Prediction of the Wrist Joint Position During a Postural Tremor Using Neural Oscillators and an Adaptive Controller

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1 Short Communition Predition of the Wrist Joint Position During Posturl Tremor Using Neurl Osilltors nd n Adptive Controller Hmid Rez Korvi, Sr Hemmti Ali 1, Msood Vtndoust, Rsoul Mrvi Deprtment of Biomedil Engineering, Fulty of Eletril Engineering, Islmi Azd University of Mshhd, 1 Deprtment of Surgery, Imm Hossein Hospitl, Mshhd, Irn Sumission: Aepted: ABSTRACT The predition of the joint ngle position, espeilly during tremor ursts, n e useful for deteting, trking, nd foresting tremors. Thus, this reserh proposes new model for prediting the wrist joint position during rhythmi ursts nd inter urst intervls. Sine tremor is n pproximtely rhythmi nd roughly sinusoidl movement, neurl osilltors hve een seleted to underlie the proposed model. Two neurl osilltors were dopted. Eletromyogrm (EMG) signls were reorded from the extensor rpi rdilis nd flexor rpi rdilis musles onurrent with the joint ngle signls of stroke sujet in n rm onstnt posture. The output frequeny of eh osilltor ws equl to the frequeny orresponding to the mximum vlue of power spetrum relted to the rhythmi wrist joint ngle signls whih hd een reorded during posturl tremor. The phse shift etween the outputs of the two osilltors ws equl to the phse shift etween the musle tivtion of the wrist flexor nd extensor musles. The differene etween the two osilltors output signls ws onsidered the min pttern. Along with proportionl ompenstor, n dptive neurl ontroller hs djusted the mplitude of the min pttern in suh wy so s to minimize the wrist joint predition error during stroke ptient s tremor urst nd helthy sujet s generted rtifiil tremor. In regrd to the rnge of wrist joint movement during the oserved rhythmi motions, lulted predition error is deemed eptle. Key words: Neurl osilltor, preditive model, tremor urst, wrist joint ngle position INTRODUCTION A pthologil tremor is defined s n involuntry osilltory movement whih often involves the upper ody lims. [1 3] The qulity of life of people suffering from Prkinson, stroke, nd other onditions n severely worsen due to suh norml movements. Thus, lot of reserhes in the reent yers hve een foused on treting tremors. So fr, mny tretment methods hve een evluted. [4 13] Among the vrious pprohes whih hve een proposed to ope with suh frustrting onditions, the ssistive tehniques offer n ttrtive lterntive to trditionl tretments suh s surgery nd deep rin stimultion. [9] Assistive tehniques re sed on the intervention of tremor suppression y devies whih operte sed on the pplition of mehnil lods to the ffeted lims, [6] pssive or tive iomehnil loding working in prllel to the upper lim, [7] nd funtionl eletril stimultion (FES) sed prostheses. [8 13] In suh devies, the system prmeters do not remin onstnt s those re dpted to the ptient s Address for orrespondene: Dr. Hmid Rez Korvi, Deprtment of Biomedil Engineering, Fulty of Eletril Engineering, Islmi Azd University of Mshhd, Mshhd, Irn. E mil: hkorvi@mshdiu..ir ondition. Thus, losed loop feedk ontrol is usully designed where the suitle physiologil signls relted to the musle joint system re ontinuously monitored. The system prmeters, suh s stimultion intensity, re djusted in response to the signls vritions. [9,13] The feedk signls should predit the hnges in dynmis of tremor. Espeilly in the presene of the omputtionl nd inherent delys of mehnil tutors nd FES systems, preditive ility is desired. Some reserhers hve foused on prediting nd deteting the onset of pthologil tremor. [14,15] In reent work, [14] method ws proposed to predit the onset of pthologil tremor using noninvsively mesured surfe EMG (semg) nd elertion. In nother work, [15] n optimized method ws This is n open ess rtile distriuted under the terms of the Cretive Commons Attriution NonCommeril ShreAlike 3.0 Liense, whih llows others to remix, twek, nd uild upon the work non ommerilly, s long s the uthor is redited nd the new retions re liensed under the identil terms. For reprints ontt: reprints@medknow.om How to ite this rtile: Korvi HR, Ali SH, Vtndoust M, Mrvi R. Predition of the Wrist Joint Position During Posturl Tremor Using Neurl Osilltors nd n Adptive Controller. J Med Sign Sene 2016;6: Pulished y Wolters Kluwer Medknow 117

2 presented for tremor detetion nd temporl trking sed on the seond order moment lultions on the semg signl. However, most reently proposed reserhes hve ddressed the joint ngles s highly potentil fetures to extrt ontext informtion relted to tremors. [16] Reently, two lgorithms were presented tht enle the roust extrtion of joint ngles nd relted fetures so s to enle long term ontinuous monitoring of tremors. [16] Some other reserhers hve reported their otined results relted to urte estimtion of mplitude nd the frequeny of wrist joint tremor signls. [17,18] These employed pprohes were utilized to trk tremor movements. [17,18] The rel time estimtion of pthologil tremor hs een lso ddressed. [19] The presented lgorithm ws two stge lgorithm for the rel time estimtion of instntneous tremor prmeters using gyrosope reordings. [19] Some other reserhers hve explored the hrteriztion of pthologil tremors from the semg signls. [20] This pproh ws sed on the iterted Hilert trnsform. [20] However, it seems tht the development of simple nd urte preditive model to forest the joint ngle position during tremor urst is still n open issue to reserh. Aordingly, in the urrent study, neurl osilltor sed model hs een utilized to estimte the wrist ngle position s muh s 100 ms into the future during rhythmi posturl tremor urst. Suh neurl osilltors were previously used s forwrd ontroller for tremor suppression vi FES. [9] However, in the present work, neurl osilltors re the min omponents of proposed preditive dptive model. The roust stility properties of the limit yle ehvior of neurl osilltors nd their usge for pproprite molding of rhythmi phenomen, suh s tremors, re intriguing. The performne of the present model for predition of joint ngle position during inter urst intervls ws lso ssessed. The reorded dt used for design nd evlution of model were reorded from the wrist gonist nd ntgonist musles of stroke ptients. For further evlution, the performne of the model ws ssessed y prediting the joint ngle position of helthy ptient during generted rtifiil tremor. MATERIALS AND METHODS Experimentl Dt Colletion One stroke ptient nd one helthy sujet volunteered prtiipte in the urrent experimentl study (2 mles; ge 22). The prtiipting stroke ptient ws hemiplegi suffered from wrist musle posturl tremor. Before strting the experiments, onsent form ws ompleted y eh prtiipnt. The sujets were instruted to perform the experiments ording to the defined protool. The sujets were seted in omfortle position next to the devie with the shoulder extended 90, rm oriented in trnsverse plne [Figure 1] while elow ws fully extended nd wrist fully pronted. The sujet ws sked to keep his rm in this onstnt position. The onduted experiments 118 Goniometer Figure 1: The experimentl setup relted to dt olletion on the stroke ptient lsted up to 20 s until t lest two tremor ursts were oserved. While experiments were eing onduted on the helthy sujet, he ws moving his wrist joint in rhythmi mnner tht lsted 20 s. In ft, the helthy sujet performed two long time trils. During the movement, the EMG signls of the wrist extensor (extensor rpi rdilis) nd flexor (flexor rpi rdilis) musles were reorded y reording system (Model ME6000, Meg Eletronis, Kuopio, Finlnd). For reording, irulr Ag/AgCl surfe eletrodes hd een pled in the diretion of the musle fiers. [21] For holding down the impedne, the skin ws lened with 70% lohol efore reording. The EMG signls were smpled t frequeny of 1 KHz nd filtered through nd pss filter ( Hz). Sine the reording devie ws ttery powered, noth filter (50 Hz) ws not needed. A goniometer (model SG56, Biometris Ltd, Gwent, UK) ws tthed to the wrist joint. The joint ngle signl ws smpled with frequeny of 1 KHz. Proposed Preditive Model Reording Eletrodes Figure 2 presents the lok digrm of the proposed dptive model. It ontins three mjor prts: Osilltors, dptive neuron, nd proportionl (P) ontroller s the ompenstor. Two neurl osilltors re in hrge of pttern genertion. The differene etween dptive ontroller output nd the output of P ompenstor djusts the mplitude of the output signl of the osilltors. The premise of the presented model is sed on the rhythmi ehvior of tremor. A tremor is rhythmi semi sinusoidl ehvior. Suh movement t the joints rises from rhythmi involuntry tivtion of the gonist nd ntgonist musles. It hs een shown tht the EMG signl is very losely orrelted with the joint ngle. [22] This indites diret reltion etween the musle tivtion profile nd vritions of joint ngle during joint movement. It hs een shown tht some neurl osilltors in some res of the rin nd spinl ord re in hrge of rhythmi neurl tivity nd rhythmi movements, [23,24] ut tremor is used y type of pthologil neurl Vol 6 Issue 2 Apr Jun 2016

3 osilltor. [9] Aordingly, in the urrent proposed model, two distint neurl osilltors re seleted to simulte the effet of the pthologil neurl osilltor tht genertes the motor ptterns of involuntry rhythmi movement, lso lled tremors. The first nd the seond osilltors orrespond to the flexor nd the extensor musles of the wrist joint, respetively. The flexor nd extensor musles hve opposite roles nd the ontrtion of one ounterts the torque eliited y ontrtion of the other. Thus, in the present model, the min rhythmi is provided y finding the differene etween the rhythmi output signls of the two osilltors orresponding to eh musle. The dptive neuron nd P ontroller, s will e disussed lter, re used to modulte the output of the pttern genertor to trk the rhythmi hnges of wrist joint ngle position. The min prts of the proposed preditive model will e demonstrted in the next three susetions. Neurl Osilltors of the Model As previously mentioned, in the proposed preditive model, two distint neurl osilltors re hosen to simulte the effet of the pthologil neurl osilltor tht genertes the tremor. In the present reserh, Mtsuok neurl osilltor ws hosen nd implemented. The Mtsuok neurl osilltor hs een fully investigted in some literture. [25 28] A single Mtsuok neurl osilltor is omposed of two oupled neurons with self inhiition. [27] The mthemtil desription is given elow. 2 T1 xi = ij yj + si fi ( i =12, ) (1) j= 1 T 2 f i + f i = y i (2) where y i = g (x )[g (x ) = mx {0, x }] (3) i i i The output of the neurl osilltor is s follows: O i = y 2 y 1 (4) where ij ( 0 for i j nd = 0 for i = j) is the weight of inhiitory synpti onnetion from the j th neuron to the i th neuron, x i is the vrile of the memrne voltge in neuron, f i is the memrne urrent, nd g (x i ) is nonliner funtion with unit gin for x i when it is nonnegtive or otherwise is zero. In this model of the neuron, y i is the output of the neuron nd O is the output of the neurl osilltor. The prmeter s i is onstnt drive input nd represents the dpttion onstnt eing relted to the self inhiition of eh neuron. The prmeter T 1 is the rise time onstnt nd T 2 is the dpttion time onstnt. Figure 3 shows the struture of the Mtsuok model. The Mtsuok model n generte stle rhythm 12 s1 under two onditions; (1) 1+ < 21 s2 s2 1+ < s nd 1 T1 (2) ( 2112 ) < 1+ T while must e lrge. [27] In ddition, 2 the output frequeny of n osilltor is roughly proportionl [28] to 1/T 1. Adptive Controller nd Proportionl Compenstor The proposed model is preditive model. Sine the mjor prt of the model is rhythmi pttern genertor, some other prts re needed to modulte the output signl of the pttern genertor for preditive trking of wrist joint ngle hnges. Beuse the musle joint system is nonliner nd time vrying system, [29] n dptive modultor should e seleted. In the present work, nonliner dptive ontroller, whih hd een used erlier, [30,31] ws hosen s the nonliner modultor. The mthemtil desription is given elow. 1 Neurl Osilltor 1 Neurl Osilltor 2 O 1 O 2 - Adptive Controller O U + - U C Proportionl Compenstor Model Output 100ms Dely Atul Wrist Joint Angle - e 2 - Figure 2: The lok digrm relted to the struture of the proposed dptive preditive model Figure 3: The Mtsuok osilltor model Vol 6 Issue 2 Apr Jun

4 I = e+ e + e dt t 0 U = f (I) = α tnh (β [I γ]) (6) where e is the wrist joint predition error. In other words, e is the error vlue etween the tul wrist joint position nd the predited vlue y the model 100 ms erlier. In ft, the model is forwrd preditor whih should estimte the wrist ngle position s muh s 100 ms into the future. The U is the output of the ontroller eing dded to the output of the pttern genertor. This signl, s ontrol signl, djusts the mplitude of the pttern genertor output in suh wy tht it trks the tul wrist joint ngle nd leds to low predition error. The prmeters θ = [α β γ] re dpted online during the predition without offline trining. To gurntee the glolly symptotilly stility of the system, the following dpttion rules hve een used: [32] θ = δ U θ Out e sgn (7) U where δ >0 is the lerning rte prmeter, out is the model output [Figure 2], nd sgn(.) is sign funtion. The dptive models inevitly enounter unmolded dynmis. Therefore, s proportionl ontroller, fixed prmeter proportionl ompenstor (proportionl gin = 1) ws dopted to ompenste for the effet of unmolded dynmis on the performne of the predition model. The output of the proportionl ontroller is s follows: U = K e (8) where e is the wrist joint predition error nd K = 1 is the proportionl gin. Adjustment of the Design Prmeters Two design prmeters should e hosen: Output frequeny of the osilltors nd phse shift etween the outputs of the two osilltors. Sine the output of rhythmi pttern genertor should e synhronized with the wrist joint tremor signl, the frequeny of the two neurl osilltors, s the mjor prts of the pttern genertor, ws equl to the omputed verge of the frequeny orresponding to the mximum vlue of power spetrum relted to the rhythmi wrist joint ngle signls whih hd een reorded during tremor ursts. Figure 3 shows the power spetrl density relted to the two different ursts. The rnge of the otined frequeny relted to 10 different tremor ursts nd the generted rtifiil tremors relted to helthy sujet ws from 3.9 Hz to 4 Hz. Therefore, the prmeters of the osilltor were hosen in wy [26 28] tht the frequeny of the neurl osilltors ws 4 Hz [Tle 1 nd Figure 4]. (5) Tle 1: Prmeters of dopted neurl osilltors τ 1 τ 2 S 1 S f 1 f Power Spetrl Density Welh Power Spetrl Density Estimte Frequeny [Hz] Figure 4: The power spetrl density of reorded joint ngle signl during smple tremor urst Oviously, the phse shift etween the outputs of the two osilltors is key prmeter. As previously explined, eh osilltor orresponds to one wrist musle (extensor nd flexor). Thus, strtegy ws dopted to determine the phse lg using nlyses of the reorded EMG signls of the wrist extensor nd flexor musles. The tul EMG signls were retified, normlized, nd filtered using the 8 th order Butterworth low pss filter with utoff frequeny of 17 Hz. Figure 5 shows retified nd normlized smple EMG signl reorded during tremor urst, its filtered signl, nd the orresponding wrist joint ngle signl ourring during the sme tremor urst. As Figure 5 demonstrtes, with suh filtering, the tul EMG signl is trnsformed to yli signl whih n revel the rhythmi ehvior of the EMG signl during ursts. Clerly, eh yle of the filtered EMG signls lies within yle of rhythmi wrist joint ngle signls. It should e emphsized tht EMG signls do not ontin voluntry omponent euse of the reording protool. Therefore, extrting the tremor omponent, s disussed in some literture, [20] is not n issue rised y the present study. In ft, the rhythmi omponent of the musle tivtion pttern ws extrted through low pss filter. In this mnner, the yles of tremulous musle tivtion eome oservle nd detetle. Figure 6 provides the filtered EMG signls relted to the wrist extensor nd flexor musles. There is phse lg etween the filtered EMG signls of the gonist musle nd the ntgonist s musle. However, eh yle of oth filtered EMG signls lies within yle of rhythmi wrist joint ngle signl. The vlues of the time intervls etween the peks of extrted yli signls during eh yle intervl ourring within tremor urst were mesured. The otined verge vlue ws 70 ± 2 ms. Therefore, 70 ms phse lg time ws oserved etween the outputs of the two osilltors. 120 Vol 6 Issue 2 Apr Jun 2016

5 Figure 5: () Normlized retified eletromyogrm signl relted to the wrist extensor musle during time intervl within the tremor urst, () orresponding low pssing filtered signl, () orresponding ngulr vritions of the wrist joint Figure 6: () The low pssing filtered signl relted to the wrist extensor musle (solid line) nd wrist flexor musle (dsh line) during time intervl within tremor urst, () orresponding ngulr vritions of the wrist joint It is worth mentioning tht the proposed model should e identified in se dependent mnner. In other words, the output frequeny of the neurl osilltors nd the phse lg time etween their outputs should e determined for eh ptient sed on nlyses of relted reorded EMG signls. Here, the forementioned prmeters were determined for stroke ptient. RESULTS Predition of Rhythmi Wrist Movement Figures 7 9 present some typil results. In ft, these figures show exmples of joint ngles otined with the proposed preditive model, long with hnges of the dptive ontroller output, proportionl ompenstor output during two distint tremor ursts in the stroke ptient, nd rtifiil tremor generted in the led odied ptient. The first interesting oservtion is the fst onvergene of the model output. The output of the model onverged on the tul wrist joint ngle trjetory so fst tht no onsiderle onvergene lteny n e oserved. It should e noted tht the min prmeters of the model, output frequeny of the neurl osilltors, nd the phse lg time etween them, were determined using nlyses of the reorded dt relted to the first tril. These prmeters were fixed for evluting the model performne in the predition of wrist joint movement using reorded dt during the different trils. In other words, no prmeter Vol 6 Issue 2 Apr Jun

6 Figure 7: () Atul reorded joint ngle during smple tremor urst (solid line) nd predited joint ngle during tremor urst (dsh line), () output of dptive ontroller, () output of proportionl ompenstor Figure 8: () Atul reorded joint ngle during smple tremor urst (solid line) nd predited joint ngle during tremor urst (dsh line), () output of dptive ontroller, () output of proportionl ompenstor Figure 9: () Atul reorded joint ngle during n rtifiilly generted tremor (solid line) nd predited joint ngle during n rtifiilly generted tremor (dsh line), () output of dptive ontroller, () output of proportionl ompenstor 122 Vol 6 Issue 2 Apr Jun 2016

7 tuning ws needed nd the model performne in the predition of the joint position, s reorded during the different trils, ws similr. A summry of the results over 12 reorded experimentl dt on the two sujets is founded in Tles 2 nd 3. The verge root men squre (RMS) prediting error for out 95 rnge of joint movement during rhythmi movement is 0.27 ±0.09 for the le odied sujet nd ±0.03 for out 35 rnge of joint movement during tremor ursts for the stroke ptient. The lulted verge vlue of the RMS prediting errors relted to ll omputed RMS prediting errors ws ±0.04. The verge orreltion oeffiient etween the model output nd the tul wrist joint ngle for the le odied nd stroke ptient ws out 1. Suh results indite tht the model ws le to hieve n eptle predition performne. Tle 2: The lulted root men squred prediting errors relted to the predition of the wrist joint ngle during the tremor urst in the stroke ptient Tremor urst Root men squred ( ) Tle 3: The lulted root men squred prediting errors relted to the predition of the wrist joint ngle during the 20 s of rtifiilly generted rhythmi motions in the helt hy sujet Rhythmi motion 1 2 Root men squred ( ) It is worth noting tht the time durtion of the oserved tremor ursts in the stroke ptient vried. It ws etween 2 s nd 5 s. Predition of Wrist Movement During the Inter urst Intervl Intriguing oservtion is low predition error even during the inter urst intervl. Figure 10 shows typil wrist joint trjetory during the 2.62 s time segment of n inter urst intervl. The verge RMS prediting error of the wrist joint movement during the reorded intr urst intervls is ± Suh low verge vlue eluidtes tht the presented model hs trked the dynmis of joint ngle hnges, in preditive mnner, even etween two onseutive urst. The neuromusulr system is dynmi system. [30] Thus, the ehvior of this system during the urst nd inter urst intervls nnot e onsidered s two independent ehviors. Therefore, suh results n indite the effetive role of the dptive ontroller. Beuse the model performne (RMS prediting error) hd not dropped during the inter urst intervl, the output frequeny of the neurl osilltors nd phse lg time etween them were set using the nlyses of the wrist joint hnges nd EMG signls reorded during the tremor ursts. Aording to the results [Figure 10], during the inter urst intervl, the dptive ontroller output ws mostly sturted while the proportionl ompenstor output hnged. It n e onluded tht during the inter urst intervl, when the mplitude of flututions lowered onsiderly, the ontriution of the dptive ontroller in sutly tuning the model output deresed. In this mnner, the role of the proportionl ompenstor on sutly djusting the output of the neurl osilltor sed pttern genertor is further lrified. Figure 10: () Atul reorded joint ngle (solid line) nd predited joint ngle (dsh line), () output of dptive ontroller, () output of proportionl ompenstor Vol 6 Issue 2 Apr Jun

8 Sensitivity Anlysis with Respet to Initil Vlues When using n dptive model, one of the ruil issues tht should e nlyzed is the ssessment of model sensitivity with respet to the initil vlues. Sine mjor prt of the presented model is n dptive ontroller, suh nlysis is vitl. It ws oserved tht if is set s 1 nd two other prmeters re dpted, the predition error will signifintly derese. Therefore, α ws fixed while β nd γ were dpted using the dpttion rules. In this study, the initil vlues of ontroller prmeters β nd γ were set s rndom vriles with uniform distriution etween 0 nd 1 while the other prmeter, α, ws fixed s 1. It ws oserved tht the initil vlues eyond this rnge leds to instility of the ontrol system. Figures 10 nd 11 show two typil trjetories for two different smple initil onditions relted to ontroller prmeter hnges, long with hnges of the dptive prmeters, during the sme tremor urst. Aording to severl simultion studies tht were rried out, the rnge of the RMS of the predition error for 10 different initil onditions ws within to 0.11 while the vlue of the orreltion oeffiient ws 1. As previously mentioned, the reported results [Figures 7 9] were otined while the initil vlues of the prmeters were 0. Of ourse, suh results show the dependeny of model performne on the initil ondition of the dptive ontroller. Nevertheless, onerning the rnge of wrist joint movement during the oserved rhythmi motions, out 35 for the stroke ptient nd out 95 for the helthy sujet, the lulted RMS predition errors re eptle [Figures 11 nd 12]. Figure 11: () Atul reorded joint ngle during tremor urst (solid line) nd predited joint ngle during tremor urst (dsh line), () hnges of β prmeter over time, () hnges of γ prmeter over time while β(0) =0 nd γ(0)=0 re the initil onditions Figure 12: () Atul reorded joint ngle during tremor urst (solid line) nd predited joint ngle during tremor urst (dsh line), () hnges of β prmeter over time, () hnges of γ prmeter over time while β(0)=0.01 nd γ(0)=0.02 re the initil onditions 124 Vol 6 Issue 2 Apr Jun 2016

9 It is worth noting tht the onvergene time of the model output hs remined nerly onstnt nd independent of initil onditions. Sensitivity Anlysis with Respet to Phse Lg Time As previously explined, the vlue of the phse lg time etween neurl osilltor outputs ws otined through the nlyses of the phse shift vlue etween two filtered EMG signls relted to the first ptient tril. This vlue ws onstnt nd no more tuning ws needed. The model performne ws similr to predition of the joint position s reorded during the different trils. Figure 13 shows the three otined results. Eh result ws hieved s different vlue of the phse lg time within its rnge (70 ± 2 ms) while the predited signl ws the sme, whih ws smple reorded signl from the stroke ptient. In eh of three oserved simultions, the phse lg time ws determined through the nlyses of three different reorded dt. Nevertheless, the lulted RMS nd orreltion oeffiients were nd 1, respetively. The omputed RMS nd orreltion oeffiients were equl. Aording to severl studies tht hve een rried out, the similr results were seen. Aording to suh results, it n e limed tht single reording tril is enough for determining the phse lg time etween the neurl osilltors. DISCUSSION The min interest nd purpose of the urrent study were to exploit neurl osilltors for development of n dptive model to predit the wrist joint position during posturl tremor ursts. While some literture hd ddressed the issue of tremor trking nd tremor estimtion, in the present work, the estimtion of the wrist ngle position hs een ddressed with s muh s 100 ms into the future during the rhythmi posturl tremor urst. The neurl osilltor ws formerly dopted to develop the feed forwrd ontroller for tremor suppression using FES. [9] In this work, the neurl osilltor ws pplied s the mjor prt of preditive model for the forwrd predition of the wrist joint during tremor urst. In ddition, in the proposed modeling strtegy, n dptive ontroller ws dopted for djusting model output. Inorporting ontroller into model, s suh, n e onsidered n innovtion. Sine the min ide lying ehind the proposed model struture is relted to the role of rhythmi musle tivtion on rhythmi wrist joint movement, the performne of the presented model ws evluted not only with reorded dt relted to stroke ptient ut lso with reorded dt relted to three le odies. In the first step, the output frequeny of neurl osilltors nd the phse lg time etween them were determined y power spetrl nlysis of the wrist joint trjetory nd nlyses of EMG signls from the first reording tril. The men vlues of the lulted quntittive evlution mesures [Tles 2 nd 3] testify to proposed model s promising performne euse the men vlue of the RMS for rnge of movement of out 35 is ±0.03, nd the men vlue of the orreltion oeffiient is very ner to 1. The firly fst onvergene time of model output is lso onvining. As suh, the neuromusulr system is dynmi one. It hs een suggested tht tremor n e generted y pthologil tivity within sensory feedk loop. [13] In ddition, it hs een shown tht inresing gin within the musle spindle reflex loop n determine system instility resulting in tremor like osilltions. [14] Aordingly, the Figure 13: Atul reorded joint ngle during tremor urst (solid line) nd predited joint ngle during single tremor urst (dsh line). () The phse lg is 70 ms, () the phse lg is 68 ms, () the phse lg is 72 ms Vol 6 Issue 2 Apr Jun

10 osilltory ehvior of the neuromusulr system during urst intervl is relted to hnge in system dynmis. Thus, the ssessment of the proposed model y trking dynmi hnges fter tremor urst ws entiing. The model performne ws eptle s regrds the furting of the wrist joint movement during tremor urst. In ny se, in the next step, the ility of the presented model to predit of wrist joint movement during n inter urst intervl ws evluted. Aording to the results, its performne in prediting the wrist joint movement during urst intervl nd n inter urst intervl ws omprle. Suh findings eluidte the intriguing ility of neurl osilltor sed model for trking the dynmis of neuromusulr system fter the onset of tremor urst. Another point oserved is the prt plyed y the dptive ontroller nd proportionl ontroller in djusting the mplitude of the pttern genertor output during n inter urst intervl. The results show tht the ontriution of the dptive ontroller nd proportionl ompenstor in modulting the output of the pttern genertor differs during urst intervls from wht is oserved during inter urst intervls. This indites the presene of n eliited intertion etween the dopted ontroller nd the ompenstor whih leds to eptle model performne. In different trils, the time durtion of the oserved tremor ursts differed, lying within rnge of 3 s (etween 2 s nd 5 s). Thus, ording to suh dt, model performne is not dependent on the time durtion of tremor urst. The present study nlyzed the sensitivity of the presented model with respet to the initil ondition of the dptive ontroller s prmeters nd the vlue of the phse lg time etween the osilltors. It ws found tht the predition error is not sensitive to these prmeters. This finding n e onsidered n dvntge s it shows tht the model s si prmeters n e set mnully in person driven mnner employing reorded dt relted only to single reording tril. In the urrent work, numerous studies were onduted to evlute the performne of the presented model from vrious spets. From n overll perspetive, it n e stted tht the performne of the proposed model is eptle in prediting rhythmi wrist joint movement, espeilly during n involuntry posture tremor urst. Future work will fous on design of ontrol strtegy for tremor suppression sed on this model. Aknowledgments This work ws supported y Neuromusulr Control L, Biomedil Deprtment, Islmi Azd University, Mshhd Brnh. Finnil Support nd Sponsorship Nil. 126 Conflits of Interest There re no onflits of interest. REFERENCES 1. Elle RJ. Tremor: Clinil fetures, pthophysiology, nd tretment. Neurol Clin 2009;27:679 95, v vi. 2. Wenning GK, Kiehl S, Seppi K, Müller J, Högl B, Sletu M, et l. Prevlene of movement disorders in men nd women ged yers (Brunek Study ohort): A popultion sed study. Lnet Neurol 2005;4: Elle R, Koller W. Tremor. USA: Johns Hopkins University Press; Lyons KE, Phw R. 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