Skip to main content
Log in

Statistical analysis of multipath neural systems

  • Published:
Biological Cybernetics Aims and scope Submit manuscript

Abstract

Peripheral sensory and motor systems may be characterized by models consisting of multiple parallel convergent pathways, each described by the same set of equations, but having different parameter values in each path. Such models, although deterministic, are best analyzed using a statistical approach, which is illustrated here by analysis of several simple multipath models composed of linear dynamic elements and static non-linear elements. Relationships between instantaneous means of signals at different points in such systems are used to show that a multipath system can exhibit behaviour which would not be expected from observations of individual pathways. Mechanisms for linearization of static non-linearities are briefly described. Important implications for neurophysiologists are discussed.

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.

Similar content being viewed by others

References

  • Amari, S.: A method of statistical neurodynamics. Kybernetik 14, 201–215 (1974)

    Google Scholar 

  • Bayly, E.J., Cervetto, L., Fiorentini, A., Maffei, L.: On and off retinal cells in parallel channel neural communication. Kybernetik 8, 52–58 (1971)

    Google Scholar 

  • Borg, E.: Nonlinear dynamic properties of a somatomotor reflex system. A model study. Acta Physiol. Scand. 87, 15–26 (1973)

    Google Scholar 

  • Carpenter, R.H.S.: Movements of the eyes. London: Pion 1977

    Google Scholar 

  • Davenport, W.B., Root, W.L.: An introduction to the theory of random signals and noise. New York: McGraw-Hill 1958

    Google Scholar 

  • Douglas, P.R., Ferrington, D.G., Rowe, M.: Coding of information about tactile stimuli by neurones of the cuneate nucleus. J. Physiol. (London) 285, 493–513 (1978)

    Google Scholar 

  • Erickson, R.P.: Parallel “population” neural coding in feature extraction. In: The neurosciences, 3rd study program, pp. 155–169. Schmitt, F.O., Worden, F.G. (eds.). Cambridge, Mass.: MIT Press 1974

    Google Scholar 

  • Feldman, J.L., Cowan, J.D.: Large-scale activity in neural nets. I. Theory with application to motoneuron pool responses. Biol. Cybernetics 17, 29–38 (1975)

    Google Scholar 

  • Freeman, W.J.: Mass action in the nervous system. New York: Academic Press 1975

    Google Scholar 

  • Gersch, W.: Stochastic model for real and simulated neurophysiological behavior. IEEE Trans. Syst. Sci. Cybern. 3, 86–92 (1967)

    Google Scholar 

  • Greenleaf, J.F., Knopp, T.J., Coulam, C.M., Bassingthwaighte, J.B.: Identification of parallel pathway systems. 21st Ann. Conf. Eng. Med. Biol., Houston, Texas, Paper 50.6 (1968)

  • Harrington, T., Merzenich, M.M.: Neural coding in the sense of touch: human sensations of skin indentations compared with the responses of slowly adapting mechanoreceptive afferents innervating the hairy skin of monkeys. Exp. Brain Res. 10, 251–264 (1970)

    Google Scholar 

  • Johnson, K.O.: Reconstruction of population response to a vibratory stimulus in quickly adapting mechanoreceptive afferent fiber population innervating glabrous skin of monkey. J. Neurophysiol. 37, 48–72 (1974)

    Google Scholar 

  • Knibestol, M.: Stimulus-response functions of rapidly adapting mechanoreceptors in the human glabrous skin area. J. Physiol. (London) 232, 427–452 (1973)

    Google Scholar 

  • Kruger, L., Kenton, B.: Quantitative neural and psychophysical data for cutaneous mechanoreceptive function. Brain Res. 49, 1–24 (1973)

    Google Scholar 

  • Laszlo, C.A.: Measurement, modelling and simulation of the cochlear potentials. Ph.D. Thesis, Department of Electrical Engineering, McGill University, Montreal, 1968

  • Lee, H.C., Milsum, J.H.: Statistical analysis of multiunit multipath neural communication. Math. Biosci. 11, 181–202 (1971)

    Google Scholar 

  • Maffei, L.: Spatial and temporal averages in retinal channels. J. Neurophysiol. 31, 283–287 (1968)

    Google Scholar 

  • Manetsch, T.J.: Transfer function representation of the aggregate behaviour of a class of economic processes. IEEE Trans. Autom. Control 11, 693–698 (1966)

    Google Scholar 

  • Manetsch, T.J., Park, G.L.: System analysis and simulation, with applications to economic and social systems, Part II. East Lansing: Michigan State University 1973

    Google Scholar 

  • Milgram, P., Inbar, G.F.: Distortion suppression in neuromuscular information transmission due to interchannel dispersion in muscle spindle firing thresholds. IEEE Trans. Biomed. Eng. 23, 1–15 (1976)

    Google Scholar 

  • Papoulis, A.: Probability, random variables and stochastic processes. New York: McGraw-Hill 1965

    Google Scholar 

  • Poppele, R.E., Terzuolo, C.A.: Myotatic reflex: its input-output relation. Science 159, 743–745 (1968)

    Google Scholar 

  • Pubols, B.H., Pubols, L.M.: Coding of mechanical stimulus velocity and indentation depth by squirrel monkey and raccoon glabrous skin mechanoreceptors. J. Neurophysiol. 39, 773–787 (1976)

    Google Scholar 

  • Rall, W.: A statistical theory of monosynaptic input-output relations. J. Cell Comp. Physiol. 46, 373–411 (1955)

    Google Scholar 

  • Rosenblueth, A., Wiener, N., Pitts, W., Garcia Ramos, J.: A statistical analysis of synaptic excitation. J. Cell. Comp. Physiol. 34, 173–205 (1949)

    Google Scholar 

  • Segal, B.N.: An analysis of multipath neural systems using random parameter models. M.Eng. Thesis, Department of Electrical Engineering, McGill University, Montreal 1973

  • Sherrington, Sir C.S.: Selected writings of Sir Charles Sherrington. London: hamish Hamilton Medical Books 1939

    Google Scholar 

  • Somjen, G.: Sensory coding in the mammalian nervous system. New York: Meridith Corp. 1972

    Google Scholar 

  • Werner, G., Mountcastle, V.B.: Neural activity in mechanoreceptive cutaneous afferents: stimulus-response relations, Weber, functions, and information transmission. J. Neurophysiol. 28, 359–397 (1965)

    Google Scholar 

  • Williams, W.J.: Transfer characteristics of dispersive nerve bundles. IEEE Trans. Syst. Man Cybern. 2, 72–85 (1972)

    Google Scholar 

  • Wilson, H.R., Cowan, J.D.: A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13, 55–80 (1973)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Segal, B.N., Outerbridge, J.S. Statistical analysis of multipath neural systems. Biol. Cybernetics 37, 209–218 (1980). https://doi.org/10.1007/BF00337039

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00337039

Keywords

Navigation