IMPULSES AND PHYSIOLOGICAL STATES IN THEORETICAL MODELS OF NERVE MEMBRANE
IMPULSES AND PHYSIOLOGICAL STATES IN THEORETICAL MODELS OF NERVE MEMBRANE
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DOI：
10.1016/s0006-3495(61)86902-6
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发表时间：
1961-01-01
影响因子：
3.4
通讯作者：
FITZHUGH, R
中科院分区：
文献类型：
--
作者：
FITZHUGH, R
将弛张振子的货车der Pol方程推广为一对非线性微分方程，该方程具有稳定奇点或极限环.由此产生的“BVP模型”有两个状态变量，代表兴奋性和不应性，并定性地类似于Bonhoos的神经铁丝模型的理论模型。此BVP模型作为一类可激振荡系统的简单代表，包括鱿鱼巨轴突的Hodgkin-Huxley（HH）模型。BVP相平面可分为与神经纤维的生理状态（静息、活动、不应、增强、抑制等）相对应的区域。形成一个“生理状态图”，许多生理现象可以用它来概括。从4维HH相空间到平面上的适当选择的投影产生类似的图，其示出了两个模型之间的潜在关系。脉冲序列发生在BVP和HH模型的恒定施加电流的范围内，这使得代表静止状态的奇异点不稳定。
Van der Pol''s equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of non-linear differential equations with either a stable singular point or a limit cycle. The resulting "BVP model" has two variables of state, representing excitability and refractoriness, and qualitatively resembles Bonhoeffer''s theoretical model for the iron wire model of nerve. This BVP model serves as a simple representative of a class of excitable-oscillatory systems including the Hodgkin-Huxley (HH) model of the squid giant axon. The BVP phase plane can be divided into regions corresponding to the physiological states of nerve fiber (resting, active, refractory, enhanced, depressed, etc.) to form a "physiological state diagram," with the help of which many physiological phenomena can be summarized. A properly chosen projection from the 4-dimensional HH phase space onto a plane produces a similar diagram which shows the underlying relationship between the two models. Impulse trains occur in the BVP and HH models for a range of constant applied currents which make the singular point representing the resting state unstable.