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Coordination dynamics of trajectory formation

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Abstract

The present study aims to understand the neurally based coordination dynamics (multistability, loss of stability, transitions, etc.) of trajectory formation in a simple task. Six subjects produced two spatial patterns of coordination in the xy plane by alternating the abduction-adduction and flexion-extension motions of their right index finger. Each pattern was characterized by a unique temporal ratio between the x and y directions of motion: (1) a figure zero, a 1∶1 temporal pattern; and (2) a figure eight, a 2∶1 temporal pattern. The patterns were produced rhythmically and movement frequency was scaled across ten frequency plateaus, with ten cycles of motion per step. As movement frequency increased, switching from a figure eight to a figure zero was observed at critical cycling frequencies. The switch from pattern (2) to pattern (1) was identified in the spatial trajectory and power spectra of x(t) and y(t). En route to the transition, enhancement of fluctuations was observed in the Fourier amplitudes of x(t) and y(t), specifically at f 0 (the metronome frequency) and 2f 0 (the first harmonic off 0). Interestingly, there was no difference in the spatial variability of the two patterns. Overall, the data demonstrate that spatial patterns of coordination can be characterized in terms of the temporal relationship between the spatial components of the trajectory itself. We discuss the experimental findings in relation to other end-point planning and multijoint control strategies, as well as the much more general problem of temporal synchronization in many interlimb and intralimb coordination tasks.

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References

  • Abend W, Bizzi E, Morasso P (1982) Human arm trajectory formation. Brain 105:331–348

    Google Scholar 

  • Atkeson CG, Hollerbach JM (1985) Kinematic features of unrestrained vertical arm movements. J Neurosci 5:2318–2330

    Google Scholar 

  • Beek PJ (1989) Timing and phase-locking in cascade juggling. Eco Psychol 1:55–96

    Google Scholar 

  • Beek PJ, Peper CE, Wieringen PCW van (1992) Frequency locking, frequency modulation, and bifurcation in dynamic movement systems. In: Stelmach GE, Requin J (eds) Tutorials in motor behavior, vol 2. North-Holland, Amsterdam, pp 599–622

    Google Scholar 

  • Bizzi E, Mussa-Ivaldi FA, Giszter S (1991) Computations underlying the execution of movement: a biological perspective. Science 253:287–291

    Google Scholar 

  • Bizzi E, Hogan N, Mussa-Ivaldi FA, Giszter S (1992) Does the nervous system use equilibrium point control to guide single and multijoint movements. Behav Brain Sci 15:603–631

    Google Scholar 

  • Buchanan JJ, Kelso JAS (1993) Posturally induced transitions in rhythmic multijoint limb movements. Exp Brain Res 94:131–142

    Google Scholar 

  • Buchanan JJ, Deguzman GC, Kelso JAS, Treffner PJ (1994) The suppression and activation of degrees of freedom in trajectory formation. In: Proceedings of the 24th Annual Society for Neuroscience Meeting, vol 20, p 544

    Google Scholar 

  • DeGuzman GC, Kelso JAS (1991) Multifrequency behavioral patterns and the phase attractive circle map. Biol Cybern 64:485–495

    Google Scholar 

  • DeGuzman GC, Kelso JAS (1992) The flexible dynamics of biological coordination: living in the niche between order and disorder. In: Baskin AB, Mittenthal JE (eds) Principles of organization in organisms. (Proceedings of the Santa Fe Institute, vol 12) Addison-Wesley, Reading, Mass. pp 11–34

    Google Scholar 

  • Flash T, Hogan N (1985) The coordination of arm movements: an experimentally confirmed mathematical model. J Neurosci 5:1688–1703

    Google Scholar 

  • Fuchs A, Kelso JAS, Buchanan JJ (1993) Trajectory formation and the coordination dynamics of spatiotemporal patterns. II. Theoretical results. In: Proceedings of the 23rd Annual Society for Neuroscience Meeting, vol 19, p 544

    Google Scholar 

  • Fuchs A, Kelso JAS, Buchanan JJ (in preparation) Order parameters for the coordination dynamics of trajectory formation.

  • Greene PH (1982) Problems of organization of motor systems. In: Rosen R, Snell FM (eds) Progress in theoretical biology. Academic Press, New York, pp 303–338

    Google Scholar 

  • Haken H (1983) Synergetics, an introduction: non-equilibrium phase transitions and self-organization in physics, chemistry and biology. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Haken H (1987) Information compression in biological systems. Biol Cybern 56:11–17

    Google Scholar 

  • Haken H (1988) Information and self-organization: a macroscopic approach to complex systems. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Haken H, Kelso JAS, Bunz H (1985) A theoretical model of phase transitions in human hand movements. Biol Cybern 51:347–356

    Google Scholar 

  • Hollerbach JM (1981) An oscillation theory of handwriting. Biol Cybern 39:139–156

    Google Scholar 

  • Kelso JAS (1981) On the oscillatory basis of movement. Bull Psychon Soc 18:63

    Google Scholar 

  • Kelso JAS (1984) Phase transitions and critical behavior in human bimanual coordination. Am J Physiol 15:R1000-R1004

    Google Scholar 

  • Kelso JAS (1990) Phase transitions: foundations of behavior. In: Haken H (eds) Synergetics of cognition. Springer, Berlin Heidelberg New York, pp 249–268

    Google Scholar 

  • Kelso JAS (1994) Elementary coordination dynamics. In: Swinnen S, Heuer H, Massion J, Casaer P (eds) Interlimb coordination: neural, dynamical and cognitive constraints. Academic Press, New York, pp 301–318

    Google Scholar 

  • Kelso JAS (1995) Dynamic patterns: the self-organization of brain and behavior. MIT Press, Cambridge, Mass

    Google Scholar 

  • Kelso JAS, DeGuzman GC (1988) Order in time: how cooperation between the hands informs the design of the brain. In: Haken H (eds) Neural and synergetic computers. Springer, Berlin Heidelberg New York, pp 180–196

    Google Scholar 

  • Kelso JAS, Scholz JP (1985) Cooperative phenomena in biological motion. In: Haken H (eds) Complex systems: operational approaches in neurobiology, physical systems and computers. Springer, Berlin Heidelberg New York, pp 124–149

    Google Scholar 

  • Kelso JAS, Schöner G (1987) Toward a physical (synergetic) theory of biological coordination. Springer Proc Phys 19:224–237

    Google Scholar 

  • Kelso JAS, Southard DL, Goodman D (1979) On the nature of human interlimb coordination. Science 203:1029–1031

    Google Scholar 

  • Kelso JAS, Scholz JP, Schöner G (1986) Non-equilibrium phase transitions in coordinated biological motion: critical fluctuations. Phys Lett 118A:279–284

    Google Scholar 

  • Kelso JAS, Scholz JP, Schöner G (1988) Dynamics governs switching among patterns of coordination in biological movement. Phys Lett. 134A:8–12

    Google Scholar 

  • Kelso JAS, Buchanan JJ, Wallace SA (1991a) Order parameters for the neural organization of single, multijoint limb movement patterns. Exp Brain Res 85:432–444

    Google Scholar 

  • Kelso JAS, DeGuzman GC, Holroyd T (1991b) Synergetic dynamics of biological coordination with special reference to phase attraction and intermittency. In: Haken H, Köepchen HP (eds) Rhythms in physiological systems. (Springer series in synergetics, vol 55) Springer, Berlin Heidelberg New York, pp 195–213

    Google Scholar 

  • Kelso JAS, Delcolle JD, Schöner G (1990) Action-perception as a pattern formation process. In Jeannerod M (eds) Attention and performance, vol 13. Erlbaum, Hillsdale, NJ, pp 136–169

    Google Scholar 

  • Kelso JAS, Buchanan JJ, DeGuzman GC, Ding M (1993) Spontaneous recruitment and annihilation of degrees of freedom in biological coordination. Phys Lett 179A:364–371

    Google Scholar 

  • Kelso JAS, Buchanan JJ, Murata T (1994) Multifunctionality and switching in the coordination dynamics of reaching and grasping. Hum Mov Sci 13:63–94

    Google Scholar 

  • Lacquaniti F, Soechting JF (1982) Coordination of arm and wrist motion during a reaching task. Neuroscience 2:399–408

    Google Scholar 

  • Morasso P (1981) Spatial control of arm movements. Exp Brain Res 42:223–227

    Google Scholar 

  • Morasso P (1983) Three dimensional arm trajectories. Biol Cybern 48:187–194

    Google Scholar 

  • Morasso P, Mussa-Ivaldi FA (1982) Trajectory formation and handwriting, a computation model. Biol Cybern 45:131–142

    Google Scholar 

  • Saltzman EL, Kelso JAS (1987) Skilled actions: a task dynamic approach. Psychol Rev 94:84–106

    Google Scholar 

  • Schmidt RC, Carello C, Turvey MT (1990) Phase transitions and critical fluctuations in the visual coordination of rhythmic movements between people. J Exp Psychol Hum Percept Perform 16:227–247

    Google Scholar 

  • Scholz JP, Kelso JAS (1989) A quantitative approach to understanding the formation and change of coordinated movement patterns. J Motor Behav 21:122–144

    Google Scholar 

  • Scholz JP, Kelso JAS (1990) Intentional switching between patterns of bimanual coordination is dependent on the intrinsic dynamics of the patterns. J Motor Behav 22:98–124

    Google Scholar 

  • Scholz JP, Kelso JAS, Schöner G (1987) Non-equilibrium phase transitions in coordinated biological motion: critical slowing down and switching time. Phys Lett 123A:390–394

    Google Scholar 

  • Schöner G, Kelso JAS (1988a) Dynamic pattern generation in behavioral and neutral systems. Science 239:1513–1520

    Google Scholar 

  • Schöner G, Kelso JAS (1988b) Dynamic patterns in biological coordination: theoretical strategy and new results. In: Kelso JAS, Mandell AJ, Shlesinger MF (eds) Dynamic patterns in complex systems. World Scientific, Singapore, pp 77–102

    Google Scholar 

  • Schöner G, Haken H, Kelso JAS (1986) A stochastic theory of phase transitions in human hand movement. Biol Cybern 53:442–452

    Google Scholar 

  • Soechting JF (1989) Elements of coordinated arm movements in three dimensional space. In: Wallace SA (eds) Perspectives on the coordination of movement. Elsevier, Amsterdam, pp 47–83

    Google Scholar 

  • Soechting JF, Lacquaniti F (1981) Invariant characteristics of a pointing movement in man. Neuroscience 1:710–720

    Google Scholar 

  • Soechting JF, Terzuolo CA (1986) An algorithm for the generation of curvilinear wrist motion in an arbitrary plane in threedimensional space. Neuroscience 19:1393–1406

    Google Scholar 

  • Soechting JF, Terzuolo CA (1987a) Organization of arm movement is segmented. Neuroscience 23:39–52

    Google Scholar 

  • Soechting JE, Terzuolo CA (1987b) Organization of arm movements in three dimensional space: wrist motion is piecewise planar. Neuroscience 23:53–61

    Google Scholar 

  • Soechting JF, Terzuolo CA (1990) Sensorimotor transformations and the kinematics of arm movements in 3-d space. In: Jeannerod M (eds) Attention and performance, vol 13. Erlbaum, Hillsdale, NJ, pp 474–494

    Google Scholar 

  • Soechting JF, Lacquaniti F, Terzuolo CA (1986) Coordination of arm movements in three dimensional space: sensorimotor mapping during drawing movements. Neuroscience 17:295–311

    Google Scholar 

  • Treffner PJ, Turvey MT (1993) Resonance constraints on rhythmic movements. J Exp Psychol Hum Percept Perform 9:1221–1237

    Google Scholar 

  • Uno Y, Kawato M, Suzuki R (1989) Formation and control of optimal trajectory in human multijoint arm movement. Biol Cybern 61:89–101

    Google Scholar 

  • Viviani P, Schneider R (1991) A developmental study of the relationship between geometry and kinematics in drawing movements. J Exp Psychol Hum Percept Perform 17:198–218

    Google Scholar 

  • Wimmers RH, Beek PJ, Wieringen PCW van (1992) Phase transitions in rhythmic tracking movements: a case of unilateral coupling. Hum Mov Sci 11:217–226

    Google Scholar 

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Authors and Affiliations

  1. Program in Complex Systems and Brain Sciences, Center for Complex Systems, Florida Atlantic University, PO Box 3091, 33431-0991, Boca Raton, FL, USA

    J. J. Buchanan, J. A. S. Kelso & A. Fuchs

  2. Institut für Theoretische Physik und Synergetik, Universität Stuttgart, Pfaffenwaldring 57, D-70550, Stuttgart, Germany

    A. Fuchs

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  1. J. J. Buchanan
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  2. J. A. S. Kelso
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  3. A. Fuchs
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Buchanan, J.J., Kelso, J.A.S. & Fuchs, A. Coordination dynamics of trajectory formation. Biol. Cybern. 74, 41–54 (1996). https://doi.org/10.1007/BF00199136

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  • DOI: https://doi.org/10.1007/BF00199136

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