Muscle Synergy Analysis Between Young and Elderly People in Standing-Up Motion

Transcription

1 An, Q., Ikemoto, Y., and Asama, H. Paper: Muscle Synergy Analyss Between Young and Elderly People n Standng-Up Moton Q An, Yusuke Ikemoto, and Hajme Asama The Unversty of Tokyo Hongo, Bunkyou-ku, Tokyo , Japan E-mal: anq@robot.t.u-tokyo.ac.jp [Receved May 13, 2013; accepted October 23, 2013] Standng up s fundamental to daly actvtes of the elderly. It s necessary both to enhance muscle strength and to strengthen muscle coordnaton for mprovement of ther motor functon. In ths paper, we extract mportant data related to muscle coordnaton, called synergy, to perform standng moton by young and elderly partcpants. The contrbuton of muscle synergy to body knematcs s calculated through neural networks that estmate jont torque and body knematcs. To explan defcent motor functon n elderly persons, extracted synergy s classfed nto 4 clusters based on how synergy contrbute to body knematcs. Cluster analyss explans that elderly partcpants have weaker synergy than young persons n bendng ther backs to generate momentum. Compared to younger persons, older persons requre addtonal muscle coordnaton to stablze posture after standng-up n order to avod fallng. Keywords: standng-up moton, muscle synergy, agng, neural networks 1. Introducton The agng socety has rased severe healthcare ssues n developed countres. As lfe expectancy ncreases, the rato of elderly to young ndvduals has ncreased rapdly, potentally decreasng the qualty of lfe for both old and young persons. For the elderly, actvtes of daly lvng (ADL) gettng up from a bed or char, dressng, or usng the tolet often become more dffcult wth age [1]. Smlarly, nformal famly caregvers suffer physcal and mental stress due to the unfamlar tasks [2]. To mprove ths stuaton, preventve medcne has been suggested to enable the elderly to take more care of themselves. Many assstve systems, such as care beds or external exoskeletons, have been developed to enhance ADL for the elderly. Assstve robotcs, n fact, can ad defcent body functons, but preventve medcne has not been wdely mplemented yet. In ths study, we focus on standng up moton because the elderly who are not able to perform ths basc acton have dffculty n moblty necessary for ADL [3, 4]. Preventng ndvduals from becomng bedrdden requres both supplementng ther nsuffcent strength and retranng ther motor control. There are many prevous studes whch focus on tranng methodology to tran motor control of elderly persons. It s known that the elderly can enhance muscle strength [5], but tranng a sngle muscle may not mprove functonal ablty. Motor functon performance decreased only when muscle strength was below a certan threshold [6, 7]. It s therefore mpled that as long as the elderly persons have a certan amount of muscle strength, tranng a sngle muscle would not mprove motor functon. On the other hand, t has been reported that tranng should examne the actvaton of dfferent knds of muscles specfcally to mprove motor ablty [8]. Complex human moton usually conssts of movng dfferent muscles and jonts, so the effect of tranng a sngle muscle s lmted. To enhance motor functon as opposed to muscle strength t s mportant to know what groups of muscles are actvated together to generate moton. In ths study, the synergy hypothess s used to extract necessary groups of muscle actvaton from the standng. The dea was orgnally ntroduced by Bernsten, who suggested that complex human moton be dvded nto smplfed modules of coordnated muscle actvaton called synergy [9]. Some recent studes have shown that complex human motor tasks are smplfed by small sets of muscle coordnaton [10, 11]. If muscle coordnaton (synergy) dffers between the elderly and younger persons, t would be useful to develop tranng methodology specfcally for the defcent synergy of the elderly. Our objectves n ths paper are thus to extract synerges necessary to acheve standng-up from both the elderly and the young. Synerges are also classfed nto several groups based on ts contrbuton to standng-up moton, and how muscle synergy dffers between the elderly and the young s explaned. 2. Methods 2.1. Overvew A synergy s focused to elucdate the dfferent motor functons between elderly and young people. An experment s conducted to measure body knematcs, 1038 Journal of Robotcs and Mechatroncs Vol.25 No.6, 2013

2 Synergy1Synergy Analyss of St-to-Stand Moton n Young and Elderly People ground reacton force, and muscle electrocardography data (semg) from young and elderly people durng standng-up moton. From the obtaned semg patterns, necessary synerges to acheve the moton are extracted. In addton, two relatonshps between semg patterns and jont torque and between jont torque and body knematcs are developed for ndvduals to test how muscle synerges contrbute body knematcs. Furthermore, extracted synerges are classfed nto dfferent clusters accordng to the contrbuton of synerges to body knematcs. Fnally, contrbuton of synerges and the weaker motor functons of elderly people are clarfed Muscle Synergy Analyss The synergy model n ths study regards semg patterns as lnear combnatons of small sets of dfferent synerges [12]. Let d n the model be the number of measured muscles, t max the maxmum tme steps of obtaned semg data, and m(t) a matrx ndcatng actvaton of d muscles durng moton at tme t(0 < t t max ) as shown n Eq. (1). Muscle actvaton m(t) s expressed as a vector m. Element of m s (m 1 (t),m 2 (t),...,m d (t)) T where m ( j=1,...,d) represents muscle actvaton of the j-th muscle. m =[m(1), m(2),...,m(t max )] m 1 (1) m 1 (t max ) = (1) m d (1) m d (t max ) m(t) s approxmated usng the lnear summaton of tme-varyng synerges w =1,2,...,N (t) wth non-negatve coeffcent c and onset tme delay t as shown n Eq. (2). N s the total number of extracted synerges. Synergy s expressed as shown n Eqs. (3) (4). Elements of w (t) s also expressed as a vector of (w 1 (t),w2 (t),...,wd (t))t where w ( j=1,...,d) represents muscle actvaton of j-th muscle n -th synergy and T w s the duraton of muscle synergy. m(t) = N =1 c w (t t ) (2) w 1 (1) w1 (T w) w = (3) w d (1) wd (T w) 0 (t 0) w j (t)= w j (0 < t T w ) (4) 0 (T w < t). Fgure 1 shows the schematc desgn of the synergy model. Three muscle synerges are shown n sold lnes, dashed lnes, and sold lnes wth crcle markers respectvely (Fg. 1(a)) and observed d muscle patterns are dsplayed n gray graphs (Fg. 1(b)). Observed muscle patterns durng human moton are expressed as a lnear summaton of 3 synerges wth coeffcent (c 1,2,3 ) and onset tme delay (t 1,2,3 ) shown as vertcal sold black arrows and Synergy2Synergy3 (a) (b) Synergy1 Synergy2 (c)synergy3 Fg. 1. Synergy model: semg patterns are expressed as a lnear summaton of 3 synerges wth non-negatve coeffcent (c 1,2,3 ) and onset tme delay (t 1,2,3 ). (a) represents 3 sets of muscle synerges. (b) represents d muscle semg patterns. (c) represents synergy onset tme delay (horzontal dashed arrows) and synergy weghtng coeffcent (vertcal sold arrows) of synerges. horzontal dashed black arrows n Fg. 1(c). Dfferent strateges of motons are acheved by changng values of c and t for each synergy. When c s changed, the muscle exctaton level n synerges s controlled and the tme for startng each synergy s adjusted by the value of t Muscle Synergy Extracton A non-negatve matrx factorzaton,.e., a decomposton algorthm, s used to determne synergy patterns and tme delays for each synergy [13]. The algorthm uses the multplcatve update rule to optmze elements of synerges w, non-negatve coeffcents c, and tme delays t. The decomposton algorthm assumes that muscle actvaton m s expressed as lnear summaton of muscle synerges w wth weghtng coeffcent c and onset tme delay t. The decomposton algorthm fnds the muscle synerges w, weghtng coeffcent c, and onset tme delay t that mnmze squared error (E 2 ) between observed muscle actvaton (m) and reconstructed actvaton from muscle synerges as shown n Eq. (5). E 2 = ( ) T ( ) N N trace m w H (c,t ) m w H (c,t ) (5) =1 In the equaton, H(c,t ) s the matrx (T w t max )whch has the functon of scalng muscle synerges wth coeffcent c and shftng wth tme t (Eqs. (6) (7)). h 1 1 h t max 1 H(c,t )= (6) h 1 T w h t max T w =1 Journal of Robotcs and Mechatroncs Vol.25 No.6,

3 An, Q., Ikemoto, Y., and Asama, H. 0 (l t ) h l k = c (t l < t + T w,l = k)..... (7) 0 (t + T w < l) The followng steps are conducted n order to decde muscle synergy pattern, weghtng coeffcent, and onset tme delay: Step 1: Intal patterns of muscle synergy are determned randomly n ths study. Step 2: In order to mnmze E 2, t s necessary to fnd the onset tme delay t opt for muscle synergy w that maxmze the followng functon (Eq. (8)): t max ϕ = t=0 m(t) T w (t t ) (8) All possble values for t are tested to determne t opt. Step 3: Weghtng coeffcent c s updated wth calculated onset tme delay t opt by the followng equaton (Eq. (9)): c new m = ( ) trace(mt m) = c trace( m T, (9) m) N =1 ( ) w H c,t opt, (10) where m s the muscle actvty pattern generated from muscle synerges by Eq. (10). Step 4: Component of muscle synerges w j s updated from Eq. (11): ( w j (t)=w j m j ) (t) (t) m j (11) (t) RepeatStep2toStep4untlE 2 converges. Ths decomposton algorthm s repeated 10 tmes n order to avod fndng only local mnma. The best muscle synergy w and onset tme delay t to mnmze E 2 are selected as a soluton. Cross-valdaton method s employed n order to evaluate model accuracy. Synergy patterns are frst calculated from random selected trals of observed data, and model accuracy s tested from applyng these synergy models to the rest of observed data. determnaton (R 2 ) s used for model accuracy. Cross-valdaton s repeated 20 tmes for dfferent random data dvsons. The number of muscle synerges to be extracted s determned from the cross-valdaton method because t may be dfferent among ndvduals or t depends on ther strateges of the standng-up moton. To ascertan the number of synerges, the accuracy of the model s calculated for dfferent numbers of synerges to test how many synerges are superor for representng the standng-up moton. In order to decde the number of synerges, one factor analyss of varance (ANOVA) s performed to assess the effect of the number of synerges on the accuracy of the model. If there s a statstcal sgnfcance, a post hoc test (Tukey-Kramer) s performed for each neghborng numbers of synerges. Sgnfcance level (p) ssetto 5 n ths analyss Jont Torque and Body Knematcs Estmate The model wth 4 lnks and 3 jonts (shown n Fg. 2) s used to represent the human body. Planer movement of standng-up moton s focused on because flexon and extenson of jont excurson manly occur n the sagttal plane of body. From our experment, 3 jont angles, θ {=ankle,knee,hp}, are obtaned. Three jont torque, τ (=ankle,knee,hp), are calculated usng nverse dynamcs calculatons as shown n Eq. (12), M(θ) θ + h(θ, θ)+g(θ)+r = τ..... (12) M(θ) ndcates an nerta term, h(θ, θ) ndcates an magnary force term, g(θ) ndcates a gravty term, and R ndcates a ground reacton term. Lnk length s measured n our experment, and postons of center of mass and weght of each lnks are determned by the statstcal data of ndvdual body nformaton [14]. To understand how human body moton s generated from synerges, the relatonshps between semg and body knematcs are developed for ndvdual partcpants. Two of 3-layer neural networks are used to create mappng between semg patterns and jont torque, and between jont torque and body knematcs (Fg. 2) [15]. In our neural networks, muscular tenson generates jont torque and torque actvates jonts to acheve moton, so frstly semg patterns are used to estmate jont torque, τ =ankle,knee,hp (NN1). In addton, jont torque and ther body postons θ =ankle,knee,hp (t) and θ =ankle,knee,hp (t) at tme t are used to estmate body knematcs n the subsequent perod θ =ankle,knee,hp (t +dt) and θ =ankle,knee,hp (t + dt) (NN2). The schematc desgn of moton estmaton s shown n Fg. 2. Input varables b 1 and b 2 ndcate based threshold that are added to neural networks, NN1 and NN2. In order to tran these neural networks and update weght between nodes and based threshold b 1 and b 2,all data observed n our experment semg, jont torque, and jont angles are used. A cross-valdaton s used to calculate model accuracy wth coeffcents of determnaton R 2. A detaled confguraton of the neural network s shown n Table Synergy Classfcaton To compare synerges among ndvduals, all extracted muscle synerges are classfed nto several groups based on synergy contrbuton toward body knematcs of the standng-up. To explan ndvdual functon of synergy, changed muscle patterns are generated by weakenng partcular patterns of one synergy. Dfferent body knematcs are generated by puttng these changed muscle patterns through learned neural networks. Ths dfference s at Journal of Robotcs and Mechatroncs Vol.25 No.6, 2013

4 Synergy Analyss of St-to-Stand Moton n Young and Elderly People 0 Synerges Normal Muscle semg Moton Estmaton Generated Moton Normal Moton Jont Torque Estmate (NN1) Body Knematcs Estmate (NN2) Synergy Weakened semg Lnear Functon Tangent Sgmod Functon Synergy Weakened Moton (a) (b) (c) Fg. 2. Estmaton of jont torque and body knematcs and synergy effect computaton: above fgure shows methodology of jont torque and body knematcs estmaton and calculaton of contrbuton of synerges toward body knematcs. (a) shows a synergy model used n ths study. In ths example, eght muscle actvatons consst of two synerges (sold and dashed lnes). The top patterns (normal muscle semg) ndcate observed semg n our experment whereas the bottom patterns (synergy weakened semg) are used to analyze the effect of partcularly weakened synergy. (b) shows the neural networks whch estmates body knematcs from semg patterns. (c) shows the lnk model used n our study. Sold arrows ndcate the normal moton generaton, whereas the dashed arrows ndcate the changed moton caused by the synergy-weakened muscle patterns. Dfferences between normal moton and synergy weakened moton are compared to elucdate the effects of synerges. Table 1. Neural network confguraton. NN1 NN2 Number of Input Nodes 8 9 Number of Output Nodes 3 6 Number of Hdden Nodes 15 5 Transfer Functon of Hdden Nodes Transfer Functon of Output Nodes Learnng Rule Lnear Tangent Sgmod Tangent Sgmod Levenberg-Marquardt Number of Tranng Iteratons trbutable to the specfc weakened synergy, whch shows the effect of synerges. To prepare these changed muscle patterns, t s necessary to change the coeffcent of the extracted synergy. Eq. (13) shows how synergy-weakened muscle patterns are generated. In the equaton, m j (t) represents synergyweakened muscle actvaton of the j-th muscle at tme t, c s the changed coeffcent of -th weakened synergy, c s the actually calculated coeffcent, N represents the total number of extracted synerges, and t s the tme delay for -th synergy. c s set to 75% of orgnal coeffcent c. m j (t)= N N c w j (t t ) c w j (t t ) m j (t) (13) Fgure 2 shows normal muscle patterns and synergyweakened muscle patterns. Ths example ncludes muscle actvaton of 8 muscles approxmated by 2 synerges (shown n sold lnes and dashed lnes). Synergyweakened muscle patterns, descrbed at bottom of Fg. 2(a), are generated by weakenng one synergy shown by dashed lnes. We calculate the percentage of changes usng Eq. (14) to evaluate synergy contrbuton. The degree of absolute change between normal body knematcs and changed knematcs s calculated for the whole duraton of the moton. In the equaton, θ =ankle,knee,hp (t) shows the jont angles of the ankle, knee, and hp at certan tme t whch are generated from normal muscle actvaton. θ (t) s calculated from weakened synergy muscle patterns. Changed body knematcs are calculated from all trals of all partcpant. sc =ankle,knee,hp (t)= θ (t) θ (t)..... (14) θ (t) In ths study, the synergy contrbuton to body knematcs s calculated as the average of sc =ankle,knee,hp (t) between four phases of standng-up moton; the synergy contrbuton vector n Eq. (15) s used to represent synergy contrbuton n four phases. In the equaton, sgnfes the number of partcpants, and j denotes the ordnal number of synerges extracted from partcpants. Hence, sc k=i,ii,iii,iv θ l=ankle,knee,hp shows the average of synergy contrbuton on a specfc jont angle l durng a partcular phase k. Journal of Robotcs and Mechatroncs Vol.25 No.6,

5 An, Q., Ikemoto, Y., and Asama, H. Moton Capture semg Measurement Force Plate Data Analyss HUB hp knee ankle shoulder Quadrceps Femors (Quad Fem) Tbals Anteror (Tb Ant) Vastus Laterals (Vas) Soleus (Sol) Bceps Femors (B Fem) Gastrocnemus (Gast) Latssmus Dors (Lat Dor) Gluteus Maxmus (Glu Max) (a) Expermental setup (b) Lnk model (c) Measured semg Fg. 3. Experment desgn: (a) Schematc desgn of expermental setup. (b) Moton capture sensor stes. Sensors were attached to the shoulder, hp, knee, and ankle. (c) Muscle actvaton was obtaned from 16 muscles descrbed above. sc j =[sci θ ankle sc II θ ankle sc III θ ankle sc IV θ ankle sc I θ knee sc II θ knee sc III θ knee sc IV θ knee sc I θ hp sc II θ hp sc III θ hp sc IV θ hp ] (15) Cluster Analyss In ths paper, cluster analyss s used to classfy extracted synerges based on contrbuton on body knematcs. Synerges effects on body knematcs are dfferent among synerges because body knematcs (θ(t + dt), θ(t + dt)) s decded from both muscle actvaton generated by synerges and prevous body knematcs (θ(t), θ(t)). Each synergy therefore has dfferent effects on body knematcs although ther patterns or tme delays are smlar. K-means cluster analyss s used to classfy synerges based on ther contrbuton matrx. In the procedure, smlar synerges are dstrbuted n the same cluster. To calculate ther smlarty, the cosne of 2 synergy contrbuton vectors, sc j, s used. In order to decde the number of clusters n K-means cluster analyss, we test dfferent numbers of clusters from 2 to 5. The average of cosne of vectors between data and a md pont of a cluster s used to evaluate the classfcaton performance based on the number. If ths average s small, there are many data far from the md pont of clusters, so more clusters are needed. Ths K- means cluster analyss s appled for 100 tmes wth random ntal data dvsons. One factor repeated measures analyss of varance (ANOVA) s performed to assess effect of the number of clusters, wth post hoc two sded Tukey s smultaneous tests when approprate. The sgnfcance level s set to p = Experment Expermental Setup Fgure 3(a) shows our expermental system to measure partcpant body knematcs, ground reacton force, and semg data durng standng-up moton. MAC3D System (HMK-200RT; Moton Analyss) wth 8 cameras was used to measure body knematcs. Before recordng start, we performed calbraton to confrm the accuracy of the system. The body knematcs data were obtaned at 64 Hz. Four body parts were recorded durng experment to construct a lnk model of partcpant: shoulder, hp, knee, and ankle. Fg. 3(b) shows marker postons attached to partcpants to express the lnk model. Jont angles were calculated as angles between each lnk and a horzontal drecton. In ths study, 2 force plates were used to measure vertcal reacton force from the hps and feet at 4 Hz. We orgnally bult a force plate wth a sx-axes force sensor system (IFS-90M40A; Ntta Corp.). These forces were used to calculate ankle, knee, and hp jont torque of ndvdual partcpant from nverse dynamcs calculaton. Personal-EMG (Osaka Electroncs Devce Ltd.) was used to record semg from 8 knds of muscles (Fg. 3(c)). These muscles were chosen as flexor and extensor of ankle, knee, and hp jonts. Data were obtaned at 1600 Hz, and they were fltered wth a 10 Hz h-pass flter and Hz hum nose flter wth a flter box of the system Data Processng Measured 3-dmensonal body knematcs data were orthogonally projected onto a sagttal plane of partcpants n order to construct a 2-dmensonal lnk model. Jont angles, jont torque, and center of mass were calculated based on nverse dynamcs calculaton, body knematcs and ground reacton force data. All semg data were centered and rectfed. Both left and rght muscles were averaged to represent one muscle. semg data were fltered by the smoothng flter calculated usng Eq. (16). In the equaton, s the number of observed muscle and t s the dscrete tme step of the data. semg data were averaged for 0.2 s (320 ponts of data). Addtonally, data of jont torque and angular velocty were averaged as well Journal of Robotcs and Mechatroncs Vol.25 No.6, 2013

6 Synergy Analyss of St-to-Stand Moton n Young and Elderly People Duraton of Standng-up Moton Extended Data 0% Phase I (Flexon Momentum Phase) Phase II (Momentum Transfer Phase) Phase III (Extenson Phase) Phase IV (Stablzaton Phase) 100% Fg. 4. Four phases dvson: the four pctures portray postures of partcpants durng phases. Data were normalzed based on the start pont of each phase. 319 m (t t ) m fltered (t)= t = (16) Data Normalzaton Because the duraton of the standng-up moton dffer among partcpants, t s necessary to normalze the standng-up moton to compare dfferent trals of partcpants. It s also mportant to understand the effect of synerges from the vewpont of human body knematcs because t has been reported that muscle synergy corresponds to knematc events n human moton [10]. Consequently, 4 characterstc ponts of human standng-up moton are chosen and each phase between ponts s addressed. These 4 phases are decded from the earler study [16], and they have been wdely used to analyze the human standng-up moton [17]. The start pont of each phase s defned as follows. Phase I (Flexon Momentum Phase) It begns wth frst shoulder movement n the horzontal drecton. Phase II (Momentum Transfer Phase) It begns wth the frst hp movement n the vertcal drecton. Phase III (Extenson Phase) It begns when the ankle angle acheves the mnmum flexon. Phase IV (Stablzaton Phase) It begns when the vertcal shoulder poston acheves the maxmum heght. The end of Phase IV s determned by extendng the tme seres past the begnnng of Phase IV by an addtonal 20% of the duraton of Phases I III. In addton to the phase dvson, all data of the moton are normalzed to 100% based on total movement tme. For normalzaton, the begnnng pont of the moton s determned at the start of phase I. The end of the moton s chosen at the end of Phase IV. Fg. 4 shows a descrpton of each phase and how we normalzed data Partcpants Ten persons wth no noted mparments partcpated n our experment. The number of partcpants n ths study was suffcent for analyss compared to the number of partcpants of prevous studes (8, 9 and 10 people) that conducted the smlar experments to measure body knematcs, reacton force, and muscle actvaton [18 20]. These partcpants (P1 P10) were dvded nto 2 groups: a younger group (N = 3, P1 P3; mean age = 24.0 years, standard devaton (STD) = 3.5 years) and an elderly group (N = 7, P4 P10; mean age= 67.1 years, STD = 7.3 years). Durng experments, partcpants were told to stand up n a way they found comfortable. The number of trals they performed durng our experments dffered among partcpants rangng between 12 to 20 trals. Before experments were started, all partcpants were confrmed to be able to stand up and mantan a standng posture wthout any assstance. We have also explaned experments n detal and obtaned wrtten consent from all partcpants. 3. Results 3.1. Synergy Extracton The number of synerges to be extracted from observed semg patterns was clarfed usng the cross-valdaton method. The measured trals of standng-up moton were randomly dvded nto tranng and test data set for cross valdaton as follows: 15 trals were obtaned for P1 and were dvded nto 12 tranng data and 3 test data, 12 trals were obtaned for P2 and were dvded nto 10 tranng data and 2 test data, 16 trals were obtaned for P3 and P8 and were dvded nto 12 tranng data and 4 test data, 18 trals were obtaned for P4, P5, and P7, and were dvdednto15tranngdataand3testdata,and20trals were obtaned for P6, P9, and P10 and were dvded nto 16 tranng data and 4 test data. Changes n coeffcents of determnaton R 2 based on the number of synerges are shown n Fg. 5. Error bars n the graph show standard devaton of coeffcents of determnaton. ANOVA showed a statstcal sgnfcance of Journal of Robotcs and Mechatroncs Vol.25 No.6,

7 An, Q., Ikemoto, Y., and Asama, H. Table 2. Number of synerges and tme delay for partcpants. Number of Synerges Average Tme Delay (a) P1 (c) P3 (b) P2 (d) P4 P P P P P P P P P P Phase I II III IV Phase I II III IV (e) P5 (f) P6 P1 P6 P2 P7 (g) P7 (h) P8 P3 P8 P4 P9 () P9 (j) P10 P5 P10 Fg. 5. determnaton for partcpants: calculated averaged coeffcents of determnaton based on the change n the number of synerges are shown for all partcpants. Error bars show standard devaton. Young Elderly Muscle Actvaton Sol Tb Ant Gast Vas B Fem Quad Fem Glu Max Lat Dor P1, P2, P3, P4, P6, P7, P8, and P9. The post hoc test was appled to neghborng numbers of synerges for data of showng statstcal sgnfcance n ANOVA. Statstcal sgnfcance was found between 1 and 2 and between 2 and 3 for P1, P2, P3, P6, P7, and P9. There was a statstcal sgnfcance between 1 and 2 for P4 and P8. From ths statstcal analyss, the number of synerges was determned from how addtonal synerges contrbuted to mprovng performance, so the number of synerges was set to 1 for P5 and P10, to 2 for P4 and P8, and to 3 for P1, P2, P3, P6, P7, and P9. Fg. 6. Extracted synergy patterns: squares shown above represent extracted synerges from young partcpants (whte) and elderly partcpants (gray). Each row ndcates dfferent muscles and the X-axs shows tme steps. The brghter the color s, the more actvated each muscle s. Offsets of each synergy ndcate ther tme delays. Vertcal dashed lnes show start ponts of 4 phases. Table 2 shows the number of extracted synerges and ther tme delays. Results of extracted synergy patterns are shown n Fg. 6 wth tme delays. Each square n the fgure s an extracted synergy represented n a gray scale Journal of Robotcs and Mechatroncs Vol.25 No.6, 2013

8 Synergy Analyss of St-to-Stand Moton n Young and Elderly People Table 3. Mean dstance between data and the md pont of clusters. Table 4. Mean dstance between data and the md pont of clusters. τ ankle 0.75 ± 0.29 τ knee 0.91 ± 0.16 τ hp 0.81 ± 0.16 θ ankle 0.77 ± 0.21 θ knee 0.95 ± 9 θ hp 0.72 ± 0.16 θ ankle 0.74 ± 0.16 θ knee 0.88 ± 9 θ hp 0.76 ± 0.15 Contrbuton 40% 30% 20% 10% Number of Clusters Average Dstance STD Ankle Angle Knee Angle Hp Angle The brghter the color s, the more actvated each muscle s. The Y-axs depcts 8 measured muscles of dfferent types. Onsets for each square ndcate tme delays of the represented synergy and vertcal dashed lnes show start ponts of 4 phases Results of Cluster Synerges The musculoskeletal model was expressed as 2 neural network models to express relatonshps between semg and jont torque and between jont torque and body knematcs. Cross valdaton was used to evaluate the accuracy of neural networks. The same number of tranng and test data set was used for partcpants as n valdaton of muscle synergy extracton. Table 3 shows the average and standard devaton of coeffcent of determnaton, R 2 for estmatng jont torque, jont angle, and angular velocty. Synergy-weakened muscle patterns were put nto traned neural networks, and synergy contrbuton vectors (sc) were calculated for all 24 synerges from 10 partcpants. Body knematcs (θ(t + dt) and θ(t + dt)) were recurrently determned from the past body posture (θ(t) and θ(t)), so although duraton of some muscle synergy was only seen n specfc phases, they affected body knematcs n posteror phases. K-means cluster analyss was appled to synergy contrbuton vectors. In ths study, dt was normalzed tme step. Statstcal analyss found statstcal sgnfcance for all neghborng number of clusters to be as follows: between numbers of 2 and 3, 3 and 4, and 4 and 5. The average dstance between synerges and md pont of each cluster s shown n Table 4. The number of clusters was set to 4. If the number of clusters was more than 4, then the new cluster only ncluded a sngle data. Consequently, t seemed to mprove the performance, but the addtonal cluster caused segmentalzaton. Fgure 7 demonstrates the average synergy contrbuton of 4 clusters toward jont angles among 4 phases. The X-axs shows four phases and the Y-axs shows the mean percentage of contrbuton to each jont angle. Error bars ndcate standard devaton of synergy contrbuton. Whte bars show contrbuton toward an ankle angle. Contrbuton Contrbuton Contrbuton 0% 40% 30% 20% 10% 0% 40% 30% 20% 10% 0% 40% 30% 20% 10% 0% Phase I Phase II Phase III Phase IV (a) Cluster I Phase I Phase II Phase III Phase IV (b) Cluster II Phase I Phase II Phase III Phase IV (c) Cluster III Phase I Phase II Phase III Phase IV (d) Cluster IV Fg. 7. Average contrbuton of synerges n clusters: bar graphs show average contrbutons of synerges ncluded n 4 clusters. Error bars show standard devaton. Contrbutons to each jont angle was averaged durng each phase. The Y- axs shows ther contrbuton based on orgnal angles. Gray bars show contrbuton to a knee angle, and the black bars show contrbuton to a hp angle. Synerges nvolved n each cluster was as follows: the -th synergy of the j- th partcpant s expressed as P j-, e.g., P1-2 ndcates the second synergy of P1. Cluster I: P1-1, P1-2, P2-2, P3-1 Cluster II: P6-1, P6-2, P7-3 Journal of Robotcs and Mechatroncs Vol.25 No.6,

9 An, Q., Ikemoto, Y., and Asama, H. Cluster I Synergy Cluster II Synergy Cluster III Synergy Cluster IV Synergy Sol Tb Ant Gast Vas B Fem Quad Fem Glu Max Lat Dor Sol Tb Ant Gast Vas B Fem Quad Fem Glu Max Lat Dor Sol Tb Ant Gast Vas B Fem Quad Fem Glu Max Lat Dor Sol Tb Ant Gast Vas B Fem Quad Fem Glu Max Lat Dor Tme Steps Body Knematcs Estmaton To estmate jont torque and body knematcs, 2 neural networks were used n ths study. Estmaton results for jont torque, angle, and angular velocty showed a hgh value, whch mpled that t was able to estmate body knematcs from semg patterns. Coeffcents of determnaton, R 2, dffered n outputs of the neural networks. Specfcally, result for the knee and hp showed better estmaton results than result for the ankle a dfference was manly attrbutable to semg nput data. Among 8 nputs of NN1, muscles of 4 knds were attached to a knee and 5 attached to a hp to exert a force on t. Ths was more than the number of muscles related to a ankle jont (3 muscles), so nputs of NN1 contaned more nformaton about a knee than an ankle jont. Even so, musculoskeletal systems were developed for all subjects. Neural networks were traned wth all observed data after cross valdaton and traned networks were used for calculatng the contrbutons of synerges. Fg. 8. Average synergy patterns n clusters: average synergy patterns are shown n each cluster. The brghter the color s, the more actvated each muscle s. The Y -axs shows dfferent muscles and the X-axs shows tme steps durng synerges. Cluster III: P1-3, P2-1, P2-3, P3-2, P3-3, P4-1, P7-2, P8-1, P9-1, P9-2, P10-1 Cluster IV: P4-2, P6-3, P5-1, P7-1, P8-2, P9-3 Fgure 8 shows averaged synerges n the 4 clusters. The brghter the color s, the more actvated muscle s. Y-axs shows 8 dfferent muscles. 4. Dscusson 4.1. Synergy Extracton Muscle synerges were extracted from observed semg patterns durng standng-up moton. After cross valdaton, synergy patterns were decded based on all observed semg data. The decomposton algorthm was repeated 20 tmes for each subject, and a set of synergy was chosen that showed the hghest coeffcents of determnaton. The number of synerges to be extracted dffered between partcpants. Three synerges were extracted from all young partcpants, whereas the number of synerges were 1 3 for the elderly. Among ndvduals, strateges of standngup moton mght dffer, whch would account for dfference n the number of synerges. Dfferent standng-up strateges ndcate that muscles were actvated dfferently dependng on the strategy. Specfcally, low muscle actvaton was found n pror phases for those who used only 1 synergy (P5 and P10) whereas there was comparatvely hgher muscle actvaton observed n the earler phase for young partcpants who had 3 synerges Contrbutons of Synerges From cluster analyss, synerges n 4 clusters (Clusters I IV) were determned based on ther effects on jont angles n each phase. Snce body knematcs was affected by prevous body postures n neural networks, extracted synerges were classfed based on ther effects on body knematcs although the tme delay or patterns of synerges n each cluster dffered. Average muscle actvaton of synerges n each cluster s dscussed below (Clusters I IV Synergy) Cluster I Synergy All synerges ncluded n the Cluster I were extracted from the young group. Based on tme delays, these synerges started from the begnnng of the standng-up moton (mean tme delay = 2.25, STD = 4.50). In terms of contrbutons to each jont, synerges n Cluster I manly affected a knee jont n both Phases I and II and a hp jont n Phase II. Specfcally, n Phase II, whch was the start pont of momentum transfer, a moton of lftng-up a hp was dstracted by weakened synerges belongng to the Cluster I. Fg. 8 supports ths perspectve. The actvated muscles were the musculus soleus and musculus gastrocnemus, whch were related to the ankle, and musculus bceps femors and musculus gluteus maxmus, whch contrbuted to the hp. Ths synergy was thus presumed to work when partcpants flexed ther feet and bent ther backs to lft the hp Cluster II Synergy Synerges n Cluster II seemed to work smlarly to synerges n Cluster I Synergy. Those synerges were extracted only from the elderly group, nvolvng 2 partcpants, whch mpled that not all elderly partcpants had ths type of synerges. All these synerges started at the begnnng of the standng-up moton based on tme delays (mean tme delay 4.67, STD = 6.66). Fg. 8 shows that the 1046 Journal of Robotcs and Mechatroncs Vol.25 No.6, 2013

10 Synergy Analyss of St-to-Stand Moton n Young and Elderly People musculus gastrocnemus, musculus quadrceps femors, and musculus gluteus maxmus were actvated n the average synergy. The average actvaton of these muscles was, however, weaker and ts contrbuton to the hp angle n Phase II was also smaller than that of Cluster I Synergy Cluster III Synergy Cluster III ncluded synerges extracted from most partcpants (8 partcpants). Synergy patterns n Fg. 8 show that all muscles were actvated, and those synerges started from the mddle of the moton (mean tme delay = 32.81, STD = 10.22). Ths synergy manly contrbuted to movement n Phase III, such as extenson of whole body. Results of synergy contrbutons n the Cluster III (Fg. 7) show that Cluster III Synergy affected all 3 jont angles n the Phase III n whch people moved all 3 jonts to lft up ther upper body vertcally. Wthout ths synergy, people cannot lft up ther hp durng standng-up moton Cluster IV Synergy Synerges n Cluster IV were extracted from elderly partcpants only. These synerges started at the latter phase of the standng-up moton (mean tme delay = 50.39, STD = 13.64), and they contrbuted to the knee n Phase III and all 3 angles n Phase IV. The average synergy pattern n Fg. 8 shows that the musculus soleus, musculus gastrocnemus, musculus bceps femors, and musculus gluteus maxmus were actvated n Cluster IV Synergy. These muscles were attached and contrbute to all 3 jonts. Synerges n Cluster IV presumably functoned n stablzng posture whle compensatng for the large center-of-mass movement after the standng-up moton was acheved Dfferent Muscle Synergy Between the Young and the Elderly Extracted synerges from young and elderly partcpants were classfed nto 4 clusters clearly showng dfferences between the 2 groups. Synerges n Clusters I and II functoned smlarly; they flexed the ankle and bent ther backs. However, only two elderly people had ths type of synerges, although all young partcpants had a synergy n Cluster I. These results mpled that some elderly persons had defcent muscle coordnaton for flexng the ankle and bendng trunk to rase the hps. The reason for ths defcent motor functon mght be due to fear avodance acton. Specfcally, durng Phase II, elderly persons must transfer the center of mass from the hp to feet, whch possbly caused them to fall. For such reasons, not all of the elderly had ths type of the synergy (the Clusters I and II Synergy). Cluster III Synergy was extracted from both young and elderly partcpants and functoned as an extenson of ther whole body to complete the acton of standng-up moton. Ths suggests that the elderly also coordnated muscles when they extended the body after transferrng the center of mass on ther feet. Cluster IV Synergy, whch helped stablze posture, was seen only n elderly partcpants. Ths suggests that t was easer for elderly partcpants than for the young to lose stablty as they completed the acton of standng-up. Therefore, addtonal muscle coordnaton was necessary to stablze ther posture to avod fallng. 5. Conclusons and Future Works 5.1. Conclusons Synerges mportant to the standng-up moton were extracted from both young and elderly groups. The effects of these synerges on body knematcs has been calculated by estmatng ndvdual body knematcs estmaton. Extracted synerges were then classfed nto several groups based on ts effects. Results have shown that muscle synerges were dvsble nto 4 groups (the Clusters I IV Synergy). These synerges n each cluster functoned as follows: 1. Cluster I Synergy Cluster I Synergy was extracted only from young people and started at the begnnng of movement. It worked as flexng the ankle and rasng up ther hps to move the center of mass from ther hps to the feet. 2. Cluster II Synergy Cluster II Synergy was extracted only from two elderly people. It functoned smlarly to that of Cluster I Synergy. However, muscle actvaton nvolved n ths synergy was weaker, so ts contrbuton of movng the center of mass was less than that of ClusterISynergy. 3. Cluster III Synergy Cluster III Synergy was observed n both young and elderly partcpants. Ths synergy manly began at the mddle of the standng-up moton and affected extendng the upper body. 4. Cluster IV Synergy Cluster IV Synergy was obtaned only from some elderly partcpants. Ths synergy began at the latter phases of the standng-up moton. It stablzed posture after standng-up moton was completed. Cluster analyss explaned the dfference between the young and the elderly n terms of synerges. Compared to the young, some elderly persons had weaker synergy (Cluster II Synergy) or had no synergy at all for flexng ther ankle and bendng to rase ther hp from a char. Results also showed that some of the elderly needed addtonal synergy to stablze ther posture after the acton of standng-up had been completed. Journal of Robotcs and Mechatroncs Vol.25 No.6,

11 An, Q., Ikemoto, Y., and Asama, H Future Works Ths study has clarfed the dfference between the young and the elderly people n terms of synergy. Defcent or addtonal synerges were found from some of the elderly but not n the young. Experments and synergy analyss were performed only on the healthy elderly people, so t would be an nterestng to conduct addtonal analyss on those wth specfc dsorders, e.g., bran njury. If synerges s related to dsorders or njures, such knowledge could be useful n rehabltaton or assstve devce to support and enhance body functon. Another future drecton of our study s to mplement these fndngs n new tranng methods strengthenng the weaker synergy and corresponded body movements. Essental muscle synerges to perform the standng-up moton have been extracted n ths study. Results reported from prevous research suggest that ndvduals should tran ther motor functons n the context of moton to coordnate jont and muscle movements [21]. In tranng motor functons nvolvng bendng forward to rase ther hp, they should work on exercses nvolvng the same muscle actvaton as the extracted synerges. Squattng, for example, s one choce n tranng that trans almost all muscles nvolved n Cluster III Synergy. It surely strengthens muscles and enhances the ablty of extendng the jonts. However, squattng requres keepng the back straght up, and the exercse s usually conducted n the statc poston, whch dffers from the posture used durng Phase III. Therefore, t s necessary to tran defcent motor control n the same context of the standng-up moton. Indvduals who lose or otherwse lack synerges because of njury or dsease must regan or relearn them. Results of one study have mpled that for those who want to learn a new synergy, t would be the best to frstly try to use another exstng synergy from dfferent tasks [22]. For those who have a smlar synergy, they should just tran t ntensely. If no synergy s approprate for the standng-up moton, then they must tran and reconstruct t agan. Assstve robotcs should thus specfcally examne ths lost synergy for support or for tranng. Acknowledgements Ths research was n part supported by MEXT KAKENHI, Grantn-Ad for Scentfc Research (B) , and Grant-n-Ad for JSPS Fellows Authors thank Dr. Kaoru Takakusak of Asahkawa Medcal Unversty for gvng us the nstructon to conduct safe experment. [4] J. M. Guralnk, L. Ferrucc, E. M. Smonsck, M. E. Salve, and R. B. Wallace, Lower-extremty functon n persons over the Age of 70 years as a predctor of subsequent dsablty, New England J. of Medcne, Vol.332, pp , [5] M. A. Fatarone, E. C. Marks, N. D. Ryan, C. N. Meredth, L. A. Lpstz, and W. J. Evans, Hgh-ntensty strength tranng n nonagenarans, The J. of the Amercan Medcal Assocaton, Vol.263, pp , [6] D. G. Sale and J. D. MacDougall, Specfcty n strength tranng: a revew for the coach and athlete, Canadan J. of Appled Sports Scence, Vol.6, pp , [7] D. M. Buchnder, E. B. Larson, E. H. Wagner, T. D. Koepsell, and B. J. De Lateur, Evdence for a non-lnear relatonshp between leg strength and gat speed, Age and Ageng, Vol.25, pp , [8] S. E. Ross and K. M. Guskewcz, Effect of coordnaton tranng wth and wthout stochastc resonance stmulaton on dynamc postural stablty of subjects wth functonal ankle nstablty and subjects wth stable ankles, Clncal J. of Sport Medcne, Vol.16, No.4, pp , [9] N. Bernsten, The co-ordnaton and regulaton of movement, Pergamon, Oxford, [10] Y. P. Ivanenko, R. E. Poppele, and F. Lacquant, Fve basc muscle actvaton patterns account for muscle actvty durng human locomoton, The J. of Physology, Vol.556, pp , [11] R. R. Neptune, D. J. Clark, and S. A. Kautz, Modular control of human walkng: a smulaton study, J. of Bomechancs, Vol.42, pp , [12] A. d Avella, P. Saltel, and E. 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McGulloch, Varant and nvarant characterstcs of the st-to-stand task n healthy elderly adults, Archves of Physcal Medcne and Rehabltaton, Vol.75, pp , [19] U. P. Arborelus, P. Wretenberg, and F. Lndberg, The effects of armrests and hgh seat heghts on lower-lmb jont load and muscular actvty durng sttng and rsng, Ergonomcs, Vol.35, pp , [20] S. Kawagoe, N. Tajma, and E. Ghosa, Bomechancal analyss of effects of foot placement wth varyng char heght on the moton of standng-up, J. of Orthopaedc Scence, Vol.5, pp , [21] D. A. Jones, O. M. Rutherford, and D. F. Parker, Physologcal changes n skeletal muscle as a result of strength tranng, Quarterly J. of Experment Physology, Vol.74, pp , [22] G. C. Rchard, Changes n muscle coordnaton wth tranng, J. of Appled Physology, Vol.101, pp , References: [1] K. Andersen-Ranberg, K. Chrstensen, B. Jeune, A. Skytthe, L. Vasegaard, and J. W. Vaupel, Declnng physcal abltes wth age: a cross-sectonal study of older twns and centenarans n Denmark, Age and Ageng, Vol.28, No.4, pp , [2] P. G. Huston, Famly care of the elderly and caregver stress, Amercan Famly Physcan, Vol.42, No.3, pp , [3] J. M. Guralnk, E. M. Smonsck, L. Ferrucc, R. J. Glynn, L. F. Berkman, D. G. Blazer, P. A. Scherr, and R. B. Wallace, A short physcal performance battery assessng lower extremty functon: assocaton wth self-reported dsablty and predcton of mortalty and nursng home admsson, J. of Gerontology, Vol.49, No.2, pp , Journal of Robotcs and Mechatroncs Vol.25 No.6, 2013

12 Synergy Analyss of St-to-Stand Moton n Young and Elderly People Name: Q An Afflaton: Department of Precson Engneerng, Graduate School of Engneerng, The Unversty of Tokyo Name: Hajme Asama Afflaton: Department of Precson Engneerng, Graduate School of Engneerng, The Unversty of Tokyo Address: Hongo, Bunkyou-ku, Tokyo , Japan Bref Bographcal Hstory: Bachelor of Engneerng from The Unversty of Tokyo Master of Engneerng from The Unversty of Tokyo Doctoral Course, Department of Precson Engneerng, The Unversty of Tokyo Research Fellowshp for Young Scentst (DC1), Japan Socety for the Promoton of Scence Man Works: C. E. Stepp, Q. An, and Y. Matsuoka, Repeated Tranng wth Augmentatve Vbrotactle Feedback Increases Object Manpulaton Performance, PLoS ONE, Vol.7, e32743, Membershp n Academc Socetes: The Insttute of Electrcal and Electroncs Engneers (IEEE) The Robotcs Socety of Japan (RSJ) The Japan Socety for Precson Engneerng (JSPE) Address: Hongo, Bunkyou-ku, Tokyo , Japan Bref Bographcal Hstory: Research Assocate, RIKEN (The Insttute of Physcal and Chemcal Research) Professor, RACE (Research nto Artfacts, Center for Engneerng), The Unversty of Tokyo Professor, Department of Precson Engneerng, Graduate School of Engneerng, The Unversty of Tokyo Man Works: Y. Ikemoto, T. Mura, and H. Asama, Adaptve Dvson-of-Labor Control Algorthm for Mult-robot Systems, J. of Robotcs and Mechatroncs, Vol.22, No.4, pp , Membershp n Academc Socetes: The Insttute of Electrcal and Electroncs Engneers (IEEE) The Robotcs Socety of Japan (RSJ) The Japan Socety of Mechancal Engneers (JSME) The Socety of Instrument and Control Engneers (SICE) Name: Yusuke Ikemoto Afflaton: Graduate School of Scence and Engneerng for Research, Unversty of Toyama Address: 3190 Gofuku, Toyama , Japan Bref Bographcal Hstory: Post-Doctoral Fellow, RACE (Research nto Artfacts, Center for Engneerng), The Unversty of Tokyo Post-Doctoral Fellow, Department of Precson Engneerng, Graduate School of Engneerng, The Unversty of Tokyo Assstant Professor, Graduate School of Scence and Engneerng for Research, Unversty of Toyama Man Works: Y. Ikemoto, Y. Ishkawa, T. Mura, and H. Asama, A mathematcal model for caste dfferentaton n termte colones (Isoptera) by hormonal and pheromonal regulatons, Socobology, Vol.54, pp , Y. Ikemoto, Y. Hasegawa, T. Fukuda, and K. Matsuda, Gradual Spatal Pattern Formaton of Homogeneous Robot Group, the Int. J. of Informaton Scences, Vol.171, No.4, pp , Membershp n Academc Socetes: The Insttute of Electrcal and Electroncs Engneers (IEEE) The Japan Socety of Mechancal Engneers (JSME) The Socety of Instrument and Control Engneers (SICE) Journal of Robotcs and Mechatroncs Vol.25 No.6,