Zusammenfassung
The (standard) FitzHugh reduction of the Hodgkin-Huxley equations
for the propagation of nerve impulses ignores the dynamics of the
activation gates. This assumption is invalid and leads to an over-estimation
of the wave speed by a factor of 5 and the wrong dependence of wave
speed on sodium channel conductance. The error occurs because a non-dimensional
parameter, which is assumed to be small in the FitzHugh reduction,
is in fact large (approximately 18). We analyse the Hodgkin-Huxley
equations for propagating nerve impulses in the limit that this non-dimensional
parameter is large, and show that the analytical results are consistent
with numerical simulations of the Hodgkin-Huxley equations.
- 15998489
- action
- algorithms,
- animals,
- conductivity,
- electric
- electrophysiology,
- gov't,
- humans,
- models,
- neurological,
- non-u.s.
- potentials,
- research
- support,
- synaptic
- transmission,
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