After-effects of near-threshold stimulation in single human motor axons
1 Sobell Department of Neurophysiology, Institute of Neurology, Queen Square, London, UK and Institute of Clinical Neurosciences
2 The University of Sydney and Royal Prince Alfred Hospital, Sydney, Australia
Abstract
Subthreshold electrical stimuli can generate a long-lasting increase in axonal excitability, superficially resembling the phase of superexcitability that follows a conditioning nerve impulse. This phenomenon of ‘subthreshold superexcitability’ has been investigated in single motor axons in six healthy human subjects, by tracking the excitability changes produced by conditioning stimuli of different amplitudes and waveforms. Near-threshold 1 ms stimuli caused a mean decrease in threshold at 5 ms of 22.1 ± 6.0% (mean ±S.D.) if excitation occurred, or 6.9 ± 2.6% if excitation did not occur. The subthreshold superexcitability was maximal at an interval of about 5 ms, and fell to zero at 30 ms. It appeared to be made up of two components: a passive component linearly related to conditioning stimulus amplitude, and a non-linear active component. The active component appeared when conditioning stimuli exceeded 60% of threshold, and accounted for a maximal threshold decrease of 2.6 ± 1.3%. The passive component was directly proportional to stimulus charge, when conditioning stimulus duration was varied between 0.2 and 2 ms, and could be eliminated by using triphasic stimuli with zero net charge. This change in stimulus waveform had little effect on the active component of subthreshold superexcitability or on the ‘suprathreshold superexcitability’ that followed excitation. It is concluded that subthreshold superexcitability in human motor axons is mainly due to the passive electrotonic effects of the stimulating current, but this is supplemented by an active component (about 12% of suprathreshold superexcitability), due to a local response of voltage-dependent sodium channels.
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Introduction
Following the conduction of a nerve impulse, axons undergo a reproducible sequence of excitability changes known as the recovery cycle. Refractoriness is followed by a phase of increased excitability (the supernormal or superexcitable period), which in turn gives way to a phase of reduced excitability (late subnormal or subexcitable period) (Gasser & Erlanger, 1930; Bergmans, 1970; Kiernan et al. 1996). Apart from refractoriness (which is mainly attributable to sodium channel inactivation), the changes in excitability are closely related to afterpotentials: superexcitability to the depolarizing (negative) afterpotential and late subexcitability to after-hyperpolarization (positive afterpotential) (Gasser & Erlanger, 1930; Gasser & Grundfest, 1936; McIntyre et al. 2002). Subthreshold stimuli can also cause a long-lasting increase in excitability, analogous to superexcitability, although this is smaller and confined to the vicinity of the stimulating electrode. Potts et al. (1994) found that when two equal submaximal stimuli are delivered to a human motor nerve, the response to the second can be as much as 50% greater than the response to the first. A similar phenomenon in sensory nerves has been compared with paired-pulse studies of cortical excitability by transcranial magnetic stimulation (Chan et al. 2002). The implication of these studies is that some axons not excited by the first stimulus were nevertheless made ‘superexcitable’, and this was confirmed in a single motor unit study by Shefner et al. (1996). We shall refer to this increase in excitability following a subthreshold stimulus as ‘subthreshold superexcitability’ in contrast to the ‘suprathreshold superexcitability’ that follows an action potential.
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Since the seminal studies of Barrett & Barrett (1982) on invertebrate myelinated fibres, the depolarizing afterpotential (DAP) and (suprathreshold) superexcitability have been largely attributed to a passive depolarization of the internodal axolemma by current leaking through or under the myelin sheath during the action potential. This view was supported by subsequent studies and modelling of rat spinal cord axons (Blight, 1985; Blight & Someya, 1985). A more recent modelling study (McIntyre et al. 2002) has shown how this passive depolarization is likely to be augmented by persistent sodium currents, which may be active at the resting potential (Bostock & Rothwell, 1997).
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The mechanisms underlying subthreshold superexcitability have been the subject of less attention. Barrett & Barrett (1982) showed that the passive cable properties of myelinated axons give rise to long-lasting, DAP-like afterpotentials after subthreshold current injection, so that a hyperpolarizing pulse can cause a mirror image of the DAP. In intracellular recordings from rat sciatic axons, Bowe et al. (1987) observed that subthreshold stimuli can cause an afterpotential and a ‘supernormal-like’ period of increased excitability. Other evidence suggests that passive electrotonic behaviour is unlikely to account fully for subthreshold superexcitability. Since the classic study of Katz (1937) on frog nerves, it has been known that as stimuli approach threshold they cause a local response, a non-linear increase and prolongation of membrane depolarization, above that accounted for by passive membrane properties but falling short of that required to generate a propagated action potential. Over a short timescale, the local response in human motor and sensory axons can be revealed by the changes in excitability produced by brief, near-threshold depolarizing currents (Bostock & Rothwell, 1997). In these ‘latent addition’ experiments, excitability changes were followed for only 0.5 ms, but the extra sodium currents generated as stimuli approach threshold would be expected to increase the subsequent afterpotentials and subthreshold superexcitability.
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In this study we have sought to clarify the extent and biophysical basis of subthreshold superexcitability in human motor axons, using an automated version of Bergmans' (1970) non-invasive method of tracking the threshold of single human motor axons in vivo. Excitability changes were tracked separately, depending on whether a conditioning stimulus excited or failed to excite an impulse. To separate the expected passive (electrotonic) and active (local response) components of subthreshold superexcitability, the former was assumed to be linearly related to conditioning stimulus amplitude, and opposite in sign for depolarizing and hyperpolarizing currents. It was found that near-threshold 1 ms depolarizing currents cause a long-lasting decrease in threshold, about one-third of the size of the superexcitability after an impulse, but no refractoriness or late subexcitability. The subthreshold superexcitability behaved as the sum of a passive component, proportional to stimulus charge, and a local response component, that appeared when stimuli exceeded 60% of threshold. The linear component could be eliminated by using triphasic conditioning stimuli with zero net charge, leaving the small active component apparently unchanged.
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Methods
Subjects and isolation of single human motor units
Motor units suitable for reliable single unit recording with surface electrodes were sought in the motor nerves of six healthy volunteers with no clinical or neurological evidence of a peripheral nerve disorder. Following recent experience (Hales et al. 2004), flexor carpi ulnaris was tested first, but additional motor units were subsequently isolated from abductor pollicis brevis, in both cases stimulating the ulnar and median nerves above or at the elbow. Because the units selected by surface stimulation had the lowest thresholds (or among the lowest) at the stimulation site, it was important to be sure that they were not selected because of abnormal membrane properties. Units were therefore only accepted for further study if they had recovery cycles to suprathreshold stimuli resembling those recorded by tracking compound motor action potentials (Kiernan et al. 1996, 2000).
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The studies, which were conducted in accordance with the Declaration of Helsinki, had the approval of The University of Sydney Human Research Ethics Committee, and all subjects provided written informed consent.
Stimulation and recording
The after-effects of stimulating single human motor axons were studied by delivering 1 ms constant-current stimuli over the ulnar nerve above the elbow or median nerve at the elbow, and recording all-or-none motor unit action potentials from flexor carpi ulnaris or abductor pollicis brevis, respectively. The nerve was stimulated through a non-polarizable stimulating electrode (Red Dot, 3M Canada Inc., London, Ontario, Canada) with the anode 4 cm proximal. The orientation of the electrodes to the nerve was adjusted to stimulate an axon innervating a large motor unit selectively, even when the stimulus was > 1.5 x threshold for that unit. This was possible in only 50% of experiments. Stimuli were generated by a purpose-built isolated current source with a maximal output of 50 mA, driven by a PC, running modified QTRAC software (Institute of Neurology). New facilities were incorporated in the software to track thresholds separately, depending on whether or not the unit was excited by the conditioning stimulus. Surface EMG recording electrodes were placed over the muscle, and the signal was amplified (200 Hz–2 kHz) and sampled at 10 kHz. The stimulus intensity and positions of the stimulating and recording electrodes were adjusted manually until an all-or-none single motor unit potential could be discriminated reliably. For all subjects skin temperature was monitored continuously and maintained at > 32°C using a thermostatically controlled pad.
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The following recording protocols were applied to each unit, where T is the unconditioned threshold current and C the conditioning stimulus current, and the stimuli were rectangular current pulses of 1 ms duration unless specified otherwise.
Recovery cycle to ‘suprathreshold’ conditioning stimuli, with C= 1.04T (i.e. 1.04 xT), determined by estimating thresholds at interstimulus intervals (ISIs) of 2, 2.5, 3.2, 4.5, 6.3, 7.9, 10, 13, 18, 24, 32, 42, 56, 75, 100, 130, 160 and 200 ms.
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Recovery cycle to ‘subthreshold’ depolarizing conditioning stimuli, with C= 0.96T (and the ISIs in (i)).
‘Passive’ recovery cycle to subthreshold hyperpolarizing conditioning stimuli, with C=–0.96T (ISIs as in (i)).
Relationship of subthreshold superexcitability to conditioning stimulus intensity, at a fixed ISI of 5 ms, determined by estimating thresholds while the strength of the conditioning stimulus was changed from –1.0T to +1.0T in 0.2T intervals, +0.9T, 0.94T, 0.96T, 0.98T.
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Relationship of suprathreshold superexcitability to conditioning stimulus amplitude, at the 5 ms ISI, for conditioning stimuli from 1.0T to 1.5T in 0.1T intervals, +1.02T, 1.06T.
The following additional recording protocols were used with units in abductor pollicis brevis of three subjects.
Relationship of components of superexcitability to conditioning stimulus charge, determined for the 5 ms ISI by varying the duration of the conditioning stimuli from 0.2 to 2 ms in 0.2 ms intervals, for subthreshold conditioning stimuli of strength 0.96T and –0.96T and suprathreshold conditioning stimuli of strength 1.04T.
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Relationship of subthreshold and suprathreshold superexcitability to conditioning stimulus amplitude, as in (iv) and (v) using triphasic stimuli with zero net charge.
The zero-charge conditioning and test stimuli used for protocol (vii) were generated as symmetrical cosine-windowed sine waves, of total width 2 ms and sine wave period 1 ms. The integral of the waveform generated by QTRAC (which was altered in steps of 0.1 ms duration, corresponding to the sampling interval, as illustrated in Fig. 6) was checked to be zero.
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Data from same motor unit as in Fig. 5. and dashed line: excitability changes evoked by 1 ms rectangular stimuli as a function of conditioning stimulus amplitude, with line fitted to data for conditioning stimuli from –100% to 60% of threshold (as in Fig. 4). , similar data obtained by making conditioning and test stimuli triphasic, so that the net charge transfer was zero.
Tracking suprathreshold and subthreshold excitability changes
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The QTRAC program allows one response to be measured and compared with a target response for each of up to 16 stimulus/response channels. Testing of responses to both conditioning and test stimuli in the same sweep was achieved by using the same response for multiple channels and analysing it in different ways. For this experiment the channels were split into groups of three, which received the same response to a single or double stimulus. In each group, the first channel (a) was always used, but the next channel (b) was skipped unless the response tested in ‘a’ was positive, and the third channel (c) was skipped unless there was no response in ‘a’. This conditional skipping enabled suprathreshold and subthreshold recovery cycles to be tracked separately when the first stimulus was close to threshold, despite the intrinsic variability of axonal thresholds (Hales et al. 2004). Figure 1 illustrates the response waveforms from one unit, testing suprathreshold superexcitability with conditioning stimuli of 1.04T (Fig. 1A) and subthreshold superexcitability with conditioning stimuli of 0.96T (Fig. 1B), and an interstimulus interval of 5 ms. The functions of the different channels were as follows.
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In this example, conditioning stimuli were set to 104% (A) and 96% (B) of the unconditioned threshold, and the interstimulus interval was 5 ms. The unit was considered excited when the response crossed the horizontal line. For the significance of channel numbers and waveform manipulation see text. Unconditioned thresholds were tracked in channel 1. Channels 2 and 4 were used for stimulus artefact suppression. Conditioned thresholds were tracked in channel 3b (when conditioning stimulus did excite, but the response to the conditioning stimulus had been subtracted) and channel 5c (when conditioning stimulus did not excite).
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Channel 1. This was used to determine the unconditioned threshold, T, and also to generate waveforms for subtraction from the double responses in channel 3. Stimulus: 1st only, strength determined by tracking an all-or-none response in 1a. Responses: 1a, response to 1st stimulus tested to track unconditioned threshold; 1b, generates running average of positive responses to the first stimulus (see 3b); 1c, generates running average of the no-responses to the first stimulus (see 5c).
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Channel 2. This channel was used solely to generate stimulus artefact waveforms for the second stimulus, for subtraction from the double responses when the second response overlapped the first. Stimulus: second only, amplitude set to 2/3 of the amplitude of the second stimulus on channel 3, to avoid generating a response. Responses: 2a, response to second stimulus tested after multiplication by 3/2, to check that it did not excite; 2b, this channel was nearly always skipped, and response not used; 2c, generates running average of stimulus artefact, after multiplication by 3/2, for subtraction from channel 3.
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Channel 3. Used to track changes in excitability after suprathreshold conditioning stimuli. Stimulus: first set to a specified fraction ( 1) of unconditioned threshold (i.e. first stimulus on channel 1); the second stimulus tracks conditioned threshold, determined by responses in 3b. Responses: 3a, response to the first stimulus tested after subtraction of the second stimulus artefact (2c); 3b, response to the second stimulus tested after subtraction of response to the first stimulus (1b); 3c, not used.
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Channel 4. Like channel 2, but with the second stimulus set to 2/3 of the second stimulus on channel 5.
Channel 5. Used to track changes in excitability after subthreshold conditioning stimuli. Stimulus: first set to specified fraction ( 1) of unconditioned threshold (i.e. first stimulus on channel 1); the second stimulus tracks conditioned threshold, determined by responses in 5c. Responses: 5a, response to the first stimulus tested after subtraction of the second stimulus artefact (4c); 5b, not used; 5c, response to the second stimulus tested after subtraction of negative response to the first stimulus (1c).
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Channels 2 and 4 were only required for protocols (i) to (iii) in which the second stimulus artefact sometimes affected recording of the response to the first stimulus. In protocols (vi) and (vii), when the duration of the conditioning stimulus was altered, channel 1 was used to generate the unconditioned threshold for a stimulus duration corresponding to the conditioning stimulus. An extra stimulus channel was required to track the unconditioned threshold to the 1 ms test stimulus.
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Results
Suprathreshold and subthreshold recovery cycles
Figure 2 shows suprathreshold recovery cycles for protocol (i) in Methods for six single units, each from a separate subject, for conditioning stimulus intensities that were just above threshold (1.04T). Each unit underwent phases of refractoriness, superexcitability and late subexcitability, and qualitatively these resembled the recovery cycles recorded for compound muscle action potentials (CMAPs), e.g. for median nerves at the wrist (Kiernan et al. 2000) or peroneal nerves at the knee or ankle (Kuwabara et al. 2000), which also used 1 ms stimuli. Quantitatively, the peak superexcitability and subexcitability measurements for each single unit were within the 95% confidence limits for CMAPs documented in the above studies, suggesting that the single units selected by surface stimulation were representative of human motor axons in general.
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All units exhibited superexcitability (range –18 to –32%) and late subexcitability (5–19%) within the normal range for recordings made using compound EMG potentials.
Figure 3A compares the mean excitability cycles for just-suprathreshold and just-subthreshold stimuli (protocols (i) and (ii)). As previously reported by Bowe et al. (1987) and Shefner et al. (1996), a just-subthreshold conditioning stimulus caused a ‘supernormal-like’ period of superexcitability. However, at intervals down to 2 ms there was no subthreshold analogue of refractoriness, and there was no subthreshold late subexcitability. Subthreshold superexcitability was maximal at an ISI of 5 ms, but did not change significantly between 2 ms and 6.3 ms. At 5 ms, the subthreshold superexcitability at –7.2 ± 2.4% (mean ±S.D.) was about one-third of the suprathreshold superexcitability of –22.4 ± 6.6%.
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A: , suprathreshold recovery cycle for 1 ms conditioning stimuli 104% of threshold (mean ±S.E.M., n= 6); , subthreshold recovery cycle for conditioning stimuli 96% of threshold. B, active and passive components of subthreshold recovery cycles: , subthreshold recovery cycle as in A; , excitability changes following hyperpolarizing current pulses, –96% of threshold; , sum of excitability changes evoked by equal and opposite conditioning pulses, indicating active component of subthreshold superexcitability, not accounted for by passive effects of conditioning currents.
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Active and passive components of subthreshold superexcitability
Figure 3B compares the subthreshold recovery cycle from Fig. 3A (protocol (ii)) with the recovery cycle following conditioning stimuli of the same amplitude but opposite polarity (protocol (iii)), and with their sum, which represents the non-linear or active component of subthreshold superexcitability. The depolarizing and hyperpolarizing recovery cycles were of similar shape, but the excitability changes for conditioning stimuli 96% of threshold (C= 0.96T) were on average –1.48 times those for C=–0.96T. With 1 ms conditioning stimuli, the active component of subthreshold superexcitability was therefore close to half the amplitude of the passive component, and at the 5 ms ISI contributed a threshold change of –2.6 ± 1.3%, about 12% of the suprathreshold superexcitability.
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This method of estimating the active and passive components assumes that the passive component is linear, supplemented by an active component when the conditioning stimulus approaches threshold and a local response is generated by activation of sodium channels. This assumption was tested for the 5 ms ISI by recording the threshold changes for conditioning stimuli which did not excite, in the range –100% to 100% of threshold (protocol (iv)). To test for an effect of conditioning stimulus strength on suprathreshold superexcitability, we also tracked the threshold changes for stimuli which did excite, in the range 100–150% of threshold (protocol (v)). The means (±S.E.M.) of these excitability changes are plotted in Fig. 4. There was no consistent effect of conditioning stimulus strength on suprathreshold superexcitability, but there was a good linear relationship for subthreshold stimuli in the range –80% to +60% of threshold. No meaning could be attached to the apparent deviation from linearity at –100%, which was not significant. From +80% to +100%, however, the excitability changes deviated systematically from the linear relationship, as shown on an expanded scale in the inset plot, presumably because of the activation of sodium channels. There was no further increase in excitability for subthreshold stimuli in the range 96% to 100% of threshold, indicating that the data in Fig. 3 for near-threshold stimuli would have been little different if we had used threshold stimuli which did and did not excite (but the experiments would have taken nearly twice as long). For stimuli equal to threshold (on the vertical dashed line), the threshold changes were –6.6 ± 2.9% (mean ±S.D.) if excitation did not o ccur, but –21.8 ± 5.6% if excitation did occur. As expected, these values correspond closely to those for 96% subthreshold and 104% suprathreshold conditioning stimuli in the previous section. Accordingly, the best estimates of just-subthreshold and just-suprathreshold superexcitability at 5 ms were obtained by averaging the values from Figs 3 and 4 for each subject, i.e. –6.9 ± 2.6% and –22.1 ± 6.0%, respectively.
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Data plotted are mean ±S.E.M. for the 6 units in Fig. 3. For conditioning stimuli < 60% of threshold, the excitability changes were directly proportional to current. From 80 to 100%, stimuli which did not excite produced a non-linear increase in excitability. Note that this decrease in threshold (–6.6%) corresponds to that in Fig. 3A and B (–7.2%; ). Conditioning stimuli 100–150% of threshold that did excite showed no significant dependence on amplitude. Note that the threshold change produced by these suprathreshold stimuli (–21.8%) is similar to the peak of superexcitability in Fig. 3A (–22.4%).
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Sub- and suprathreshold superexcitability and conditioning stimulus waveform
In the studies above, both the conditioning and test stimuli were rectangular pulses of 1 ms duration. The passive component of subthreshold superexcitability is linearly related to the strength of the conditioning stimulus, but it might also be expected to depend on the duration of the conditioning stimulus. Figure 5 illustrates one of three similar experiments in which the effects of this parameter were explored systematically for a conditioning–test interval of 5 ms. The duration of the conditioning stimulus was varied from 0.2 to 2 ms and excitability changes measured for conditioning stimuli of –0.96T, 0.96T (not exciting) and 1.04T (exciting), i.e. protocol (vi). Changes in threshold with membrane potential depend on stimulus duration, since the strength–duration time constant is potential dependent (Bostock et al. 1998). To avoid changes in superexcitability due to this phenomenon, the test stimulus duration was kept constant at 1 ms. An extra stimulus/response channel was therefore needed for this experiment, to track the unconditioned threshold to the stimuli of 1 ms duration, as well as the unconditioned threshold to the stimuli of variable duration.
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Data from single motor unit. A: , subthreshold superexcitability, evoked by conditioning stimuli 96% of threshold, increases with conditioning stimulus width (although conditioning stimulus amplitude decreases according to the strength–duration relationship); , similar increase in threshold change caused by equal hyperpolarizing pulses; , sums of the measured threshold changes, representing the non-linear component of subthreshold superexcitability; , suprathreshold superexcitability, measured at constant interstimulus interval; , suprathreshold superexcitability measured at interstimulus intervals adjusted manually to keep the interspike interval constant. B: , threshold changes evoked by hyperpolarizing current pulses ( in A), replotted as a function of conditioning stimulus charge (threshold current in mA x duration in ms). Continuous line is best least-squares fit passing through the origin. Dotted line is regression line for non-linear component of subthreshold superexcitability ( in A), which showed no significant relationship with conditioning stimulus charge.
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Figure 5A shows that the effects of subthreshold conditioning stimuli, whether 96% or –96% of threshold, increased approximately linearly with duration, even though the stimulus amplitudes fell, given that the unconditioned threshold current was much lower for 2 ms than for 0.2 ms stimuli. When the threshold changes to the hyperpolarizing conditioning stimuli, representing (minus) the passive component of subthreshold superexcitability, were plotted against absolute conditioning stimulus charge (filled circles in Fig. 5B), the relationship was well fitted by a straight line through the origin. The passive component of excitability change is therefore linearly related to conditioning stimulus charge, whether stimulus duration or stimulus amplitude is altered.
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In contrast, the active component of subthreshold superexcitability, indicated by the sums of the excitability changes to conditioning stimuli 96% and –96% of threshold (open squares in Fig. 5A; dotted line in Fig. 5B), appears to be independent of the duration of the conditioning stimulus. The active and passive components of subthreshold superexcitability are about the same for conditioning stimuli of 0.2 ms duration, and for shorter conditioning stimuli the active component is predicted to be more important.
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Also shown in Fig. 5A is the dependence of suprathreshold superexcitability on the duration of the conditioning stimulus (filled circles). There appears to be a progressive reduction in superexcitability with conditioning stimulus width, especially above 1.5 ms. However, this experiment was complicated by the fact that altering the conditioning stimulus width altered the interspike interval, because the delay from the onset of the conditioning stimulus to spike initiation depended on the conditioning stimulus width. To compensate for this, the experiment was repeated with the onset of the test stimulus adjusted manually to keep the interspike interval constant. When this was done there was no significant change in suprathreshold superexcitability with conditioning stimulus width (open circles and dotted lines in Fig. 5A).
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Figure 5B implies that if a just-subthreshold conditioning stimulus had zero charge, it should induce no passive component of subthreshold superexcitability, but a normal active component of about –2.9%. To test this we generated triphasic stimulus waveforms (conditioning and test) that delivered no net charge and repeated the experiment illustrated in Fig. 4 (protocol (vii)) in three subjects. Figure 6 shows that, as predicted, there was no trace of a passive threshold change, linearly related to conditioning stimulus amplitude. However, for conditioning stimuli greater than 60% of threshold there was a non-linear increase in excitability, similar to the active component obtained with the 1 ms rectangular stimuli. Qualitatively similar results were obtained with the two other subjects tested. Figure 6 also shows that the suprathreshold superexcitability induced by the zero-charge stimuli was similar to that obtained with 1 ms rectangular stimuli.
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Discussion
This study has been the first to use automatic threshold tracking to explore the effects of near-threshold stimuli on the excitability of human motor axons. It has also been the first to separate these effects into active and passive components. The main findings are that just-subthreshold stimuli of 1 ms duration generate a period of increased excitability analogous to superexcitability, but about one-third of the amplitude, without a preceding phase of refractoriness or a late phase of subexcitability. Most of the subthreshold superexcitability evoked by 1 ms rectangular pulses is passive or electrotonic in origin, directly proportional to the stimulus charge (though with conditioning stimuli of < 0.2 ms, the active component may exceed the passive electrotonic component). The active component is about 12% of the amplitude of the suprathreshold superexcitability.
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The use of threshold tracking has enabled single unit excitability changes to be documented more quantitatively than was possible in a previous study (Shefner et al. 1996) which used conditioning and test stimuli of equal intensity. This meant that the recovery cycle could only be measured in terms of the changes in probability of a threshold stimulus (i.e. with amplitude equal to the unconditioned threshold) exciting the unit. Thresholds of human motor axons normally vary about their mean value with a standard deviation of about 1.65% (Hales et al. 2004), so that although this method is sensitive to small changes in threshold, it cannot reliably distinguish between changes of more than a few per cent. That is presumably why Shefner et al. (1996) found little difference between suprathreshold and subthreshold superexcitability. The probability of excitation also depends critically on both the short-term variations in threshold, which vary between units, and the longer-term stability of the threshold. The method of threshold tracking used in the present study, in which thresholds with and without conditioning stimuli are tracked continuously, avoids these limitations.
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Accurate quantification of the threshold changes evoked by subthreshold and near-threshold conditioning stimuli allows the threshold changes to be resolved into passive and active components, assuming that the passive electrotonic component is linearly related to the strength of the conditioning stimulus. This assumption appears to be justified by the data in Fig. 4. There was a linear relationship for conditioning stimuli between –80% and 60% of threshold. As the conditioning stimulus approached threshold, the excitability change deviated more and more from the linear relationship. This was not because occasional conditioning stimuli evoked action potentials, since the program reliably excluded this possibility. A possibility raised by Shefner et al. (1996) was that near-threshold stimuli would have activated some sensory axons, which have a lower threshold than motor axons, and that action currents in the sensory fibres might then have ephaptically increased the excitability of the tested motor axon. This possibility was excluded by Bergmans (1970) who applied conditioning stimuli at another site and found that subthreshold stimuli, even though they excited sensory axons, did not evoke measurable superexcitability. It seems most likely therefore that the non-linear component of subthreshold superexcitability is due to activation of voltage-dependent ion channels in the stimulated axon, insufficient to trigger a propagated impulse, i.e. a local response.
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Subthreshold superexcitability and latent addition
Another manifestation of a local response in human motor axons is the asymmetry of the excitability changes induced by brief depolarizing and hyperpolarizing currents, recorded as ‘latent addition’ (Bostock & Rothwell, 1997). Current pulses 90% of threshold, and 0.06–0.2 ms wide, produced an increase in excitability that lasted considerably longer than the decrease in excitability following hyperpolarizing current pulses of the same amplitude, although these were only tracked for 0.5 ms in that study. Modelling of the excitability changes showed that the prolongation of the depolarization and increased excitability was caused by a small sodium current. The subthreshold superexcitability measurements can be regarded as an extreme type of latent addition measurement, in which the conditioning stimuli extend even closer to threshold, and the excitability changes are followed to much longer interstimulus intervals. In the latent addition study (Bostock & Rothwell, 1997), the modelled local responses were larger, in terms of prolongation of depolarization and total charge carried by the sodium current, for sensory than for motor axons. This was attributed to a greater activation of persistent sodium currents in the sensory axons. This suggests that the active component of subthreshold superexcitability may also be more prominent in sensory fibres. The type of sodium channel most likely to be involved is Nav1.6, since this is thought to be the dominant type at peripheral nodes of Ranvier, and is also known to generate persistent as well as transient sodium current (Baker, 2005).
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Subthreshold superexcitability and threshold electrotonus
The subthreshold superexcitability measurements can also be regarded as a type of threshold electrotonus. Threshold electrotonus is normally measured as the excitability changes during and after a subthreshold conditioning current lasting 100 ms or more (e.g. Bostock et al. 1998), whereas in this study the subthreshold recovery cycles were measured following stimuli of 0.2 to 2 ms duration. In the experiment in Fig. 5, subthreshold superexcitability increased linearly with the duration of the conditioning stimulus, prompting the question of how far this linear relationship holds. Studies of threshold electrotonus show that if a subthreshold conditioning stimulus lasts longer than about 20 ms, the threshold reaches a minimum and then increases again, due to accommodation caused by the activation of slow potassium channels (Bostock & Baker, 1988). Similarly, the residual drop in threshold left after the end of the subthreshold conditioning stimulus, i.e. the subthreshold superexcitability, must reach a limit and decrease when the stimulus duration exceeds about 20 ms. The studies of threshold electrotonus show that when the conditioning stimuli are very long, the activation of slow potassium channels results in an after-hyperpolarization, the subthreshold analogue of late subexcitability. It follows that the lack of appreciable subthreshold late subexcitability in this study and that of Shefner et al. (1996) is not because an action potential is absolutely necessary to activate it, but rather because subthreshold depolarization activates it relatively slowly, and it would take a near-threshold stimulus lasting many milliseconds to evoke substantial subthreshold late subexcitability.
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Zero-charge stimuli
The experiments with zero-charge stimuli have confirmed the dependence of the passive component of subthreshold superexcitability on stimulus charge, and provided a convenient means to minimize this component. These observations are relevant to studies of nerves and central fibre tracts with transcranial magnetic stimulation (TMS), in which a monophasic pulse of current in the magnetic coil generates a biphasic electric field pulse, proportional to the time differential of the magnetic field (Mills, 1999), and therefore in principle a zero net charge transfer across the axon. Subthreshold superexcitability in TMS experiments is therefore expected to be restricted to the active component caused by a local response, which in the motor axons studied was limited to an average of 2.6%. However, the neural components activated in most TMS experiments have not been clearly identified, and their excitability properties are mostly unknown, so there is a possibility that subthreshold superexcitability may be higher than in peripheral motor axons.
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It is worth noting here that even a 2.6% change in threshold can have appreciable effects, depending on the stimulus–response function. For human median nerves stimulated at the wrist, the results of Kiernan et al. (2000) showed an almost linear relationship between the log of the stimulus current and the log of CMAP amplitude, over the range 0.1–2 mV, such that a 2.6% fall in threshold would correspond to an increase in response to a fixed stimulus of more than 30%.
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Suprathreshold superexcitability and conditioning stimulus parameters
One reason for exploring subthreshold superexcitability was a concern that factors such as conditioning stimulus amplitude and duration, which determine the passive component of subthreshold superexcitability, might also affect (suprathreshold) superexcitability, which is being studied increasingly in patients with peripheral nerve disease as part of a test of multiple nerve excitability parameters (Kiernan et al. 2000; Lin et al. 2005). The results in Figs 4 and 5 show that neither conditioning stimulus amplitude (in the range 100–150% of threshold) nor conditioning stimulus duration (in the range 0.2–2 ms) has any appreciable effect on superexcitability, except in so far as they affect interspike intervals.
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In conclusion, subthreshold superexcitability is a type of stimulus-dependent excitability change that is more closely related to latent addition and to threshold electrotonus than to the suprathreshold recovery cycle. The prolonged increase in excitability following near-threshold stimuli is caused by a depolarizing charge stored on the capacitance of the internodal axolemma. The depolarizing charge has two components, a passive component directly proportional to the stimulus charge, and an active component caused by the activation of sodium currents during the local response. With 1 ms stimuli the passive component dominates, by about 2: 1, but with zero-charge stimuli only the local response contributes.
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References
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Blight AR (1985). Computer simulations of action potentials and afterpotentials in mammalian myelinated axons: the case for a lower resistance myelin sheath. Neuroscience 15, 13–31.
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Hales JP, Lin CS-Y & Bostock H (2004). Variations in excitability of single human motor axons, related to stochastic properties of nodal sodium channels. J Physiol 559, 953–964.
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2 The University of Sydney and Royal Prince Alfred Hospital, Sydney, Australia
Abstract
Subthreshold electrical stimuli can generate a long-lasting increase in axonal excitability, superficially resembling the phase of superexcitability that follows a conditioning nerve impulse. This phenomenon of ‘subthreshold superexcitability’ has been investigated in single motor axons in six healthy human subjects, by tracking the excitability changes produced by conditioning stimuli of different amplitudes and waveforms. Near-threshold 1 ms stimuli caused a mean decrease in threshold at 5 ms of 22.1 ± 6.0% (mean ±S.D.) if excitation occurred, or 6.9 ± 2.6% if excitation did not occur. The subthreshold superexcitability was maximal at an interval of about 5 ms, and fell to zero at 30 ms. It appeared to be made up of two components: a passive component linearly related to conditioning stimulus amplitude, and a non-linear active component. The active component appeared when conditioning stimuli exceeded 60% of threshold, and accounted for a maximal threshold decrease of 2.6 ± 1.3%. The passive component was directly proportional to stimulus charge, when conditioning stimulus duration was varied between 0.2 and 2 ms, and could be eliminated by using triphasic stimuli with zero net charge. This change in stimulus waveform had little effect on the active component of subthreshold superexcitability or on the ‘suprathreshold superexcitability’ that followed excitation. It is concluded that subthreshold superexcitability in human motor axons is mainly due to the passive electrotonic effects of the stimulating current, but this is supplemented by an active component (about 12% of suprathreshold superexcitability), due to a local response of voltage-dependent sodium channels.
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Introduction
Following the conduction of a nerve impulse, axons undergo a reproducible sequence of excitability changes known as the recovery cycle. Refractoriness is followed by a phase of increased excitability (the supernormal or superexcitable period), which in turn gives way to a phase of reduced excitability (late subnormal or subexcitable period) (Gasser & Erlanger, 1930; Bergmans, 1970; Kiernan et al. 1996). Apart from refractoriness (which is mainly attributable to sodium channel inactivation), the changes in excitability are closely related to afterpotentials: superexcitability to the depolarizing (negative) afterpotential and late subexcitability to after-hyperpolarization (positive afterpotential) (Gasser & Erlanger, 1930; Gasser & Grundfest, 1936; McIntyre et al. 2002). Subthreshold stimuli can also cause a long-lasting increase in excitability, analogous to superexcitability, although this is smaller and confined to the vicinity of the stimulating electrode. Potts et al. (1994) found that when two equal submaximal stimuli are delivered to a human motor nerve, the response to the second can be as much as 50% greater than the response to the first. A similar phenomenon in sensory nerves has been compared with paired-pulse studies of cortical excitability by transcranial magnetic stimulation (Chan et al. 2002). The implication of these studies is that some axons not excited by the first stimulus were nevertheless made ‘superexcitable’, and this was confirmed in a single motor unit study by Shefner et al. (1996). We shall refer to this increase in excitability following a subthreshold stimulus as ‘subthreshold superexcitability’ in contrast to the ‘suprathreshold superexcitability’ that follows an action potential.
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Since the seminal studies of Barrett & Barrett (1982) on invertebrate myelinated fibres, the depolarizing afterpotential (DAP) and (suprathreshold) superexcitability have been largely attributed to a passive depolarization of the internodal axolemma by current leaking through or under the myelin sheath during the action potential. This view was supported by subsequent studies and modelling of rat spinal cord axons (Blight, 1985; Blight & Someya, 1985). A more recent modelling study (McIntyre et al. 2002) has shown how this passive depolarization is likely to be augmented by persistent sodium currents, which may be active at the resting potential (Bostock & Rothwell, 1997).
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The mechanisms underlying subthreshold superexcitability have been the subject of less attention. Barrett & Barrett (1982) showed that the passive cable properties of myelinated axons give rise to long-lasting, DAP-like afterpotentials after subthreshold current injection, so that a hyperpolarizing pulse can cause a mirror image of the DAP. In intracellular recordings from rat sciatic axons, Bowe et al. (1987) observed that subthreshold stimuli can cause an afterpotential and a ‘supernormal-like’ period of increased excitability. Other evidence suggests that passive electrotonic behaviour is unlikely to account fully for subthreshold superexcitability. Since the classic study of Katz (1937) on frog nerves, it has been known that as stimuli approach threshold they cause a local response, a non-linear increase and prolongation of membrane depolarization, above that accounted for by passive membrane properties but falling short of that required to generate a propagated action potential. Over a short timescale, the local response in human motor and sensory axons can be revealed by the changes in excitability produced by brief, near-threshold depolarizing currents (Bostock & Rothwell, 1997). In these ‘latent addition’ experiments, excitability changes were followed for only 0.5 ms, but the extra sodium currents generated as stimuli approach threshold would be expected to increase the subsequent afterpotentials and subthreshold superexcitability.
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In this study we have sought to clarify the extent and biophysical basis of subthreshold superexcitability in human motor axons, using an automated version of Bergmans' (1970) non-invasive method of tracking the threshold of single human motor axons in vivo. Excitability changes were tracked separately, depending on whether a conditioning stimulus excited or failed to excite an impulse. To separate the expected passive (electrotonic) and active (local response) components of subthreshold superexcitability, the former was assumed to be linearly related to conditioning stimulus amplitude, and opposite in sign for depolarizing and hyperpolarizing currents. It was found that near-threshold 1 ms depolarizing currents cause a long-lasting decrease in threshold, about one-third of the size of the superexcitability after an impulse, but no refractoriness or late subexcitability. The subthreshold superexcitability behaved as the sum of a passive component, proportional to stimulus charge, and a local response component, that appeared when stimuli exceeded 60% of threshold. The linear component could be eliminated by using triphasic conditioning stimuli with zero net charge, leaving the small active component apparently unchanged.
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Methods
Subjects and isolation of single human motor units
Motor units suitable for reliable single unit recording with surface electrodes were sought in the motor nerves of six healthy volunteers with no clinical or neurological evidence of a peripheral nerve disorder. Following recent experience (Hales et al. 2004), flexor carpi ulnaris was tested first, but additional motor units were subsequently isolated from abductor pollicis brevis, in both cases stimulating the ulnar and median nerves above or at the elbow. Because the units selected by surface stimulation had the lowest thresholds (or among the lowest) at the stimulation site, it was important to be sure that they were not selected because of abnormal membrane properties. Units were therefore only accepted for further study if they had recovery cycles to suprathreshold stimuli resembling those recorded by tracking compound motor action potentials (Kiernan et al. 1996, 2000).
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The studies, which were conducted in accordance with the Declaration of Helsinki, had the approval of The University of Sydney Human Research Ethics Committee, and all subjects provided written informed consent.
Stimulation and recording
The after-effects of stimulating single human motor axons were studied by delivering 1 ms constant-current stimuli over the ulnar nerve above the elbow or median nerve at the elbow, and recording all-or-none motor unit action potentials from flexor carpi ulnaris or abductor pollicis brevis, respectively. The nerve was stimulated through a non-polarizable stimulating electrode (Red Dot, 3M Canada Inc., London, Ontario, Canada) with the anode 4 cm proximal. The orientation of the electrodes to the nerve was adjusted to stimulate an axon innervating a large motor unit selectively, even when the stimulus was > 1.5 x threshold for that unit. This was possible in only 50% of experiments. Stimuli were generated by a purpose-built isolated current source with a maximal output of 50 mA, driven by a PC, running modified QTRAC software (Institute of Neurology). New facilities were incorporated in the software to track thresholds separately, depending on whether or not the unit was excited by the conditioning stimulus. Surface EMG recording electrodes were placed over the muscle, and the signal was amplified (200 Hz–2 kHz) and sampled at 10 kHz. The stimulus intensity and positions of the stimulating and recording electrodes were adjusted manually until an all-or-none single motor unit potential could be discriminated reliably. For all subjects skin temperature was monitored continuously and maintained at > 32°C using a thermostatically controlled pad.
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The following recording protocols were applied to each unit, where T is the unconditioned threshold current and C the conditioning stimulus current, and the stimuli were rectangular current pulses of 1 ms duration unless specified otherwise.
Recovery cycle to ‘suprathreshold’ conditioning stimuli, with C= 1.04T (i.e. 1.04 xT), determined by estimating thresholds at interstimulus intervals (ISIs) of 2, 2.5, 3.2, 4.5, 6.3, 7.9, 10, 13, 18, 24, 32, 42, 56, 75, 100, 130, 160 and 200 ms.
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Recovery cycle to ‘subthreshold’ depolarizing conditioning stimuli, with C= 0.96T (and the ISIs in (i)).
‘Passive’ recovery cycle to subthreshold hyperpolarizing conditioning stimuli, with C=–0.96T (ISIs as in (i)).
Relationship of subthreshold superexcitability to conditioning stimulus intensity, at a fixed ISI of 5 ms, determined by estimating thresholds while the strength of the conditioning stimulus was changed from –1.0T to +1.0T in 0.2T intervals, +0.9T, 0.94T, 0.96T, 0.98T.
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Relationship of suprathreshold superexcitability to conditioning stimulus amplitude, at the 5 ms ISI, for conditioning stimuli from 1.0T to 1.5T in 0.1T intervals, +1.02T, 1.06T.
The following additional recording protocols were used with units in abductor pollicis brevis of three subjects.
Relationship of components of superexcitability to conditioning stimulus charge, determined for the 5 ms ISI by varying the duration of the conditioning stimuli from 0.2 to 2 ms in 0.2 ms intervals, for subthreshold conditioning stimuli of strength 0.96T and –0.96T and suprathreshold conditioning stimuli of strength 1.04T.
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Relationship of subthreshold and suprathreshold superexcitability to conditioning stimulus amplitude, as in (iv) and (v) using triphasic stimuli with zero net charge.
The zero-charge conditioning and test stimuli used for protocol (vii) were generated as symmetrical cosine-windowed sine waves, of total width 2 ms and sine wave period 1 ms. The integral of the waveform generated by QTRAC (which was altered in steps of 0.1 ms duration, corresponding to the sampling interval, as illustrated in Fig. 6) was checked to be zero.
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Data from same motor unit as in Fig. 5. and dashed line: excitability changes evoked by 1 ms rectangular stimuli as a function of conditioning stimulus amplitude, with line fitted to data for conditioning stimuli from –100% to 60% of threshold (as in Fig. 4). , similar data obtained by making conditioning and test stimuli triphasic, so that the net charge transfer was zero.
Tracking suprathreshold and subthreshold excitability changes
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The QTRAC program allows one response to be measured and compared with a target response for each of up to 16 stimulus/response channels. Testing of responses to both conditioning and test stimuli in the same sweep was achieved by using the same response for multiple channels and analysing it in different ways. For this experiment the channels were split into groups of three, which received the same response to a single or double stimulus. In each group, the first channel (a) was always used, but the next channel (b) was skipped unless the response tested in ‘a’ was positive, and the third channel (c) was skipped unless there was no response in ‘a’. This conditional skipping enabled suprathreshold and subthreshold recovery cycles to be tracked separately when the first stimulus was close to threshold, despite the intrinsic variability of axonal thresholds (Hales et al. 2004). Figure 1 illustrates the response waveforms from one unit, testing suprathreshold superexcitability with conditioning stimuli of 1.04T (Fig. 1A) and subthreshold superexcitability with conditioning stimuli of 0.96T (Fig. 1B), and an interstimulus interval of 5 ms. The functions of the different channels were as follows.
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In this example, conditioning stimuli were set to 104% (A) and 96% (B) of the unconditioned threshold, and the interstimulus interval was 5 ms. The unit was considered excited when the response crossed the horizontal line. For the significance of channel numbers and waveform manipulation see text. Unconditioned thresholds were tracked in channel 1. Channels 2 and 4 were used for stimulus artefact suppression. Conditioned thresholds were tracked in channel 3b (when conditioning stimulus did excite, but the response to the conditioning stimulus had been subtracted) and channel 5c (when conditioning stimulus did not excite).
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Channel 1. This was used to determine the unconditioned threshold, T, and also to generate waveforms for subtraction from the double responses in channel 3. Stimulus: 1st only, strength determined by tracking an all-or-none response in 1a. Responses: 1a, response to 1st stimulus tested to track unconditioned threshold; 1b, generates running average of positive responses to the first stimulus (see 3b); 1c, generates running average of the no-responses to the first stimulus (see 5c).
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Channel 2. This channel was used solely to generate stimulus artefact waveforms for the second stimulus, for subtraction from the double responses when the second response overlapped the first. Stimulus: second only, amplitude set to 2/3 of the amplitude of the second stimulus on channel 3, to avoid generating a response. Responses: 2a, response to second stimulus tested after multiplication by 3/2, to check that it did not excite; 2b, this channel was nearly always skipped, and response not used; 2c, generates running average of stimulus artefact, after multiplication by 3/2, for subtraction from channel 3.
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Channel 3. Used to track changes in excitability after suprathreshold conditioning stimuli. Stimulus: first set to a specified fraction ( 1) of unconditioned threshold (i.e. first stimulus on channel 1); the second stimulus tracks conditioned threshold, determined by responses in 3b. Responses: 3a, response to the first stimulus tested after subtraction of the second stimulus artefact (2c); 3b, response to the second stimulus tested after subtraction of response to the first stimulus (1b); 3c, not used.
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Channel 4. Like channel 2, but with the second stimulus set to 2/3 of the second stimulus on channel 5.
Channel 5. Used to track changes in excitability after subthreshold conditioning stimuli. Stimulus: first set to specified fraction ( 1) of unconditioned threshold (i.e. first stimulus on channel 1); the second stimulus tracks conditioned threshold, determined by responses in 5c. Responses: 5a, response to the first stimulus tested after subtraction of the second stimulus artefact (4c); 5b, not used; 5c, response to the second stimulus tested after subtraction of negative response to the first stimulus (1c).
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Channels 2 and 4 were only required for protocols (i) to (iii) in which the second stimulus artefact sometimes affected recording of the response to the first stimulus. In protocols (vi) and (vii), when the duration of the conditioning stimulus was altered, channel 1 was used to generate the unconditioned threshold for a stimulus duration corresponding to the conditioning stimulus. An extra stimulus channel was required to track the unconditioned threshold to the 1 ms test stimulus.
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Results
Suprathreshold and subthreshold recovery cycles
Figure 2 shows suprathreshold recovery cycles for protocol (i) in Methods for six single units, each from a separate subject, for conditioning stimulus intensities that were just above threshold (1.04T). Each unit underwent phases of refractoriness, superexcitability and late subexcitability, and qualitatively these resembled the recovery cycles recorded for compound muscle action potentials (CMAPs), e.g. for median nerves at the wrist (Kiernan et al. 2000) or peroneal nerves at the knee or ankle (Kuwabara et al. 2000), which also used 1 ms stimuli. Quantitatively, the peak superexcitability and subexcitability measurements for each single unit were within the 95% confidence limits for CMAPs documented in the above studies, suggesting that the single units selected by surface stimulation were representative of human motor axons in general.
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All units exhibited superexcitability (range –18 to –32%) and late subexcitability (5–19%) within the normal range for recordings made using compound EMG potentials.
Figure 3A compares the mean excitability cycles for just-suprathreshold and just-subthreshold stimuli (protocols (i) and (ii)). As previously reported by Bowe et al. (1987) and Shefner et al. (1996), a just-subthreshold conditioning stimulus caused a ‘supernormal-like’ period of superexcitability. However, at intervals down to 2 ms there was no subthreshold analogue of refractoriness, and there was no subthreshold late subexcitability. Subthreshold superexcitability was maximal at an ISI of 5 ms, but did not change significantly between 2 ms and 6.3 ms. At 5 ms, the subthreshold superexcitability at –7.2 ± 2.4% (mean ±S.D.) was about one-third of the suprathreshold superexcitability of –22.4 ± 6.6%.
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A: , suprathreshold recovery cycle for 1 ms conditioning stimuli 104% of threshold (mean ±S.E.M., n= 6); , subthreshold recovery cycle for conditioning stimuli 96% of threshold. B, active and passive components of subthreshold recovery cycles: , subthreshold recovery cycle as in A; , excitability changes following hyperpolarizing current pulses, –96% of threshold; , sum of excitability changes evoked by equal and opposite conditioning pulses, indicating active component of subthreshold superexcitability, not accounted for by passive effects of conditioning currents.
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Active and passive components of subthreshold superexcitability
Figure 3B compares the subthreshold recovery cycle from Fig. 3A (protocol (ii)) with the recovery cycle following conditioning stimuli of the same amplitude but opposite polarity (protocol (iii)), and with their sum, which represents the non-linear or active component of subthreshold superexcitability. The depolarizing and hyperpolarizing recovery cycles were of similar shape, but the excitability changes for conditioning stimuli 96% of threshold (C= 0.96T) were on average –1.48 times those for C=–0.96T. With 1 ms conditioning stimuli, the active component of subthreshold superexcitability was therefore close to half the amplitude of the passive component, and at the 5 ms ISI contributed a threshold change of –2.6 ± 1.3%, about 12% of the suprathreshold superexcitability.
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This method of estimating the active and passive components assumes that the passive component is linear, supplemented by an active component when the conditioning stimulus approaches threshold and a local response is generated by activation of sodium channels. This assumption was tested for the 5 ms ISI by recording the threshold changes for conditioning stimuli which did not excite, in the range –100% to 100% of threshold (protocol (iv)). To test for an effect of conditioning stimulus strength on suprathreshold superexcitability, we also tracked the threshold changes for stimuli which did excite, in the range 100–150% of threshold (protocol (v)). The means (±S.E.M.) of these excitability changes are plotted in Fig. 4. There was no consistent effect of conditioning stimulus strength on suprathreshold superexcitability, but there was a good linear relationship for subthreshold stimuli in the range –80% to +60% of threshold. No meaning could be attached to the apparent deviation from linearity at –100%, which was not significant. From +80% to +100%, however, the excitability changes deviated systematically from the linear relationship, as shown on an expanded scale in the inset plot, presumably because of the activation of sodium channels. There was no further increase in excitability for subthreshold stimuli in the range 96% to 100% of threshold, indicating that the data in Fig. 3 for near-threshold stimuli would have been little different if we had used threshold stimuli which did and did not excite (but the experiments would have taken nearly twice as long). For stimuli equal to threshold (on the vertical dashed line), the threshold changes were –6.6 ± 2.9% (mean ±S.D.) if excitation did not o ccur, but –21.8 ± 5.6% if excitation did occur. As expected, these values correspond closely to those for 96% subthreshold and 104% suprathreshold conditioning stimuli in the previous section. Accordingly, the best estimates of just-subthreshold and just-suprathreshold superexcitability at 5 ms were obtained by averaging the values from Figs 3 and 4 for each subject, i.e. –6.9 ± 2.6% and –22.1 ± 6.0%, respectively.
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Data plotted are mean ±S.E.M. for the 6 units in Fig. 3. For conditioning stimuli < 60% of threshold, the excitability changes were directly proportional to current. From 80 to 100%, stimuli which did not excite produced a non-linear increase in excitability. Note that this decrease in threshold (–6.6%) corresponds to that in Fig. 3A and B (–7.2%; ). Conditioning stimuli 100–150% of threshold that did excite showed no significant dependence on amplitude. Note that the threshold change produced by these suprathreshold stimuli (–21.8%) is similar to the peak of superexcitability in Fig. 3A (–22.4%).
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Sub- and suprathreshold superexcitability and conditioning stimulus waveform
In the studies above, both the conditioning and test stimuli were rectangular pulses of 1 ms duration. The passive component of subthreshold superexcitability is linearly related to the strength of the conditioning stimulus, but it might also be expected to depend on the duration of the conditioning stimulus. Figure 5 illustrates one of three similar experiments in which the effects of this parameter were explored systematically for a conditioning–test interval of 5 ms. The duration of the conditioning stimulus was varied from 0.2 to 2 ms and excitability changes measured for conditioning stimuli of –0.96T, 0.96T (not exciting) and 1.04T (exciting), i.e. protocol (vi). Changes in threshold with membrane potential depend on stimulus duration, since the strength–duration time constant is potential dependent (Bostock et al. 1998). To avoid changes in superexcitability due to this phenomenon, the test stimulus duration was kept constant at 1 ms. An extra stimulus/response channel was therefore needed for this experiment, to track the unconditioned threshold to the stimuli of 1 ms duration, as well as the unconditioned threshold to the stimuli of variable duration.
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Data from single motor unit. A: , subthreshold superexcitability, evoked by conditioning stimuli 96% of threshold, increases with conditioning stimulus width (although conditioning stimulus amplitude decreases according to the strength–duration relationship); , similar increase in threshold change caused by equal hyperpolarizing pulses; , sums of the measured threshold changes, representing the non-linear component of subthreshold superexcitability; , suprathreshold superexcitability, measured at constant interstimulus interval; , suprathreshold superexcitability measured at interstimulus intervals adjusted manually to keep the interspike interval constant. B: , threshold changes evoked by hyperpolarizing current pulses ( in A), replotted as a function of conditioning stimulus charge (threshold current in mA x duration in ms). Continuous line is best least-squares fit passing through the origin. Dotted line is regression line for non-linear component of subthreshold superexcitability ( in A), which showed no significant relationship with conditioning stimulus charge.
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Figure 5A shows that the effects of subthreshold conditioning stimuli, whether 96% or –96% of threshold, increased approximately linearly with duration, even though the stimulus amplitudes fell, given that the unconditioned threshold current was much lower for 2 ms than for 0.2 ms stimuli. When the threshold changes to the hyperpolarizing conditioning stimuli, representing (minus) the passive component of subthreshold superexcitability, were plotted against absolute conditioning stimulus charge (filled circles in Fig. 5B), the relationship was well fitted by a straight line through the origin. The passive component of excitability change is therefore linearly related to conditioning stimulus charge, whether stimulus duration or stimulus amplitude is altered.
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In contrast, the active component of subthreshold superexcitability, indicated by the sums of the excitability changes to conditioning stimuli 96% and –96% of threshold (open squares in Fig. 5A; dotted line in Fig. 5B), appears to be independent of the duration of the conditioning stimulus. The active and passive components of subthreshold superexcitability are about the same for conditioning stimuli of 0.2 ms duration, and for shorter conditioning stimuli the active component is predicted to be more important.
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Also shown in Fig. 5A is the dependence of suprathreshold superexcitability on the duration of the conditioning stimulus (filled circles). There appears to be a progressive reduction in superexcitability with conditioning stimulus width, especially above 1.5 ms. However, this experiment was complicated by the fact that altering the conditioning stimulus width altered the interspike interval, because the delay from the onset of the conditioning stimulus to spike initiation depended on the conditioning stimulus width. To compensate for this, the experiment was repeated with the onset of the test stimulus adjusted manually to keep the interspike interval constant. When this was done there was no significant change in suprathreshold superexcitability with conditioning stimulus width (open circles and dotted lines in Fig. 5A).
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Figure 5B implies that if a just-subthreshold conditioning stimulus had zero charge, it should induce no passive component of subthreshold superexcitability, but a normal active component of about –2.9%. To test this we generated triphasic stimulus waveforms (conditioning and test) that delivered no net charge and repeated the experiment illustrated in Fig. 4 (protocol (vii)) in three subjects. Figure 6 shows that, as predicted, there was no trace of a passive threshold change, linearly related to conditioning stimulus amplitude. However, for conditioning stimuli greater than 60% of threshold there was a non-linear increase in excitability, similar to the active component obtained with the 1 ms rectangular stimuli. Qualitatively similar results were obtained with the two other subjects tested. Figure 6 also shows that the suprathreshold superexcitability induced by the zero-charge stimuli was similar to that obtained with 1 ms rectangular stimuli.
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Discussion
This study has been the first to use automatic threshold tracking to explore the effects of near-threshold stimuli on the excitability of human motor axons. It has also been the first to separate these effects into active and passive components. The main findings are that just-subthreshold stimuli of 1 ms duration generate a period of increased excitability analogous to superexcitability, but about one-third of the amplitude, without a preceding phase of refractoriness or a late phase of subexcitability. Most of the subthreshold superexcitability evoked by 1 ms rectangular pulses is passive or electrotonic in origin, directly proportional to the stimulus charge (though with conditioning stimuli of < 0.2 ms, the active component may exceed the passive electrotonic component). The active component is about 12% of the amplitude of the suprathreshold superexcitability.
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The use of threshold tracking has enabled single unit excitability changes to be documented more quantitatively than was possible in a previous study (Shefner et al. 1996) which used conditioning and test stimuli of equal intensity. This meant that the recovery cycle could only be measured in terms of the changes in probability of a threshold stimulus (i.e. with amplitude equal to the unconditioned threshold) exciting the unit. Thresholds of human motor axons normally vary about their mean value with a standard deviation of about 1.65% (Hales et al. 2004), so that although this method is sensitive to small changes in threshold, it cannot reliably distinguish between changes of more than a few per cent. That is presumably why Shefner et al. (1996) found little difference between suprathreshold and subthreshold superexcitability. The probability of excitation also depends critically on both the short-term variations in threshold, which vary between units, and the longer-term stability of the threshold. The method of threshold tracking used in the present study, in which thresholds with and without conditioning stimuli are tracked continuously, avoids these limitations.
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Accurate quantification of the threshold changes evoked by subthreshold and near-threshold conditioning stimuli allows the threshold changes to be resolved into passive and active components, assuming that the passive electrotonic component is linearly related to the strength of the conditioning stimulus. This assumption appears to be justified by the data in Fig. 4. There was a linear relationship for conditioning stimuli between –80% and 60% of threshold. As the conditioning stimulus approached threshold, the excitability change deviated more and more from the linear relationship. This was not because occasional conditioning stimuli evoked action potentials, since the program reliably excluded this possibility. A possibility raised by Shefner et al. (1996) was that near-threshold stimuli would have activated some sensory axons, which have a lower threshold than motor axons, and that action currents in the sensory fibres might then have ephaptically increased the excitability of the tested motor axon. This possibility was excluded by Bergmans (1970) who applied conditioning stimuli at another site and found that subthreshold stimuli, even though they excited sensory axons, did not evoke measurable superexcitability. It seems most likely therefore that the non-linear component of subthreshold superexcitability is due to activation of voltage-dependent ion channels in the stimulated axon, insufficient to trigger a propagated impulse, i.e. a local response.
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Subthreshold superexcitability and latent addition
Another manifestation of a local response in human motor axons is the asymmetry of the excitability changes induced by brief depolarizing and hyperpolarizing currents, recorded as ‘latent addition’ (Bostock & Rothwell, 1997). Current pulses 90% of threshold, and 0.06–0.2 ms wide, produced an increase in excitability that lasted considerably longer than the decrease in excitability following hyperpolarizing current pulses of the same amplitude, although these were only tracked for 0.5 ms in that study. Modelling of the excitability changes showed that the prolongation of the depolarization and increased excitability was caused by a small sodium current. The subthreshold superexcitability measurements can be regarded as an extreme type of latent addition measurement, in which the conditioning stimuli extend even closer to threshold, and the excitability changes are followed to much longer interstimulus intervals. In the latent addition study (Bostock & Rothwell, 1997), the modelled local responses were larger, in terms of prolongation of depolarization and total charge carried by the sodium current, for sensory than for motor axons. This was attributed to a greater activation of persistent sodium currents in the sensory axons. This suggests that the active component of subthreshold superexcitability may also be more prominent in sensory fibres. The type of sodium channel most likely to be involved is Nav1.6, since this is thought to be the dominant type at peripheral nodes of Ranvier, and is also known to generate persistent as well as transient sodium current (Baker, 2005).
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Subthreshold superexcitability and threshold electrotonus
The subthreshold superexcitability measurements can also be regarded as a type of threshold electrotonus. Threshold electrotonus is normally measured as the excitability changes during and after a subthreshold conditioning current lasting 100 ms or more (e.g. Bostock et al. 1998), whereas in this study the subthreshold recovery cycles were measured following stimuli of 0.2 to 2 ms duration. In the experiment in Fig. 5, subthreshold superexcitability increased linearly with the duration of the conditioning stimulus, prompting the question of how far this linear relationship holds. Studies of threshold electrotonus show that if a subthreshold conditioning stimulus lasts longer than about 20 ms, the threshold reaches a minimum and then increases again, due to accommodation caused by the activation of slow potassium channels (Bostock & Baker, 1988). Similarly, the residual drop in threshold left after the end of the subthreshold conditioning stimulus, i.e. the subthreshold superexcitability, must reach a limit and decrease when the stimulus duration exceeds about 20 ms. The studies of threshold electrotonus show that when the conditioning stimuli are very long, the activation of slow potassium channels results in an after-hyperpolarization, the subthreshold analogue of late subexcitability. It follows that the lack of appreciable subthreshold late subexcitability in this study and that of Shefner et al. (1996) is not because an action potential is absolutely necessary to activate it, but rather because subthreshold depolarization activates it relatively slowly, and it would take a near-threshold stimulus lasting many milliseconds to evoke substantial subthreshold late subexcitability.
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Zero-charge stimuli
The experiments with zero-charge stimuli have confirmed the dependence of the passive component of subthreshold superexcitability on stimulus charge, and provided a convenient means to minimize this component. These observations are relevant to studies of nerves and central fibre tracts with transcranial magnetic stimulation (TMS), in which a monophasic pulse of current in the magnetic coil generates a biphasic electric field pulse, proportional to the time differential of the magnetic field (Mills, 1999), and therefore in principle a zero net charge transfer across the axon. Subthreshold superexcitability in TMS experiments is therefore expected to be restricted to the active component caused by a local response, which in the motor axons studied was limited to an average of 2.6%. However, the neural components activated in most TMS experiments have not been clearly identified, and their excitability properties are mostly unknown, so there is a possibility that subthreshold superexcitability may be higher than in peripheral motor axons.
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It is worth noting here that even a 2.6% change in threshold can have appreciable effects, depending on the stimulus–response function. For human median nerves stimulated at the wrist, the results of Kiernan et al. (2000) showed an almost linear relationship between the log of the stimulus current and the log of CMAP amplitude, over the range 0.1–2 mV, such that a 2.6% fall in threshold would correspond to an increase in response to a fixed stimulus of more than 30%.
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Suprathreshold superexcitability and conditioning stimulus parameters
One reason for exploring subthreshold superexcitability was a concern that factors such as conditioning stimulus amplitude and duration, which determine the passive component of subthreshold superexcitability, might also affect (suprathreshold) superexcitability, which is being studied increasingly in patients with peripheral nerve disease as part of a test of multiple nerve excitability parameters (Kiernan et al. 2000; Lin et al. 2005). The results in Figs 4 and 5 show that neither conditioning stimulus amplitude (in the range 100–150% of threshold) nor conditioning stimulus duration (in the range 0.2–2 ms) has any appreciable effect on superexcitability, except in so far as they affect interspike intervals.
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In conclusion, subthreshold superexcitability is a type of stimulus-dependent excitability change that is more closely related to latent addition and to threshold electrotonus than to the suprathreshold recovery cycle. The prolonged increase in excitability following near-threshold stimuli is caused by a depolarizing charge stored on the capacitance of the internodal axolemma. The depolarizing charge has two components, a passive component directly proportional to the stimulus charge, and an active component caused by the activation of sodium currents during the local response. With 1 ms stimuli the passive component dominates, by about 2: 1, but with zero-charge stimuli only the local response contributes.
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