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chronaxie : ウィキペディア英語版
chronaxie

Chronaxie is the minimum time required for an electric current double the strength of the rheobase to stimulate a muscle or a neuron. Rheobase is the lowest intensity with indefinite pulse duration which just stimulated muscles or nerves.〔IRNICH, W. (1980), The Chronaxie Time and Its Practical Importance. Pacing and Clinical Electrophysiology, 3: 292–301. doi: 10.1111/j.1540-8159.1980.tb05236.x〕 Chronaxie is dependent on the density of voltage-gated sodium channels in the cell, which affect that cell’s excitability. Chronaxie varies across different types of tissue: fast-twitch muscles have a lower chronaxie, slow-twitch muscles have a higher one. Chronaxie is the tissue-excitability parameter that
permits choice of the optimum stimulus pulse duration for stimulation of any excitable tissue. Chronaxie (c) is the Lapicque descriptor of the stimulus pulse duration for a current
of twice rheobasic (b) strength, which is the threshold current
for an infinitely long-duration stimulus pulse. Lapicque showed
that these two quantities (c,b) define the strength-duration curve
for current: I = b(1+c/d), where d is the pulse duration.
However, there are two other electrical parameters used to
describe a stimulus: energy and charge. The minimum energy
occurs with a pulse duration equal to chronaxie. Minimum
charge (bc) occurs with an infinitely short-duration pulse.
Choice of a pulse duration equal to 10c requires a current of
only 10% above rheobase (b). Choice of a pulse duration of
0.1c requires a charge of 10% above the minimum charge (bc).
==History==
The terms chronaxie and rheobase were first coined in Louis Lapicque’s famous paper on ''Définition expérimentale de l’excitabilité'' that was published in 1909.〔IRNICH, W. (2010), The Terms “Chronaxie” and “Rheobase” are 100 Years Old. Pacing and Clinical Electrophysiology, 33: 491–496. doi: 10.1111/j.1540-8159.2009.02666.x〕
The above I(d) curve is usually attributed to Weiss (1901) - see e.g. (Rattay 1990).
It is the most simplistic of the 2 'simple' mathematical descriptors of the dependence of current strength on duration, and it leads to Weiss' linear charge progression with d:
: Q(d) = I d = b (d + c)
Both Lapicque's own writings and more recent work are at odds with the linear-charge approximation.
Already in 1907 Lapicque was using a linear first-order approximation of the cell membrane, modeled using a single-RC equivalent circuit. Thus:
: I(d) = b / (1 - e^)
where \tau=R C is the membrane time constant - in the 1st-order linear membrane model:
: C \frac + \frac = I, where v \equiv V-V_.
Notice that the chronaxie (c) is not explicitly present here.
Notice also that - with very short duration d \ll \tau, by the Taylor series decomposition of the exponent (around d=0):
: I(d) \approx b \tau / d
which leads to a constant-charge approximation. Interestingly, the latter may fit well also more complex models of the excitable membrane, which take into account ion-channel gating mechanisms, as well as intracellular current flow, which may be the main contributors for deviations from both simple formulas.
These 'subtleties' are clearly described by Lapicque (1907, 1926 and 1931), but not too well by Geddes (2004) who emphasized the Weiss level, attributing it to Lapicque.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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