Hodgkin-Huxley model is the indispensable mathematics basis for the study of neuro-electro-physiology. But so far, there is few analytic study about H-H neuron model. In this paper, the features of the classical H-H model are analyzed, and then a simplified H-H model and Nagumo equation are proposed, and their solitary wave solutions are first obtained with the homogeneous balance method. The study shows that nerve impulse may propagate with the mode of solitary wave.
Action Potentials ; physiology ; Humans ; Mathematics ; Membrane Potentials ; physiology ; Models, Neurological ; Neural Conduction ; physiology

ObjectiveTo assess the repeatability （intra-operator variability） and reproducibility （inter-operator variability） of a new partial coherence interferometry （PCI）-based ocular biometer， Myopia Master， and its agreement with IOL Master 500 for measuring axial length （AL） and corneal curvature （K） in children aged 8-12 years. MethodsThe same operator measured school children with the Myopia Master and the IOL Master 500 in random order to assess agreement. Additionally， some of these children received measurements from another operator using the Myopia Master to assess repeatability and reproducibility. AL， flat keratometry （Kf）， steep keratometry （Ks）， mean keratometry （Km）， J₀ and J₄₅ were analyzed. The repeatability and reproducibility were assessed by the within-subject standard deviation （Sw）， test-retest repeatability （TRT）， coefficient of variation （CoV） and intra-class correlation coefficient （ICC）. The agreement between the Myopia Master and the IOL Master 500 was assessed by Bland-Altman plots and 95% limits of agreement （LoA）. ResultsBoth repeatability and reproducibility of the Myopia Master were high for AL measurements （Sw=0.02 mm， ICC=0.999； Sw=0.04 mm， ICC=0.998）， but moderate for K measurements （Sw range， 0.04 to 0.12 D， ICC range， 0.861 to 0.991； Sw range， 0.06 to 0.20 D， ICC range， 0.835 to 0.992）. There were significant mean differences between the Myopia Master and the IOL Master 500 in measurements of AL （-0.01±0.04） mm， Kf （-0.09 ± 0.15） D， Ks （-0.47±0.40） D， and Km （-0.28±0.23） D， J₀ （0.18±0.20） D and J₄₅ （-0.01±0.12） D. ConclusionsThe Myopia Master provided high repeatability and reproducibility for AL measurements in schoolchildren with myopia， but the Myopia Master and the IOL Master 500 cannot be used interchangeably in measuring AL and K.