A formulation concerning the electrical effects of axon variations from cylindrical shape: Spindle cells and bulbous synapses
Lieberstein, H. Melvin Mahrous, Mohamed A.
Lieberstein, H. Melvin
Mahrous, Mohamed A.
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1970
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H. Melvin Lieberstein, Mohammed Mahrous. (1970). A formulation concerning the electrical effects of axon variations from cylindrical shape: Spindle cells and bulbous synapses, Mathematical Biosciences, Volume 7, Issues 3–4, Pages 259-272, 10.1016/0025-5564(70)90127-6
Abstract
The reformulation [5, 6] of the equations of A. L. Hodgkin and A. F. Huxley, designed to eliminate a gross numerical instability found in [4], still treats axons which are circular cylinders. Here an investigation in precise terms is undertaken to determine the electrical effects of cross-section perimeter variations with distance on the axon. The H-H empirical determinations relating to the ion conductances of the membrane of the giant axon of the squid Loligo, being the only such data available in precise terms, are still used. We develop the necessary partial differential equations and find that a certain set of ordinary differential equations, modified to account for radius variations, can be used to model the electrical behavior of some important axons which are still thin but markedly noncylindrical. It is assumed that a bulbous chemical synapse can still be treated as thin, although the perimeter of the cross section at the widest girth of the cell body is quite large compared to that at the hillock. It is more obvious, but perhaps not so important, that spindle cells can be so treated.
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Elsevier
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Mathematical Biosciences
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255564