A note on the asymptotic reduction of the Hodgkin-Huxley equations for nerve impulses.
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.
Hinch
Robert
R
Centre for Mathematical Biology, Mathematical Institute, 24-29 St Giles', Oxford, OX1 3LB, UK. hinch@maths.ox.ac.uk
D000200:Action Potentials; D000465:Algorithms; D000818:Animals; D004553:Electric Conductivity; D004594:Electrophysiology; D006801:Humans; D008959:Models, Neurological; D009435:Synaptic Transmission / Q000502:physiology*