ON THE “TRANSFORMING ACTION” RELATED TO THE THRESHOLD, CHRONAXIE AND ACCOMMODATION CONSTANT OF A LIVING EXCITABLE SYSTEM

Abstract

A new concept relating to the fundamental conditions of the effective stimulus to a living excitable system is suggested: the stimulus can be regarded as being transformed in the system to its response, and the property of the system is quantitatively represented by the “transforming action” defined in the following relation:
(0.0.2)(Stimulation)·(System)=(Response),
i.e.:
(4.1)(System)=(Response)/(Stimulation),
where the parenthesis shows a certain quantitative representation of the term enclosed and (System) means that of the “transforming action”. Let the threshold and the “transforming action” concerning the strength of the stimulus be a and G₀ respectively; then
(1.0.1) G₀=1/a
is obtained. Here, G₀ is no other than the well-known concept as the excitability of the living excitable system.
The “transforming action” G_-1 definable by concerning the strength-duration curve of the stimulus is
(2.6) G_-1=G₀/(τ+t₀),
where t₀ and τ show the utilization time and chronaxie respectively. Let us take here the chronaxie as the special case of the utilization time, i.e.t₀=τ;
then
(2.6.1) G_-1=G₀/2τ
(2.6.2)=1/2G₀·Gτ,
where
(2.8)Gτ=1/τ.
The reverse value of the chronaxie Gτ shows, therefore, a characteristic property of the system definable by considering the time-or duration-factor of the stimulus.
The “transforming action” G1, which is defined concerning the accommodation phenomenon, is
(3.3) G1=1/m
or
(3.3.1) G1=λG₀,
where m and A show the “minimal gradient” and the “accommodation constant” of the system respectively. Thus the reverse value of the “minimal gradient” and the “accommodation constant” itself may be said to show a characteristic property concerning the phenomenon of the accommodation.
The relation shown by the equation (0.0.2) is not only analogous to the following relation:
(4.4.2)(Cause)·(System)=(Effect),
which is definable by the causality law, but also to (4.2.1) and (4.4.1) shown in the physical system in general:
(4.2.1)(Stress)·(System)=(Strain)
(4.4.1)(Input, External force)·(System)=(Output, Response).
Even in the complicated physical linear system, it is also shown that the above relation (4.4.1) exists, when the Laplace transforms of the input and transfer function in the system are applied. In addition, if the Fourier transforms of them are taken as the special case of the Laplace transform, this relation becomes analogous to (0.0), which was obtained previously by the author (4) and the author et al.(5, 6) as showing the characteristic property of the brain wave generator in the brain.