%0 Journal Article %1 Hinc_2005_947 %A Hinch, Robert %D 2005 %J Bull. Math. Biol. %K 15998489 Action Algorithms, Animals, Conductivity, Electric Electrophysiology, Gov't, Humans, Models, Neurological, Non-U.S. Potentials, Research Support, Synaptic Transmission, %N 5 %P 947--955 %R 10.1016/j.bulm.2004.11.007 %T A note on the asymptotic reduction of the Hodgkin-Huxley equations for nerve impulses. %U http://dx.doi.org/10.1016/j.bulm.2004.11.007 %V 67 %X 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.

@article{Hinc_2005_947, abstract = {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.}, added-at = {2009-06-03T11:20:58.000+0200}, author = {Hinch, Robert}, biburl = {https://www.bibsonomy.org/bibtex/24d120f960036152dc531d43632674927/hake}, description = {The whole bibliography file I use.}, doi = {10.1016/j.bulm.2004.11.007}, interhash = {bad60ffadcc6309e943f550d3adca097}, intrahash = {4d120f960036152dc531d43632674927}, journal = {Bull. Math. Biol.}, keywords = {15998489 Action Algorithms, Animals, Conductivity, Electric Electrophysiology, Gov't, Humans, Models, Neurological, Non-U.S. Potentials, Research Support, Synaptic Transmission,}, month = Sep, number = 5, pages = {947--955}, pii = {S0092-8240(05)00003-0}, pmid = {15998489}, timestamp = {2009-06-03T11:21:14.000+0200}, title = {A note on the asymptotic reduction of the Hodgkin-Huxley equations for nerve impulses.}, url = {http://dx.doi.org/10.1016/j.bulm.2004.11.007}, volume = 67, year = 2005 }