Chronaxie

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.[2]

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:

${\displaystyle Q(d)=Id=b(d+c)}$

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:

${\displaystyle I(d)=b/(1-e^{-d/\tau })}$

where ${\displaystyle \tau =RC}$ is the membrane time constant - in the 1st-order linear membrane model:

${\displaystyle C{\frac {dv}{dt}}+{\frac {v}{R}}=I,}$ where ${\displaystyle v\equiv V-V_{rest}.}$

Notice that the chronaxie (c) is not explicitly present here. Notice also that - with very short duration ${\displaystyle d\ll \tau }$, by the Taylor series decomposition of the exponent (around d=0):

${\displaystyle I(d)\approx b\tau /d}$

which leads to a constant-charge approximation. 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.

An electrode is inserted into the muscle of interest, which is then stimulated using surface current. Chronaxie values increase resulting from hyperventilation can be ascribed to a change in skin impedance, the physiological factors responsible for this change being under the influence of the autonomic nervous system. This example of the preponderating influence which the condition of the skin and the underlying tissues may exert compels caution in judging the results of chronaxie measurements by percutaneous stimulation.[3] A fresh and normal sartorius placed straight in a Ringer solution and stimulated through the solution without any direct contact with the electrodes is subject to give two very distinct strength-duration curves, one of them being spread over several hundredths of a second.[4]

The main value of chronaxie is comparing excitability across different experiments and measurements using the same standard, thus making data comparisons easier. Electrical stimulation based on chronaxie could regulate myoD gene expression in denervated muscle fibers. 20 muscle contractions, induced by electrical stimulation using surface electrodes and applied on alternate days based on muscle excitability, similar to protocols used in human clinical rehabilitation, were able to reduce the accumulation of mRNA in the myoD and atrogin-1 of denervated muscles, these expressions being related to muscle growth and atrophy, respectively. The increase in myoD levels after denervation is possibly related not only to activation and proliferation of the satellite cells but also to regulation of the cell cycle. Several studies have suggested that the function of denervation-induced myoD may be to prevent the muscle atrophy induced by denervation.[8] To assess contractility of denervated leg muscles, rheobase and chronaxie were determined in anaesthetized rat by surface electrical stimulation and palpation of the leg muscles. The values of chronaxie of TA muscle measured up to 9-month after sciatectomy. Muscle excitability decreased early after denervation. Chronaxie from 0.1–0.2 ms in innervated muscle changed to 0.5–1 ms within one to two days after denervation (i.e., after Wallerian degeneration of the nerve) and progressively increased to about 20 ms during the following month. Chronaxie remained at this level up to 6 months postsciatectomy (Mid-term denervation stage in the rat model: from 2 to 6 months sciatectomy). Afterwards, the twitch contraction became questionably palpable and thus chronaxie increased to much longer values (from 50 ms to infinitum, i.e., the muscle twitch was not palpable). This third stage is defined as the "long-term denervation stage" of the rat model, i.e., denervation time longer than six months). In 3 out of 36 leg muscles, reinnervation occurred spontaneously and chronaxie shortened to 0.1 ms, which is the value of normal innervated muscle.

Chronaxie is increased in the tetany of hypoparathyroidism. It must be remembered, however, that it is the rheobase which corresponds to the x.c.c. of electrical reactions and that that does show a definite reduction. The rheobase depends for its value on the electrical resistance between the two electrodes as well as on the state of excitability of the stimulated motor point and therefore the decrease in the rheobase in tetany might imply no more than a decrease in the electrical resistance of the skin. It is difficult to see, however, how such an alteration of resistance could lead to the increased excitability to mechanical stimuli unless it is that these reactions are reflexes through the proprioceptive nerves. The chronaxie, on the other hand, does not depend on the interelectrode resistance but on the time relations of the excitation process, and when the chronaxie is increased, as in parathyroidectomy, it means that the intensity of twice the rheobase must act on the tissues for a longer period than is normal before the excitation process is set going.[11]

Acute intoxication of rats with aldrin decreases chronaxie, whereas chronic exposure to this chlorinated hydrocarbon insecticide has the reverse effect. Chronic exposure of rats to the closely related epoxide, dieldrin, has been suggested to reduce their muscular efficiency in performing a work exercise. Dieldrin is a chlorinated hydrocarbon insecticide once widely used in crop protection and preservation. Among the diverse symptoms resulting from intoxication are muscular twitching, increasing in severity to epileptiform convulsions with loss of consciousness. Strychnine, which has a spinal locus of activity, causes tonic hind limb extension in mice, which is thought to be due to a removal of the effect of inhibitory interneurons on the nervous pathway to extensor muscles. Leptazol, on the other hand, produces a similar tonic extension by an excitatory action predominantly on cerebral structures. Diphenylhydantoin selectively elevated the threshold convulsive dose of leptazol but not that of strychnine hydrochloride, indicating an anticonvulsant activity on the nervous pathway between the predominant locus of activity of leptazol and the hind limbs.[12]