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1 524 Vol 30 No 5, pp , 2012 Identifying the Building Blocks of a Human Walking based on the EMG Ratio of Agonist-antagonsit Muscle Pairs Hiroaki Hirai,TaikiIimura,KeitaInoue and Fumio Miyazaki The problem of motor redundancy is well known as Bernstein s problem, named after the scientist who first posed the knotty problem in the early 1930 s At present, it is still a mystery how the central nervous system (CNS) solves the ill-posed problem of motor control We recently made a discovery that links with influential hypotheses that the CNS may produce movements by combining units of motor output This paper introduces the key concept we call the A-A ratio, which is the EMG ratio of agonist-antagonist muscle pairs The statistical analysis based on the A-A ratio specifies that (1) human lower limb movement during walking is explained as the superposition of a few modular units, and that (2) decomposed modules encode the kinematic information of body movement The results also clarifies that various hypotheses, such as the muscle synergy hypothesis, the population vector hypothesis, and the convergent force fields hypothesis, are different interpretations of a common equation derived from our analysis The concept of an A-A ratio provides a beneficial suggestion to many studies on muscle-synergy extraction and gives an important clue to solving Bernstein s problem of redundant degrees of freedom Key Words: EMG Ratio of Agonist-antagonist Muscle Pairs, Human Walking, Motor Primitive, Redundant Degrees of Freedom, Kinematics, Principal Component Analysis NA Bernstein [1] [2] [3] [] [7] [10] [11] [13] [14] [1] Graduate School of Engineering Science, Osaka University A: [cm] 48 [kg] B: [cm] [kg] 2 2 SportsArt Fitness, T50m 30 [km/h] 1 JRSJ Vol 30 No 5 72 June, 2012

2 525 Fig 1 Human lower limb (a) Definition of kinematic joint angle (b) Measuring muscle activities QuickMAG System III Fig 1 (a) φ10 [mm] 20 [cm] WEB [kHz] m 1 m 2 m 3 m 4 m 5 m m 7 m 8 8 Fig 1 (b) [17] 2 3 2, [Hz] MVC %MVC % Fig 2 A 1 8 [17] t % n m 1(t) m n(t) M (n T ) 2 3 m 1(1) m 1(2) m 1(T ) m 2(1) m 2(2) m 2(T ) M = m n(1) m n(2) m n(t ) n =8 01%1 T T = 100/01 = 1,000 M 8 1,000 Fig 2 Ensemble EMG activities recorded from Subject A during treadmill walking M m(i) =[m i(1),m i(2),, m i(t )] T (i =1,, 8) m(i) m 0(t) = TX v jc j(t) j=1 2 m 0(t) m(i) v j, c j(t) j c j(t) Fig 1 (b) m 1 m 2 r 1 = m 2/m

3 52 Table 1 Definition of the agonist-antagonist muscle-pair ratio Pair label Target muscles Movement function r 1 m 2 /m 1 Hip extension r 2 m 3 /m 4 Knee extension and Hip flexion r 3 m /m 5 Knee extension r 4 m 7 /m 8 Ankle extension r 5 m 2 /m 3 Hip extension r m 3 /m 5 Knee extension (and Hip flexion) r 7 m 1 /m 4 Hip flexion r 8 m 4 /m Knee flexion (and Hip extension) Table 1 m 7 [18] m, m 7 r i (i=1,, n) t % R (T n) n =8 01% 1 T T = 100/01 = 1,000 R 1, r 1(1) r 2(1) r n(1) r 1(2) r 2(2) r n(2) R = r 1(T ) r 2(T ) r n(t ) R r(t)(= [r 1(t),r 2(t),, r 8(t)] T ) nx r(t) r 0 = w j(t)s j 4 j=1 r 0 r(t) w j(t), s j j 4 s j 1 3 Fig 3 Table 2 Basic muscle activation patterns of subject A PCA based on original EMG data: the contribution rate % of each component 1st 2nd 3rd others Subject A [3] [] 2 [7] [10] 3 [11] [13] 3 1 Fig 3 A % Table 2 8 Ivanenko 32 [3] [5] JRSJ Vol 30 No 5 74 June, 2012

4 527 Fig 4 Basic muscle synergy patterns of subject A Fig 5 Basic muscle synergy patterns of subject B c j(t) r 1(t) r 10 s 11 s 12 s 1n r 2(t) r 20 s 21 s 22 s 2n = w 1(t) 7 + w 2(t) w n(t) r 8(t) r 80 s 81 s 82 s 8n 5 Fig 4 5 A, B Table 3 3 A 912% B 952% Fig 4 5 1, 2 3 Table 4 A, B Table 3 PCA based on the A-A ratio: the contribution rate % of each component 1st 2nd 3rd others Subject A Subject B Table 4 Agreement of the PC vectors between Subject A and B 1st 2nd 3rd ŝ (A) ŝ (B) ŝ (A), ŝ (B) A, B 1 1, 2 3 A Fig Fig 7 8 w j(t) w j(t) =

5 528 Fig Kinematic meaning of the extracted muscle synergies Fig 7 Toe position of the muscular-skeletal leg robot (Subject A) Fig 8 Toe position of the muscular-skeletal leg robot (Subject B) φ, L Fig 1 (a) A, B 1 2 B 3 Ivanenko [] 3 2 Georgopoulos JRSJ Vol 30 No 5 7 June, 2012

6 529 Fig 9 Modular control based on the population vector hypothesis (a) Gait trajectory in PC scores (w 1 -w 2 ) plane (b) Estimation of hip-joint angle during swing phase (c) Estimation of knee-joint angle during swing phase [7] [9] [10] r 1(t) r 10 s 11 s 12 s 1n w 1(t) r 2(t) r 20 s 21 s 22 s 2n w 2(t) = r 8(t) r 80 s 81 s 82 s 8n w n(t) p 1 w(t) p 1 w cos θ 1(t) p 2 w(t) p 2 w cos θ 2(t) = = p 8 w(t) p 8 w cos θ 8(t) p i (= [s i1,s i2,, s in],i =1, 2,, 8) i, w(t) r i i i θ i(t) i w(t) Fig 9 (a) A w 1 w 2 0% 100% ˆφ hip (t) =φ hip,0 + a r1(r 1(t) r 10)+a r2(r 2(t) r 20) +a r5(r 5(t) r 50)+a r7(r 7(t) r 70) = φ hip,0 + a r1 p T 1 p 1 p 1 w(t) cos θ1(t) +a r2 p T 1 p 2 p 2 w(t) cos θ 2(t) +a r5 p T 1 p 5 p 5 w(t) cos θ 5(t) +a r7 p T 1 p 7 p 7 w(t) cos θ7(t) 7 ˆφ hip (t) a r1, a r2, a r5, a r7 φ hip,0 r 1, r 2, r 5, r 7 (a r1, a r2, a r5, a r7) =( 4455, 101, 2900, 1848), ˆφ hip (t) = 3528 a r2 a r7 r 2 = m 3/m 4, r 7 = m 1/m 4 m 1, m

7 530 Fig 10 Modular control based on the CFFs hypothesis (a) Gait trajectory in PC score space (w 1 -w 2 -w 3 ) (b) Vector fields in the phase plane of each PC score at the time of gait-phase 0%, 25%, 55%, and 85% ˆφ knee (t) =φ knee,0 + b r2(r 2(t) r 20)+b r3(r 3(t) r 30) +b r4(r 4(t) r 40)+b r(r (t) r 0) +b r8(r 8(t) r 80) = φ knee,0 + b r2 p T 3 p 2 p 2 w(t) cos θ2(t) +b r3 p T 3 p 3 p 3 w(t) cos θ3(t) +b r4 p T 3 p 4 p 4 w(t) cos θ4(t) +b r p T 3 p p w(t) cos θ(t) +b r8 p T 3 p 8 p 8 w(t) cos θ8(t) 8 ˆφ knee (t) b r2, b r3, b r4, b r, b r8 φ knee,0 r 2, r 3, r 4, r, r 8 (b r2, b r3, b r4, b r, b r8) = (009557, 3338, 2470, 4882, 4924), ˆφ knee (t) = 1403 b r3, b r r 3 = m /m 5, r = m 3/m 5 m 5 Fig 9 (b), (c) 3 3 Bizzi [11] [13] r 1(t) r 10 s 11 s 12 s 1n r 2(t) r 20 s 21 = 7 w s (t)+ w s 2n 7 2(t)+ + w 7 n(t) r 8(t) r 80 s 81 s 82 s 8n 9 w (t) T JRSJ Vol 30 No 5 78 June, 2012

8 531 Table 5 Correlation between computed A A ratios from EMG data and reconstructed A A ratios from the model r 1 r 2 r 3 r 4 r 5 r r 7 r wj (t) s j Table 5 88% 4 Fig 11 A A ratio change during a gait cycle 8 ẅ >< 1(t)+c 1ẇ1(t)+k 1w1(t) 3 A 1 cos 4π t c1z1 =0 T ẅ2(t)+c 2ẇ2(t)+k 2w2(t) 3 A 2 sin 4π t c2z2 =0 T >: ẅ3(t)+c 3ẇ3(t)+k 3w3(t) 3 A 3 sin 4π t c3z3 =0 T 10 c j, k j, A j z j (j =1,2,3) Fig 10 (a) A w 1 w 2 w 3 5%10 Fig 10 (b) 1 0%: 25%: 55%: 85%: [19] Fig A Fig 12 Avice, Inc Fig 1 (b) McKibben 3 [20] [21] m 3, m 4 1 p 1(> 0), p 2(> 0) r a r = p1 p 2 a = p 1 + p 2 A1 A2 r

9 532 Fig 12 Human-like muscular-skeletal leg robot a A1 A2 p 1, p 2 p 1 = 1 1+r a A3 p 2 = r 1+r a A4 p 1, p 2 r a 0 < 1/(1 + r) < 1, 0 <r/(1 + r) < 1 a a 5 8 Fig B wj (t) 10 wj (t) T T/2 2X wj (t) =c j0 + c jn cos 2nπ T t + djn sin 2nπ «T t n=1 B5 c j0, c jn, d jn (n=1, 2) Fig 13 A Fig 13 Table Fourier-series approximation of the PC scores of subject A (a) the first PC score w 1 ; (b) the second PC score w 2 ;(c)thethirdpcscorew 3 Model parameters of the forced Duffing equation c k A z w w w B5 B sin, cos B c j, k j, A j, z j B5 c j = func 1(c j0,c j1,c j2,d j1,d j2,z j) k j = func 2(c j0,c j1,c j2,d j1,d j2,z j) A j = func 3(c j0,c j1,c j2,d j1,d j2,z j) B B7 B8 func 1(), func 2(), func 3() B5 B B7 B8 A wj (t) Table JRSJ Vol 30 No 5 80 June, 2012

533 [22] [22] [24] [ 1 ] NA Bernstein: The co-ordination and regulation of movements Pergamon, 197 [ 2 ] NA Bernstein: On Dexterity and Its Development Lawrence Erlbaum Associates, Inc, 199 [ 3 ] YP

Ivanenko, RE Poppele and F Lacquaniti: Motor Patterns in Human Walking and Running, J Neurophysiol, vol95, no, pp342 3437, 200 [ 5 ] YP Ivanenko, RE Poppele and F Lacquaniti: Motor Control Programs

vol27, no41, pp11149 1111, 2007 [ 7 ] AP Georgopoulos, JF Kalaska, R Caminiti and JT Massey: On the relations between the direction of two-dimensional arm movements and cell discharge in primate

Relations between single cell discharge and direction of movement, J Neurosci, vol8, no8, pp2913 2927, 1988 [ 9 ] AB Schwartz, DM Taylor and SIH Tillery: Extraction algorithms for cortical control of

10 533 [22] [22] [24] [ 1 ] NA Bernstein: The co-ordination and regulation of movements Pergamon, 197 [ 2 ] NA Bernstein: On Dexterity and Its Development Lawrence Erlbaum Associates, Inc, 199 [ 3 ] YP Ivanenko, RE Poppele and F Lacquaniti: Five basic muscle activation patterns account for muscle activity during human locomotion, J Physiol, vol55 (Pt 1), pp27 282, 2004 [ 4 ] G Cappellini, YP Ivanenko, RE Poppele and F Lacquaniti: Motor Patterns in Human Walking and Running, J Neurophysiol, vol95, no, pp , 200 [ 5 ] YP Ivanenko, RE Poppele and F Lacquaniti: Motor Control Programs and Walking, Neuroscientist, vol12, no4, pp , 200 [ ] YP Ivanenko, G Cappellini, N Dominici, RE Poppele and F Lacquaniti: Modular Control of Limb Movements during Human Locomotion, J Neurosci, vol27, no41, pp , 2007 [ 7 ] AP Georgopoulos, JF Kalaska, R Caminiti and JT Massey: On the relations between the direction of two-dimensional arm movements and cell discharge in primate motor cortex, J Neurosci, vol2, no11, pp , 1982 [ 8 ] AB Schwartz, RE Kettner and AP Georgopoulos: Primate motor cortex and free arm movements to visual targets in threedimensional space I Relations between single cell discharge and direction of movement, J Neurosci, vol8, no8, pp , 1988 [ 9 ] AB Schwartz, DM Taylor and SIH Tillery: Extraction algorithms for cortical control of arm prosthetics, Cuur Opin Neurobiol, vol11, pp , 2001 [10] M Velliste, S Perel, MC Spalding, AS Whitford and AB Schwartz: Cortical control of a prosthetic arm for selffeeding, Nature, vol453, pp , 2008 [11] E Bizzi, FA Mussa-Ivaldi and S Giszter: Computations underlying the execution of movement: a biological perspective, Science, vol253, pp , 1991 [12] FA Mussa-Ivaldi and E Bizzi: Motor learning through the combination of primitives, Phil Trans R Soc Lond B, vol355, no1404, pp , 2000 [13] MC Tresch, VCK Cheung and A d Avella: Matrix factorization algorithms for identification of muscle synergies: evaluation on simulated and experimental data sets, J Neurophysiol, vol95, no4, pp , 200 [14] H Hirai, K Matsui, T Iimura, K Mitsumori and F Miyazaki: Modular Control of Limb Kinematics During Human Walking, Proc of the 3rd IEEE/RAS-EMBS Int Conf on Biomedical Robotics and Biomechatronics (BioRob2010), pp71 721, 2010 [15] 28 DVD-ROM 1D2-3, 2010 [1] 28 DVD-ROM 1I3-2, 2010 [17] DA Neumann: Kinesiology of the Musculoskeletal System Mosby, 2002 [18] AI Kapandji II 2010 [19] J Perry: Gait analysis Slack Incorporated, 1992 [20] VM Zatsiorsky: Kinetics of human motion Human Kinetics, 2002 [21] Human body properties database [22] 11 pp , 2010 [23] T Iimura, K Inoue, HTT Pham, H Hirai and F Miyazaki: A preliminary Experiment for Transferring Human Motion to a Musculoskeletal Robot Decomposition of Human Running based on Muscular Coordination, Proc of the IEEE/RSJ Int Conf Intelligent Robots and Systems (IROS2011), pp , 2011 [24] T Iimura, K Inoue, HTT Pham, H Hirai and F Miyazaki: Decomposition of Limb Movement based on Muscular Coordination during Human Running, J Adv Comp Intel and Intel Informatics, pp , 2011 Hiroaki Hirai IEEE Keita Inoue 2010 Taiki Iimura 2010 Fumio Miyazaki IEEE

a) Extraction of Similarities and Differences in Human Behavior Using Singular Value Decomposition Kenichi MISHIMA, Sayaka KANATA, Hiroaki NAKANISHI a

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