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  • Title: Phase plane analysis of uniform and non-uniform propagation of activity in a model of squid giant axon.
    Author: de Carvalho AC, de Carvalho AP.
    Journal: An Acad Bras Cienc; 1980 Dec; 52(4):893-902. PubMed ID: 6264824.
    Abstract:
    Mathematical modeling of propagation in the squid giant axon using the Hodgkin-Huxley partial differential equation for propagation in a cable-like cell allowed us to study the effect of reduction in maximal sodium conductance in a short segment of the "axon membrane". The phase plane (V,V) display of the action potentials calculated in segments ahead of the gNa+ depressed site exhibited peculiar inflections in their ascending portion which are absent in the control situation. These inflections (upward or downward) varied with the distance from the depressed segments. The voltage of the first inflection point of the phase trajectories was an exponential function of this distance. This voltage is in close agreement with threshold voltage at points within a distance of 1.4 mm from the depressed segments. The model reproduces, qualitatively, the experimental behaviour of the squid axon topically exposed to TTX.
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