Skip to main content
Log in

Neural computations underlying the exertion of force: a model

  • Original Papers
  • Published:
Biological Cybernetics Aims and scope Submit manuscript

Abstract

We have developed a model that simulates possible mechanisms by which supraspinal neuronal signals coding forces could converge in the spinal cord and provide an ongoing integrated signal to the motoneuronal pools whose activation results in the exertion of force. The model consists of a three-layered neural network connected to a two-joint-six-muscle model of the arm. The network layers represent supraspinal populations, spinal cord interneurons, and motoneuronal pools. We propose an approach to train the network so that, after the synaptic connections between the layers are adjusted, the performance of the model is consistent with experimental data obtained on different organisms using different experimental paradigms: the stiffness characteristics of human arm; the structure of force fields generated by the stimulation of the frog's spinal cord; and a correlation between motor cortical activity and force exerted by monkey against an immovable object. The model predicts a specific pattern of connections between supraspinal populations coding forces and spinal cord interneurons: the weight of connection should be correlated with directional preference of interconnected units. Finally, our simulations demonstrate that the force generated by the sum of neural signals can be nearly equal to the vector sum of forces generated by each signal independently, in spite of the complex nonlinearities intervening between supraspinal commands and forces exerted by the arm in response to these commands.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Google Scholar 

  • Caminiti R, Johnson PB, Urbano A (1990) Making arm movements within different parts of space: dynamic aspects in the primate motor cortex. J Neurosci 10:2039–2058.

    Google Scholar 

  • Evarts EV, Fromm C, Kroller J, Jennings VA (1983) Motor cortex control of finely graded forces. J Neurophysiol 49:1199–1215.

    Google Scholar 

  • Feldman AG (1966) Functional tuning of the nervous system with control of movement or maintenance of a steady posture. II. Controllable parameters of the muscles. Biophysics 11:565–578.

    Google Scholar 

  • Flash T (1987) The control of hand equilibrium trajectories in multijoint arm movements. Biol Cybern 57:257–274.

    Google Scholar 

  • Flash T, Mussa-Ivaldi F (1990) Human arm stiffness characteristics during the maintenance of posture. Exp Brain Res 82:315–326.

    Google Scholar 

  • Georgopoulos AP (1988) Neural integration of movement: role of motor cortex in reaching. FASEB J 2:2849–2857.

    Google Scholar 

  • Georgopoulos AP (1994) New concepts in generation of movement. Neuron 13:257–268.

    Google Scholar 

  • Georgopoulos AP, Kalaska JF, Caminiti R, Massey JT (1982) On the relations between the direction of two-dimensional arm movements and cell discharge in primate motor cortex. J Neurosci 2:1527–1537.

    Google Scholar 

  • Georgopoulos AP, Schwartz AB, Kettner RE (1986) Neuronal population coding of movement direction. Science 233:1416–1419.

    Google Scholar 

  • Georgopoulos AP, Ashe J, Smyrnis N, Taira M (1992) The motor cortex and the coding of force. Science 256:1692–1695.

    Google Scholar 

  • Georgopoulos AP, Taira M, Lukashin AV (1993) Cognitive neurophysiology of the motor cortex. Science 260:47–52.

    Google Scholar 

  • Giszter SF, Mussa-Ivaldi FA, Bizzi E (1993) Convergent force fields organized in the frog's spinal cord. J Neurosci 13:467–491.

    Google Scholar 

  • Hocherman S, Wise SP (1991) Effects of hand movement path on motor cortical activity in awake, behaving rhesus monkeys. Exp Brain Res 83:285–302.

    Google Scholar 

  • Hogan N (1985) The mechanics of multi-joint posture and movement control. Biol Cybern 52:315–331.

    Google Scholar 

  • Kalaska JF, Crammond DJ (1992) Cerebral cortical mechanisms of reaching movements. Science 259:1517–1523.

    Google Scholar 

  • Kalaska JF, Cohen DAD Hyde ML, Prud'homme M (1989) A comparison of movement direction-related versus load direction-related activity in primate motor cortex, using a two-dimensional reaching task. J Neurosci 9:2080–2102.

    Google Scholar 

  • Katayama M, Kawato M (1993) Virtual trajectory and stiffness ellipse during multijoint arm movement predicted by neural inverse models. Biol Cybern 69:353–362.

    Google Scholar 

  • Mussa-Ivaldi FA, Giszter SF (1992) Vector field approximation: a computational paradigm for motor control and learning. Biol Cybern 67:491–500.

    Google Scholar 

  • Mussa-Ivaldi FA, Hogan N, Bizzi E (1985) Neural, mechanical, and geometric factors subserving arm posture in humans. J Neurosci 5:2732–2743.

    Google Scholar 

  • Mussa-Ivaldi FA, Giszter SF, Bizzi E (1994) Linear combinations of primitives in vertebrate motor control. Proc Natl Acad Sci USA 91:7534–7538.

    Google Scholar 

  • Redish AD, Touretzky DS (1994) The reaching task: evidence for vector arithmetic in the motor system? Biol Cybern 71:307–317.

    Google Scholar 

  • Schwartz AB (1994) Direct cortical representation of drawing. Science 265:540–542.

    Google Scholar 

  • Shadmehr R, Arbib MA (1992) A mathematical analysis of the forcestiffness characteristics of muscles in control of a single joint system. Biol Cybern 66:463–477.

    Google Scholar 

  • Shadmehr R, Mussa-Ivaldi FA, Bizzi E (1993) Postural force fields of the human arm and their role in generating multijoint movements. J Neurosci 13:45–62.

    Google Scholar 

  • Tsuji T, Morasso PG, Goto K, Ito K (1995) Human hand impedance characteristics during maintained posture. Biol Cybern 72:475–485.

    Google Scholar 

  • Wise SP (1993) Monkey motor cortex: movements, muscles, motoneurons and metrics. Trends Neurosci 16:46–49.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lukashin, A.V., Amirikian, B.R. & Georgopoulos, A.P. Neural computations underlying the exertion of force: a model. Biol. Cybern. 74, 469–478 (1996). https://doi.org/10.1007/BF00206713

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00206713

Keywords

Navigation