Abstract
The propagation of a transverse disturbance along a tubular membrane enclosing a fluid medium and embedded in another is considered. It is shown that the velocity of propagation of such a disturbance can be identified with the velocity of the conduction process of thin-sheathed nerve fibers. The required values of the associated parameters, tension and pressure, appear not unreasonable. The results obtained indicate that experimental observations on the relation between the conduction velocity and the fiber diameter, as well as the effects of longitudinal stretching and transverse squeezing on the velocity of the conduction process in nerve, may be correlated on such a basis.
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Abbreviations
- a,A i ,A e :
-
amplitude constants
- c i ,c e :
-
acoustic velocity of internal and external fluid respectively
- k z :
-
=ω/V ω
- ΔP :
-
=P′ io -P′ eo
- P i ,P e :
-
pressure deviations from equilibrium in the respective media
- P i o,P e o :
-
deviations in pressure from equilibrium value at surface of membrane in respective media
- P′ i o,P′ e o :
-
pressure at membrane in the respective media
- P iA P eA :
-
pressure displacement amplitudes in respective media
- P iAo ,P eAo :
-
pressure displacement amplitudes in respective media at the membrane surface
- r :
-
radical coordinate
- r o :
-
radius of cylindrical membrane
- T :
-
tension per unit length in the membrane
- t :
-
time
- u r :
-
radial velocity
- V g :
-
group velocity
- V S :
-
signal velocity
- V ω :
-
phase velocity for sinusoidal disturbance on the membrane
- z :
-
coordinate, distance along membrane
- I o,K o,I 1,K 1 :
-
Bessel functions order zero and one, respectively
- ω:
-
2πf wheref is the frequency
- δ:
-
width of exciting pulse at half amplitude
- ϕ:
-
angular coordinate
- ξ:
-
radial displacement of membrane
- ξA :
-
radial displacement amplitude of membrane
- ρ i , ρ e :
-
densities of internal and external media, respectively
- σ:
-
mass of membrane per unit area
Literature
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Fry, W.J., Fry, R.B. Theoretical consideration of a possible mechanism in the conduction process of thin-sheathed nerve fibers. Bulletin of Mathematical Biophysics 12, 303–315 (1950). https://doi.org/10.1007/BF02477901
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DOI: https://doi.org/10.1007/BF02477901