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A Flexible Neural Analog Using Integrated Circuits

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TLDR
An electronic neural analog is described which contains variable absolute and relative refractory periods, two time constants, and separate control of the ``accommodation'' to sub-threshold voltage changes and the ``adaptation'' produced by the occurrence of output pulses (spikes).
Abstract
An electronic neural analog is described which contains variable absolute and relative refractory periods, two time constants, and separate control of the ``accommodation'' to sub-threshold voltage changes and the ``adaptation'' produced by the occurrence of output pulses (spikes). The extensive use of integrated-circuit operational amplifiers permits an accurate description of input-output relationships over a wide range of values for all parameters. This facilitates comparison of the results obtained both with neural data and mathematical or digitally simulated models of neural activity. The effect of white noise on interval histograms and their parameters is described and its effect when added to other inputs. Noise disrupts the phase-locked patterns produced by sinusoidal stimuli and the averaged response may become a smooth sinusoidal function in the presence of added noise. Adaptation may produce a phase lead to sinusoidal stimuli, while accommodation may produce a phase lag. Corresponding overshoots or undershoots are seen with square-wave inputs.

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References
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Journal ArticleDOI

A quantitative description of membrane current and its application to conduction and excitation in nerve

TL;DR: This article concludes a series of papers concerned with the flow of electric current through the surface membrane of a giant nerve fibre by putting them into mathematical form and showing that they will account for conduction and excitation in quantitative terms.
Journal ArticleDOI

Impulses and Physiological States in Theoretical Models of Nerve Membrane

TL;DR: 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, which qualitatively resembles Bonhoeffer's theoretical model for the iron wire model of nerve.
Journal ArticleDOI

A theoretical analysis of neuronal variability.

TL;DR: The assumptions of the model are relaxed and the effects of such experimentally found phenomena as relative refractory and supernormal periods, adaptation, potentiation, and rhythmic slow potentials are discussed.
Journal ArticleDOI

Electrophysiology of a Dendritic Neuron Model

Wilfrid Rall
- 01 Mar 1962 - 
TL;DR: The development of a mathematical model of dendritic neurons was begun because of a need to combine three different kinds of knowledge into a coherent theory, namely, the anatomical concept of the neuron, the theoretical development of the nerve membrane models, and a detailed body of quantitative electrophysiological information obtained from individual neurons by means of intracellular and extracellular microelectrodes.
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