524 Vol 30 No 5, pp524 533, 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 1 1930 NA Bernstein [1] [2] [3] [] [7] [10] [11] [13] [14] [1] 1 2 2010 12 20 Graduate School of Engineering Science, Osaka University 2 3 4 2 2 1 2 A: 23 175 [cm] 48 [kg] B: 23 19 [cm] [kg] 2 2 SportsArt Fitness, T50m 30 [km/h] 1 JRSJ Vol 30 No 5 72 June, 2012
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-5000 1[kHz] m 1 m 2 m 3 m 4 m 5 m m 7 m 8 8 Fig 1 (b) [17] 2 3 2,000 10 150 [Hz] MVC %MVC 1 1 0 100% Fig 2 A 1 8 [17] 2 3 1 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 = 1 7 4 5 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) 1 2 3 2 Fig 1 (b) m 1 m 2 r 1 = m 2/m 1 30 5 73 2012
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 1,000 8 2 3 r 1(1) r 2(1) r n(1) r 1(2) r 2(2) r n(2) R = 3 7 4 5 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 40 322 15 20 1[3] [] 2 [7] [10] 3 [11] [13] 3 1 Fig 3 A 231 8 3 938% Table 2 8 Ivanenko 32 [3] [5] JRSJ Vol 30 No 5 74 June, 2012
527 Fig 4 Basic muscle synergy patterns of subject A Fig 5 Basic muscle synergy patterns of subject B c j(t) 232 4 2 3 2 3 2 3 2 3 2 3 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) 7 + + w n(t) 7 7 7 4 5 4 5 4 5 4 5 4 5 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 488 334 899 881 Subject B 435 335 182 480 Table 4 Agreement of the PC vectors between Subject A and B 1st 2nd 3rd ŝ (A) ŝ (B) 073 0871 050 ŝ (A), ŝ (B) A, B 1 1, 2 3 A Fig 1 2 3 1 2 Fig 7 8 w j(t) w j(t) =0 30 5 75 2012
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
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] 4 2 3 2 3 2 3 2 3 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) = 7 7 7 7 4 5 4 5 4 5 4 5 r 8(t) r 80 s 81 s 82 s 8n w n(t) 2 3 2 3 p 1 w(t) p 1 w cos θ 1(t) p 2 w(t) p 2 w cos θ 2(t) = = 7 7 4 5 4 5 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 3 30 5 77 2012
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] 4 2 3 2 3 2 3 2 3 2 3 r 1(t) r 10 s 11 s 12 s 1n r 2(t) r 20 s 21 = 7 w s 22 7 1(t)+ w s 2n 7 2(t)+ + w 7 n(t) 7 4 5 4 5 4 5 4 5 4 5 r 8(t) r 80 s 81 s 82 s 8n 9 w (t) T JRSJ Vol 30 No 5 78 June, 2012
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 8 094 0912 0949 0755 0789 082 0910 0891 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] 10 1 9 Fig 11 10 4 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 30 5 79 2012
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 1 00593004 0012033 04150 120 w 2 0025428 00198345 0282257 045 w 3 007703 00501977 0293535 010 B5 B510 10 sin, cos B510 0 0 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: 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, pp342 3437, 200 [ 5 ] YP Ivanenko, RE Poppele and F Lacquaniti: Motor Control Programs and Walking, Neuroscientist, vol12, no4, pp339 348, 200 [ ] YP Ivanenko, G Cappellini, N Dominici, RE Poppele and F Lacquaniti: Modular Control of Limb Movements during Human Locomotion, J Neurosci, 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 motor cortex, J Neurosci, vol2, no11, pp1527 1537, 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, pp2913 2927, 1988 [ 9 ] AB Schwartz, DM Taylor and SIH Tillery: Extraction algorithms for cortical control of arm prosthetics, Cuur Opin Neurobiol, vol11, pp701 707, 2001 [10] M Velliste, S Perel, MC Spalding, AS Whitford and AB Schwartz: Cortical control of a prosthetic arm for selffeeding, Nature, vol453, pp1098 1101, 2008 [11] E Bizzi, FA Mussa-Ivaldi and S Giszter: Computations underlying the execution of movement: a biological perspective, Science, vol253, pp287 291, 1991 [12] FA Mussa-Ivaldi and E Bizzi: Motor learning through the combination of primitives, Phil Trans R Soc Lond B, vol355, no1404, pp1755 179, 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, pp2199 2212, 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] http://riodbibaseaistgojp/dhbodydb/properties/s/index-ehtml, Human body properties database [22] 11 pp904 907, 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), pp449 4501, 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, pp980 987, 2011 Hiroaki Hirai 1997 1999 2004 2005 2010 IEEE Keita Inoue 2010 Taiki Iimura 2010 Fumio Miyazaki 1979 198 1991 1987 1988 1995 1997 IEEE 30 5 81 2012