KdV方程在神经细胞脉冲传导的孤立子性质
The Isolated Properties of KdV Equation in Nerve Cell Impulse Conduction
摘要:
本文主要是通过利用齐次平衡法来求解神经细胞脉冲传导应满足的KdV方程的解,并进一步去验证神经细胞脉冲传导是孤立子波,从而分析神经细胞脉冲传导的孤立子性质及其意义。从医学的角度来看,可以通过检测神经细胞脉冲传导孤立子波的参数来辅助诊断神经细胞的病变。
Abstract:
In this paper, the homogeneous equilibrium method is mainly used to solve the KdV equation that nerve cell impulse conduction should satisfy, and further verify that nerve cell impulse conduction is an isolated wavelet, so as to analyze the properties and significance of the isolated wavelet of nerve cell impulse conduction. From a medical point of view, the diagnosis of nerve cell lesions can be assisted by detecting the parameters of nerve cell pulse conduction solitary wavelet.
参考文献
|
[1]
|
王定江. 应用偏微分方程[M]. 杭州: 浙江大学出版社, 2007.
|
|
[2]
|
郭柏灵, 苏凤秋. 孤立子[M]. 沈阳: 辽宁教育出版社, 1998.
|
|
[3]
|
包霞, 斯仁道尔吉. 孤立子理论在中国的早期发展——纪念中国孤立子理论研究40周年[J]. 数学的实践与认识, 2019, 49(2): 279-285.
|
|
[4]
|
Hodgkin, A.L. and Huxley, A.F. (1952) A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve. Journal of Physiology, 117, 500-544. [Google Scholar] [CrossRef] [PubMed]
|
|
[5]
|
Fitzhugh, R. (1961) Impulse and Physiological States in Theoretical Models of Nerve Membrane. Biophysical Journal, 1, 445-466. [Google Scholar] [CrossRef]
|
|
[6]
|
Mckean, H.P. (1970) Nagumo’s Equation. Advances in Mathematics, 4, 209-223. [Google Scholar] [CrossRef]
|
|
[7]
|
李向正, 张卫国, 原三领. 神经脉冲传播的一种特殊模型的研究[J]. 生物医学工程学杂志, 2010, 27(5): 1142-1145.
|
|
[8]
|
胡建峰, 王锦丽, 包学才. 含损耗神经脉冲传输的耦合孤波特性[J]. 中国组织工程研究与临床康复, 2009, 13(30): 5911-5914.
|
|
[9]
|
柴玉珍, 张建文, 杨桂通. 神经脉冲波传播形态的研究[J]. 生物医学工程学杂志, 2008, 25(5): 1184-1188.
|
|
[10]
|
岳超, 刘照军, 张敬军, 等. 大动脉血管中孤立子波的性质分析[J]. 中泰山医学院学报, 2015, 36(2): 121-123.
|
|
[11]
|
范恩贵, 张鸿庆. 非线性孤子方程的齐次平衡法[J]. 物理学报, 1998, 47(3): 353-362.
|