A model fo the neuro-musculo-skeletal system for human locomotion. I: Emergence of basic gait. (English) Zbl 0826.92012

Summary: The generation of human locomotion was examined by linking computational neuroscience with biomechanics from the perspective of nonlinear dynamical theory. We constructed a model of human locomotion, which includes a musculo-skeletal system with 8 segments and 20 muscles, a neural rhythm generator composed of 7 pairs of neural oscillators, and mechanisms for processing and transporting sensory and motor signals. Using a computer simulation, we found that locomotion emerged as a stable limit cycle that was generated by the global entrainment between the musculo-skeletal system, the neural system, and the environment. Moreover, the walking movements of the model could be compared quantitatively with those of experimental studies in humans.


92C20 Neural biology
92C10 Biomechanics


Zbl 0806.92013
Full Text: DOI


[1] Andersson O, Grillner S (1983) Peripheral control of the cat’s step cycle. II. Entrainment of the central pattern generators for locomotion by sinusoidal hip movements during ’fictive locomotion’. Acta Physiol Scand 118:229–239
[2] Arshavsky YI, Gelfand IM, Orlovsky GN (1984) Cerebellum and rhythmical movements. Springer, Berlin Heidelberg New York
[3] Bässler U (1986) On the definition of central pattern generator and its sensory control. Biol Cybern 54:65–69
[4] Beer RD (1990) Intelligence as adaptive behavior. Academic Press, New York · Zbl 0743.68111
[5] Berger W, Dietz V, Quintern J (1984) Corrective reactions to stumbling in man: neuronal co-ordination of bilateral leg muscle activity during gait. J Physiol 357:109–125
[6] Clark JE, Phillips SJ (1993) A longitudinal study of intralimb coordination in the first year of independent walking: a dynamical systems analysis. Child Dev 64:1143–1157
[7] Crowninshield RD, Brand RA (1981) A physiologically based criterion of muscle force prediction in locomotion. J Biomech 14–11:793–801
[8] Cruse H (1990) What mechanisms coordinate leg movement in walking arthropods? Trends Neurosci 13:15–21
[9] Davis BL, Vaughan CL (1993) Phasic behavior of EMG signals during gait: use of multivariate statistics. J Electromyogr Kinesiol 3:51–60
[10] Davy DT, Audu ML (1987) A dynamic optimization technique for predicting muscle forces in the swing phase of gait. J Biomech 20:187–201
[11] Delcomyn F (1980) Neural basis of rhythmic behavior in animals. Science 210:492–498
[12] Dietz V (1992) Human neuronal control of automatic functional movements: interaction between central programs and afferent input. Physiol Rev 72:33–69
[13] Doya K, Yoshizawa S (1992) Adaptive synchronization of neural and physical oscillators. In: Moody JE, Hanson SJ, Lippmann RP (eds) Advances in neural information processing systems 4. Morgan Kaufmann, San Mateo, 109–116
[14] Ekeberg Ö (1993) A combined neuronal and mechanical model of fish swimming. Biol Cybern 69:363–374 · Zbl 0780.92007
[15] Flashner H, Beuter A, Arabyan A (1987) Modeling of control and learning in a stepping motion. Biol Cybern 55:387–396 · Zbl 0604.92023
[16] Forssberg H (1979) Stumbling corrective reaction: a phase-dependent compensatory reaction during locomotion. J Neurophysiol 42:936–953
[17] Forssberg H (1985) Ontogeny of human locomotor control. I. Infant stepping, supported locomotion and transition to independent locomotion. Exp Brain Res 57:480–493
[18] Grillner S (1985) Neurobiological bases of rhythmic motor acts in vertebrates. Science 228:143–149
[19] Grillner S, Matsushima T (1991) The neural network underlying locomotion in lamprey – synaptic and cellular mechanisms. Neuron 7:1–15
[20] Grillner S, Wallen P (1982) On peripheral control mechanisms acting on the central pattern generators for swimming in the dogfish. J Exp Biol 98:1–22
[21] Haken H, Kelso JAS, Bunz H (1985) A theoretical model of phase transitions in human hand movements. Biol Cybern 51:347–356 · Zbl 0548.92003
[22] Hatze H (1976) The complete optimization of a human motion. Math Biosci 28:99–135 · Zbl 0331.92003
[23] Hogan N (1985) The mechanics of multi-joint posture and movement control. Biol Cybern 52:315–331 · Zbl 0599.73101
[24] Holt KG, Hamill J, Andres RO (1990) The force-driven harmonic oscillator as a model for human locomotion. Hum Mov Sci 9:55–68
[25] Inman VT, Ralston HJ, Todd F (1981) Human walking. Williams & Wikins, Baltimore
[26] Kawahara K, Mori S (1982) A two compartment model of the stepping generator: analysis of the roles of a stage-setter and a rhythm generator. Biol Cybern 43:225–230
[27] Kimura S, Yano M, Shimizu H (1993) A self-organizing model of walking patterns of insects. Biol Cybern 69:183–193
[28] Leonard CT, Hirschfeld H, Forssberg H (1991) The development of independent walking in children with cerebral palsy. Dev Med Child Neurol 33:567–577
[29] Macpherson JM (1988) Strategies that simplify the control of quadrupedal stance. I. Forces at the ground. J Neurophysiol 60:204–217
[30] Maioli C, Poppele RE (1991) Parallel processing of multisensory information concerning self-motion. Exp Brain Res 87:119–125
[31] Matsuoka K (1985) Sustained oscillations generated by mutually inhibiting neurons with adaptation. Biol Cybern 52:367–376 · Zbl 0574.92013
[32] Matthews PBC (1991) The human stretch reflex and the motor cortex. Trends Neurosci 14:87–91
[33] McGeer (1993) Dynamics and control of bipedal locomotion. J Theor Biol 163:277–314
[34] McGraw MB (1940) Neuromuscular development of the human infant as exemplified in achievement of erect locomotion. J Pediatr 17:747–771
[35] McMahon TA (1984) Muscles, reflexes, and locomotion. Princeton Univ Press, Princeton
[36] Miller S, Scott PD (1977) The spinal locomotor generator. Exp Brain Res 30:387–403
[37] Mochon S, McMahon TA (1980) Ballistic walking. J Biomech 13:49–57 · Zbl 0447.73086
[38] Mori S (1987) Integration of posture and locomotion in acute decerebrate cats and in awake, freely moving cats. Prog Neurobiol 28:161–195
[39] Murray MP (1967) Gait as a total pattern of movement. Am J Phys Med 46:290–333
[40] Nashner LM, McCollum G (1985) The organization of human postural movements: a formal basis and experimental synthesis. Behav Brain Sci 8:135–172
[41] Nilsson J, Thorstensson (1989) Ground reaction forces at different speeds of human walking and running. Acta Physiol Scand 136:217–227
[42] Nilsson J, Thorstensson A, Halbertsma J (1985) Changes in leg movements and muscle activity with speed of locomotion and mode of progression in humans. Acta Physiol Scand 123:457–475
[43] Onyshko S, Winter DA (1980) A mathematical model for the dynamics of human locomotion. J Biomech 13:361–368
[44] Pandy M, Berme N (1988) A numerical method for simulating the dynamics of human walking. J Biomech 21:1043–1051
[45] Patla AE (1988) Analytic approaches to the study of outputs from central pattern generators In: Cohen AH, Rossignol S, Grillner S (eds) Neural control of rhythmic movements in vertebrates. Wiley, New York, pp 455–486
[46] Pearson KG, Ramirez JM, Jiang W (1992) Entrainment of locomotor rhythm by group Ib afferents from ankle extensor muscles in spinal cats. Exp Brain Res 90:557–566
[47] Raibert MH (1984) Hopping in legged systems-modeling and simulation for the two-dimensional one-legged case. IEEE Trans SMC 14:451–463
[48] Schöner G, Kelso JAS (1988) Dynamic pattern generation in behavioral and neural systems. Science 239:1513–1520
[49] Selverston AI (ed) (1985) Model neural networks and behavior. Plenum, New York
[50] Smith JL, Zernicke RF (1987) Predictions for neural control based on limb dynamics. Trends Neurosci 10:123–128
[51] Soechting FF, Flanders M (1992) Moving in three-dimensional space: frames of references, vectors, and coordinate systems. Annu Rev Neurosci 15:167–191
[52] Stein RB, Capaday C (1988) The modulation of human reflexes during functional motor tasks. Trends Neurosci 11:328–332
[53] Taga G (1994) Emergence of bipedal locomotion through entrainment among the neuro-musculo-skeletal system and the environment. Physica D 75:190–208 · Zbl 0858.92015
[54] Taga G, Yamaguchi Y, Shimizu H (1991) Self-organized control of bipedal locomotion by neural oscillators in unpredictable environment. Biol Cybern 65:147–159 · Zbl 0734.92005
[55] Thelen E (1988) Dynamical approaches to the development of behavior. In: Kelso JAS, Mandell AJ, Shlesinger MF (eds) Dynamic patterns in complex systems. World Scientific, New York, pp 348–369
[56] Thelen E, Fisher DM (1982) Newborn stepping: an explanation for a ’disappearing’ reflex. Dev Psychol 18:760–775
[57] Vukobratovic M, Stokic D (1975) Dynamic control of unstable locomotion robots. Math Biosci 24:129–157 · Zbl 0315.93018
[58] Wendler G (1974) The influence of proprioceptive feedback on locust flight coordination. J Comp Physiol 88:173–200
[59] Williams TL, Sigvardt KA, Kopell N, Ermentrout GB, Remler MP (1990) Forcing of coupled nonlinear oscillators: studies of intersegmental coordination in the lamprey locomotor central pattern generator. J Neurophysiol 64:862–871
[60] Winstein CJ, Garfinkel A (1989) Qualitative dynamics of disordered human locomotion: a preliminary investigation. J Mot Behav 21:373–391
[61] Winter DA (1987) Biomechanics and motor control of human gait. University of Waterloo Press
[62] Yamaguchi GT, Zajac FE (1990) Restoring unassisted natural gait to paraplegics via functional neuromuscular stimulation: a computer simulation study. IEEE Trans BME 37:886–902
[63] Yamazaki N (1991) Energy consumption in human musculoskeletal system during walking (in Japanese). Proc SICE Symp Decentralized Autonomous Systems, 19–22
[64] Yoon YS, Mansour JM (1982) The passive elastic moment at the hip. J Biomech 15:905–910
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