayintrem morsuppressio onprocedureewithFES

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Thus a ttotal delay o of 60Ǧ80 ms is inevitablee in the proccedure, as sh hown in Fig.. 2. With thee sampling frequenccy,100Hz,forrasignalwith hfrequencyr rangesfrom6Ǧ12Hz,thedelayof6to o8samplescorresponds to aboutt 90± phasee difference. With this phase differrence tremorr suppressio on ability is drastically decreased.Toovercom methisdelayy,multiǦsteppredictionbaasedonANFIISisdevelopeedinthispap per.

C.AdapttiveNeruoF FuzzyInferrenceSyste em(ANFIS)

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AneuroǦǦFuzzysystem misinspiredfromthesup pervisoryhum manbrain’sf feedforwardactivitiestheereforethis intelligen nthybridsysttemenjoysboththemetricsofneuralsystemandf fuzzylogicap pproaches.

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A brief description of ANFIS iss provided b below. For detailed desscription of the algorith hm and its implemeentationreferrto[5].



Fig g.3:Sugenottypefuzzymo odelillustratiionandANFIISarchitecturre[5]

Ingeneraal,ANFISstru ucturefollow wsthetakagiǦǦsugenofuzzyysetswithseetofrules(co ombinationoffnumerical and lingu uistic variablles) and mulltiǦlayers (5 layers), l as sh hown in Fig. 3. In this co onnected stru ucture, the inputnodesrepresen ntsthetrainin ngvaluesand doutputnodeesrepresentsspredictedvaalues,andinthehidden layersno odesfunction ningasmemb bershipfuncttions(MF’s)andrules.AlllnodesindifferentlayerrsofANFIS areeitheerfixedorad daptive,assh howninFig.3 [5].Differeentlayersand theircorreespondingno odescanbe described dasbelow: x

Layer1:Alln L nodesinthisl layerareadaaptive.Furtheer,parameterrsinthislayeerarenamedaspremise p parameters. 

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Layer2:Alln L nodesinthislayerarelabeelledas¦and darefixed.Th heoutputobttainedfromt thislayeris t theproducto ofalltheinpu uts.Further,thefiringstreengthofeach hruleisrepreesentedbyeaachnodein t thislayer. L Layer3:Like layer2,each hnodeinthiislayerisalso ofixedandla  abelledasN..Inthislayerr,Ithnode c computesthe eratiooffiriingstrengthssofithrules.Thereby,theeoutputsofthislayerareenamedas n normalizedfi firingstrength hs. L Layer4:Inth hislayer,allnodesaread daptive.Thep parametersc correspondst toallnodesi inthelayer a arereferreda asconsequen ntparameterss. L Layer5:This slayercontaiinsonlyonenodeandthaatnodeisalssofixedandlabelledasP P.Thenode c computesthe eoveralloutp putofthesysstembysumm mationsofalllinputstothenode.

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The paraameters of AN NFIS are opttimized with combination n of gradientt descent and d leastsquares method. LeastǦsqu uares method d is employeed to update the parametters iterativelly in the forw ward pass un ntil layer 4. The grad dient descen nt method iss to update the premise parameters with the ob btained erro or signal in backward dpass.Thee errormeasureetotraintheaboveǦmentiionedANFIS SisE=Pnk=11(fk¡^fk)2wh herefkand ^ fk are the k th dessired and esttimated outp put, respectivvely, and n is the total n number of paairs (inputs outputs)ofdatainth hetrainingseet.Duetotheeimplicationoftwoupdaatealgorithm ms,theconverrgenceofis fasteran ndreducetheesearchspaccedimensionsduetoback kpropagationalgorithm.Theoveralloutputcan beexpresssedasalineearcombinatiionofthecon nsequentparrameters,ass shown inFig.3.

D.Multistep pprediction nofpatholo ogicaltrem morwithAN NFIS

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Theproccedureemplo oyedtoperforrmmultiǦstep ppredictionw withANFISiisshowninF Fig.4.ToperfformmultiǦ steppred diction,atwo oǦdimensionalmatrixofdimensions11000£5(each hrowbeingrreferredtoassanepoch) wasconsstructedassh hownin(1).D Datapointsi  neachroww werechosent tobesixstep psapartande eachepoch containeedonedatapo oints:

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  ANFISw wastrainedw withthefirst5 500epochs.W Withthetraiiningepochss,weightsofn neuralnetwo orkandthe membersship function ns will be op ptimized for accurate preediction (witth cost functtion as minim mum mean square error). The op ptimized parrameters obtaained with th he training eepochs are em mployed for the testing operformtheemultiǦstepprediction. epochsto



 Fig.4:Multtisteppredicttionofpathologicaltremo orwithANFIS S

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III.Resultts In this section, we analyze thee multiǦstep ahead trem mor predictio on performaance with A ANFIS thru simulatio ons.Toquanttifytheperfo ormance,wee employ%Acccuracy,defineedas:



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misthenu umberofsam mples,skistheeinputsignaalatinstant

MS(s)= whereRM kandeissthepredictiionerror.

A.PerforrmanceAn nalysis

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 Fiig. 5: Multtistep predicction with A ANFIS(a)Wh holemotion( (Subject#1, acction trem mor); (b) Tremulous m motion obtaained after bandpass filltering ; (c) Predicttion error ob btainedduet to80msdelaaytogether w with multisttep predicttion error ob btainedwithANFIS

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Th he proceduree employed to perform m multiǦstep preediction with h ANFIS is sh hown in Fig. 4. First 500 samples of th he collected d tremor data was prrovidedforo offlinetrainin ngofANFIS to o obtain the optimized w weights for neeural netwo ork and m membership fu unctions. Forr multiǦstep prediction, th he whole motion sen nsed with gyyroscopeisprovidedasan ninputtoa fiffth order Butterworth bandpass fillterwithpassband2Ǧ20Hztofilter th hetremulousmotionfrom mthewhole seensed motio on. Further, multiǦstep prredictionfor6samples(6 60ms)and 8 samples (80 0ms) is perfo ormed with LS SǦSVM to overcome the delay asssociated wiith bandpasss filtering an nd EMD. T To validate multǦistep prrediction w with ANFIS S, filtered tremulou usmotionforrmazeroǦph hasebandpasssfilterwiths samespecificationsisemp ployed,asshowninFig. 4.

f 80 ms and the predictio on error obttained after For illustration, the prediction errror due to tthe delay of n for the sam me delay for ssubject #1 aree shown in F Fig. 5. In Fig g. 5 (a), the performiing multiǦsteep prediction wholem motionisshow wn,whereasinFig.5(b),filteredtrem mulousmotion nobtainedaffterbandpasssfilteringis shown.I  nFig.5(c),predictionerrrorobtainedd dueto80mssisshowntog getherwitht themultistep pprediction

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errorobtainedwithANFISforcomparison.Thepredictionaccuracyobtainedforsubject#1is49:21§1:21%. Theaveragepredictionaccuracyobtainedoverallsubjectsandtrialsfor60mspredictionlengthis50§2% and80mspredictionlengthis45:25§5%.

IV.Conclusions

References

3.

4.

5.

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7.

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2.

R. J. Elbe and W. C. Koller, Tremor, U. MD, Ed. John Hopkins University Press: Baltimore, MD, USA,1985. P. R. Cavanagh, and P. V. Komi, “Electromechanical delay in human skeletal muscle under concentricandeccentriccontractions,”Eur.J.Appl.Physiol.,vol.42,pp.159–163,1979. F. Widjaja, C. Y. Shee, W. L. Au, P. Poignet, and W. T. Ang, “ Using electromechanical delay for realǦtime antiǦphase tremor attenuation system using functional electrical stimulation,” Proc. Int. Conf.IEEEonRobo.Auto.,Shanghai,2011. A. P. L. Bo, P. Poignet, F. Widjaja, and W. T. Ang, “Online pathological tremor characterization using extended kalman filtering,” in Proc. 30th Annu. Int. Conf. IEEE Eng. in Med. Bio. Soc., Vancouver,Canada,2008,pp.1753–1756. K.Manish,H.Nystrom,L.R.Aarup,T.J.Nottrup,andD.R.Olsen,“Respiratorymotionprediction byusingtheadaptiveneurofuzzyinferencesystem(ANFIS),”inPhy.inMed.Bio.,vol.50,pp.4721Ǧ 4728,2005. S.Tatinati,K.C.Veluvolu,S.M.Hong,W.T.Latt,andW.T.Ang,“Physiologicaltremorestimation withautoregressive(AR)modelandKalmanfilterforroboticapplications,”inIEEESensorsJ.,vol. 13,pp.4977Ǧ4985,2013. K. C. Veluvolu, S. Tatinati, S. M. Hong and W. T. Ang, ” Multistep prediction of physiological tremorforsurgicalroboticapplications,”inIEEETran.onBiomed.Eng.,vol.60,pp.3074Ǧ3082,2013. G.N.Reeke,ModelingintheNeurosciences,www.MotusBioengineering.com.

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1.

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Inthispaper,ANFISisemployedformultiǦsteppredictionofpathologicaltremortoovercomethephased delay and to improve the performance. The performance of ANFIS was experimentally assessed with the tremor data collected from eight patients. An average prediciton accuracy of 50§2% is obtained with the multiǦstep prediction with ANFIS for 60 ms ahead prediction and an average accuracy of 45:25 § 5% is obtainedforpredictionlength80ms.

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