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A feedback model of the neuron for the study of small neuron networks

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Abstract

A feedback model of the neuron is described, based on a double-locus representation of the cat spinal cord motoneuron. This analog is equivalent to the Hodgkin and Huxley membrane model in which all the components of the action current have been lumped. By using the technique of the “second method” of Liapunov a stability analysis is made which yields results pertaining to the use of the action potential and its first time derivative for the characterization of nerve cells. Finally an exmple is given in which the model is used to investigate a neuronal network involving Renshaw cell negative feedback.

Sommaire

Un modèle en boucle du neurone est décrit, basé sur une représentation à deux lieus du motoneurone de la moëlle épinière du chat. Cette analogie est équivalente au modèle de membrane deHodgkin etHuxley dans lequel tous les composants du courant d'action ont été réunis. En utilisant la technique de la “deuxième méthode” de Liapunov, on effectue une analyse de la stabilité qui fournit des résultats concernant l'utilisation du potentiel d'action et de sa dérivée première pour représenter les cellules nerveuses. On donne enfin un exemple dans lequel le modèle est utilisé pour étudier un réseau de neurones comprenant dans la boucle de réaction négative une cellule de Renshaw.

Zusammenfassung

Ein Feedbackmodell des Neurons wird beschrieben, das auf der doppelörtigen Repräsentierung der Rückenmarksneurone der Katze beruht. Dieses Analogon ist dem Membranmodell von Hodgkin und Huxley äquivalent, das alle Komponenten des Aktionsstroms enthält. Unter Verwendung des Verfahrens der “zweiten Methode” nach Liapunow wird eine Stabilitätsanalyse unternommen, die Ergebnisse bezüglich der Brauchbarkeit des Aktionspotentials und seiner ersten Ableitung nach der Zeit für die Charakterisierung von Nervenzellen liefert. Schließlich wird ein Beispiel der Anwendung des Modells gegeben, in dem ein Neuronennetzwerk untersucht wird, das den negativen Feedback von Renshawzellen betrifft.

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Authors and Affiliations

  1. Department of Electrical Engineering, McGill University, Montreal, Canada

    F. A. Roberge & J. H. Milsum

Authors
  1. F. A. Roberge
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  2. J. H. Milsum
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Additional information

This work was supported by a grant from the National Research Council of Canada. A preliminary report of this study was presented at the 6th International Conference on Medical Electronics and Biological Engineering, Tokyo, Japan, August 22–27, 1965.

Work done during tenure of a Scholarship from the National Research Council of Canada. Present address: Department of Physiology, University of Montreal, Canada.

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Roberge, F.A., Milsum, J.H. A feedback model of the neuron for the study of small neuron networks. Med. & biol. Engng. 4, 357–366 (1966). https://doi.org/10.1007/BF02476153

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