Propagation of excitation in a model of the inhomogeneous nerve fibre-III. Interaction of pulses in the region of the branching node of a nerve fibre

V. F. Pastushenko, V. S. Markin, Yu A. Chizmadzhev

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Abstract

In the work we consider the traversal of one nerve pulse across a branching node. It is shown that branching influences the movement of the approaching pulse in the same way as widening or narrowing of the fibre. In this sense branching is equivalent to an inhomogeneous fibre of variable dimensions. There is total agreement if the sum of the wave conductivities of the branches lying behind the branching node is equal to the wave conductivity of the fibre with changed dimensions. This relation becomes particularly graphic if the resistance of the external medium may be disregarded. Then the radius of the equivalent fibre is connected with the radii of the branches by the simple relation requiv 3 2 = r2 3 2 + r3 3 2. The criterion has been found for the passage of a pulse across a branching node. It consists in the fact that the equivalent radius must not exceed the radius of the initial fibre by more than K 2 3 times. As an example we consider the case in which a thin fibre adjoins a thick one. With a safety factor of 7 the pulse running along the thin fibre can pass through the branching node if the radius of the thick fibre exceeds the radius of the thin by not more than 2·5 times. We have considered the simultaneous passage across the node of two pulses. If the pulses move synchronously then on approaching the branching node their speed changes uniformly increasing or falling in relation to the radius of the third fibre. If the pulses approach the node with a certain shift in time, then their interaction leads to fall in this shift, i.e. to greater synchronization. Equations quantitatively describing these processes have been derived.

Original languageEnglish (US)
Pages (from-to)929-937
Number of pages9
JournalBiophysics
Volume14
Issue number5
StatePublished - Dec 1 1969

ASJC Scopus subject areas

  • Biophysics

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