Velocity recovery cycles of C fibres innervating human skin

Authors


Abstract

Velocity changes following single and double conditioning impulses were studied by microneurography in single human C fibres to provide information about axonal membrane properties. C units were identified as mechano-responsive (n= 19) or mechano-insensitive (12) nociceptors, cold-sensitive (8) or sympathetic fibres (9), and excited by single, double and triple electrical stimuli to the skin at mean rates of 0.25–2 Hz. The interval between single or paired (20 ms apart) conditioning stimuli and test stimulus was then varied between 500 and 2 ms, and recovery curves of velocity change against inter-spike interval constructed, allowing for changes in these variables with distance. All fibres exhibited an initial (4–24 ms) relative refractory phase, and a long-lasting (>500 ms) ‘H2’ phase of reduced velocity, attributed to activation of Na+/K+-ATPase. Mechano-responsive nociceptors exhibited an intermediate phase of either supernormality or subnormality, depending on stimulation rate. Mechano-insensitive nociceptors behaved similarly, but all were supernormal at 1 Hz. Sympathetic units exhibited only a long-lasting supernormality, while cold fibres exhibited a briefer supernormal and a late subnormal phase (H1), similar to A fibres. A pre-conditioning impulse doubled H2 and increased H1, but did not augment supernormality or the subnormality of similar time course. Like A fibre supernormality, these phenomena were explained by a passive cable model, so that they provide an estimate of membrane time constant. Nociceptor membrane time constants (median 110 ms, n= 17) were rather insensitive to membrane potential, indicating few active voltage-dependent potassium channels, whereas sympathetic time constants were longer and reduced by activity-dependent hyperpolarisation.

Recent studies on human cutaneous C fibres by microneurography have shown that different functional classes of C fibre (e.g. polymodal nociceptors, mechano-insensitive nociceptors, cold fibres, sympathetic fibres) exhibit different profiles of activity-dependent velocity changes when stimulated at different rates (Serra et al. 1999; Weidner et al. 1999). These differences suggest that different specific membrane properties are responsible, probably including differences in the electrogenic Na+ pump. To obtain more information about the different membrane properties, we have explored the short-lived effects (up to 500 ms) of single and double conditioning impulses on conduction velocity. The effects of single conditioning stimuli were recently investigated by Weidner et al. (2000). They stimulated single C units regularly at 0.25 Hz and measured the effects (up to 2000 ms) of additional, interpolated impulses on the velocity of the next impulse. They found that 16 mechano-insensitive units exhibited a supernormal period of increased velocity, which peaked at an interstimulus interval of 69 ± 10 ms, whereas 20 mechano-sensitive units exhibited only subnormality, with a time course that resembled a mirror-image of the supernormality of the mechano-insensitive units. However, all units conducted more slowly when preceded by an extra stimulus at intervals of 1000 ms or more, and this long-lasting slowing was linearly related to the number of interpolated impulses (1, 2 or 4). The long-lasting slowing is clearly analogous to the post-tetanic depression and hyperpolarisation (H2) of myelinated axons, and presumably reflects membrane hyperpolarisation by the electrogenic Na+ pump (Rang & Ritchie, 1968). However, the mechanism of the supernormality was not specifically addressed by Weidner et al. (2000).

Three different mechanisms have been proposed for supernormal conduction, or for the associated negative (depolarising) afterpotential, in unmyelinated axons. First, Frankenhaeuser & Hodgkin (1956) attributed the negative afterpotential in the squid giant axon to a transient increase in the K+ concentration in the immediate vicinity of the axon following activity. This explanation was applied to mammalian C fibres by Greengard & Straub (1958) and many subsequent studies have concentrated on the relationship between afterpotentials or supernormality and extracellular K+ (Zucker, 1974; Kocsis et al. 1983; Shin & Raymond, 1991). However, Bliss & Rosenberg (1979) argued against this mechanism for the supernormality in tortoise olfactory nerve, and suggested that it might be due to a spike-dependent increase in Na+ channel conductance. Finally, Barrett & Barrett (1982). who showed that the depolarising afterpotential in amphibian A fibres is primarily a passive electrical phenomenon, suggested that the depolarising afterpotential in unmyelinated axons might have a similar origin. This explanation, which was recently supported by the microneurography experiments of Weidner et al. (2002). has the interesting implication that the time course of the afterpotential (and therefore of supernormality) should reflect the passive membrane time constant of the axons. To distinguish between these three proposed mechanisms, we have tested the effects of a second conditioning impulse on C fibre recovery cycles. If the velocity changes are due to ion accumulation, they should roughly double after a second impulse, whereas if they are passive, as in myelinated fibres, then a second conditioning impulse should have only a minimal effect on the recovery cycle. Slow changes in channel properties might be expected to result in an intermediate effect of a second conditioning impulse.

A complication that occurs when measuring the velocity recovery cycle of a C fibre, especially over the long distances sometimes achieved in humans, is that the time interval between the conditioning and test impulses is not constant but changes as the second impulse speeds up or slows down. These changes in the conditioning-test interval can be substantial, and cause serious distortion of the shape of the recovery cycle with conduction distance, especially when a second conditioning stimulus is added. The distortion is greater the longer the conduction distance, and Weidner et al. (2002) found that when recording over distances of 300–400 mm, the amount of speeding up recorded during the supernormal period is often limited by the second impulse catching up the first and reaching the ‘entrainment interval’, of about 10 ms, when the velocities become the same. We have minimised this problem in two ways: first by recording over shorter distances (mean 108 mm) to reduce the absolute latency changes, and secondly by recording the recovery cycles with sufficient time resolution that we were able to make corrections for the latency changes and infer the underlying relationship between velocity and interspike interval. In this study we therefore recorded recovery cycles with as many as 48 interstimulus intervals, from 2 to 500 ms, and with both a single conditioning stimulus and with two conditioning stimuli 20 ms apart. Our results provide the first data on recovery cycles of cold-specific and sympathetic C fibres, and provide strong support for Barrett & Barrett's (1982) hypothesis of the passive origin of supernormality in C fibres.

Methods

Subjects

Fifteen healthy adult volunteers participated in 27 microneurographic recording sessions. There were nine males and six females, with ages ranging from 19 to 47 years (mean 27.8 years). The study had the approval of the local ethics committee and conformed to the Declaration of Helsinki. All subjects gave their informed, written consent.

Microneurographic recordings

Microneurography was used to record action potentials of human C fibres from cutaneous nerve fascicles of the superficial peroneal nerve at the ankle. The subjects sat relaxed with the leg or arm firmly supported in a padded platform. The technique of microneurography has been described in detail by Vallbo & Hagbarth (1968). Intraneural recordings were obtained using a 0.2 mm diameter lacquer-insulated tungsten microelectrode (MNG active/1 MΩ FHC Inc., Bowdoinham, ME, USA), which was inserted percutaneously into a sensory nerve. A subcutaneous reference electrode was inserted 1–2 cm outside the nerve trunk. The neural signals were amplified by a commercial differential amplifier (FHC Inc., 3+ Cell Isolated Microamplifier) and filtered with an adjustable analogue filter (band-pass 100–2000 Hz). Line interference was removed with an on-line noise eliminator (Hum Bug, Quest Scientific, North Vancouver, Canada). Signals were displayed on a Tektronix 5113a oscilloscope and digitised by a personal computer with a Data Translation DT2812 A/D board at a sampling rate of 10 kHz. Digitised signals were stored on the hard drive of the personal computer as raw data for off-line analysis. Digital filtering (band pass 300–2000 Hz) and clamping of the baseline were performed both on-line and during off-line analysis for a better visualisation of the action potentials. Temperature of the skin was measured with a thermocouple placed on the skin adjacent to the receptive fields of the units under study. Skin temperature was maintained above 30 °C with an infrared lamp.

Protocol of electrical stimulation and fibre classification

Search for the electrical receptive fields of C fibres was conducted in areas of skin where intraneural electric microstimulation evoked painful sensations at near threshold levels (Torebjörk & Ochoa, 1990). This area of the skin was stimulated electrically with a pair of needle electrodes resting on the surface of the skin, using rectangular pulses of 0.25–0.3 ms duration (Grass S48, stimulus isolation unit SIU 5) at a rate of 0.25 Hz. Only fibres with latencies compatible with conduction velocities in the C fibre range (<2 ms−1) were studied. When time-locked responses with such latencies were recorded at 0.25 Hz baseline stimulation, a sequence of 3 min pause followed by 6 min baseline and 3 min 2 Hz train was given to enable the types of fibre present to be categorised (Serra et al. 1999). Units which slowed progressively at 2 Hz were classified as Type 1 (nociceptors) and further subdivided according to the effects of the 3 min pause into Type 1A units (mechano-responsive), which were unaffected by the pause, and Type 1B units (mechano-insensitive), which slowed appreciably (by more than 1.5 %) at 0.25 Hz following the pause. This ‘pause protocol’ has been found to unambiguously separate mechano-responsive and mechano-insensitive Type 1 units (J. Serra, M. Campero, H. Bostock & J. Ochoa, unpublished observations) in accordance with the findings of Weidner et al. (1999). Units which reached a plateau of slowing at ≈5 % within 1 min were classified as Type 2 (cold units) (Campero et al. 2001). In many cases, the functional classification of sensory fibres was later confirmed by natural stimulation of their receptors, but typing by repetitive stimulation was considered more reliable and performed for every unit before measurement of recovery cycles. Sympathetic units were recognised by their spontaneous activity, which was not directly related to skin temperature, but responded to sympathetic manoeuvres (Delius et al. 1972), and which was blocked by injecting lidocaine (lignocaine 2 %, ≈4 ml) close to the nerve, a few centimetres proximal to the recording site. Sympathetic units, like cold units, reached a plateau of slowing within a minute of stimulation at 2 Hz, but the time course was distinct from that of cold fibres, enabling a separate classification as Type 4 (M. Campero, J. Serra, H. Bostock & J. Ochoa, unpublished observations): the plateau was reached more quickly, and was often followed by a slight acceleration, and there were clear fast and slow phases of recovery at the end of the tetanus. NB, to improve the readability of this manuscript, we have used convenient shorthand names for the four types of C fibre identified: CMR for Type 1A (high threshold mechano-responsive afferents), CMI for Type 1B (mechanically insensitive afferents), Cold for Type 2 and Sympathetic for Type 4. Heat-sensitivity was not tested, and is not to our knowledge revealed by the activity-dependent slowing, so that the CMR group may have included CMHi (i.e. mechano-sensitive and heat-insensitive) as well as the more common polymodal CMH units, and the CMI group may have included CMiH as well as CMiHi units.

Measurement of recovery cycles

Recovery cycles were recorded with a Qtrac protocol (RC500N.QRP) which recorded three separate stimulus conditions (1: test stimulus alone, 2: conditioning + test stimuli, and 3: preconditioning + conditioning + test stimuli) on channels 1–3. In each 805 ms sweep, the test stimulus was delivered at tT= 550 ms; on channels 2 and 3 the conditioning stimulus was delivered at tC=tT− D ms, where the conditioning-test delay (D) varied between 500 and 2 ms; and on channel 3 a pre-conditioning stimulus was delivered at tP=tC− 20 ms =tT− D − 20 ms. The primary measurements made were of the latencies to the responses to the three test stimuli, which were measured from the start of the stimulus to the peak of the filtered and inverted neurogram (Fig. 1A): L0 was the latency to the test stimulus alone, and L1 and L2 the latencies of the test stimuli after one and two conditioning stimuli resepectively. To ensure that these latencies were always measured to the test response (even though, as in Fig. 2, the response to the conditioning stimulus could occur at about the same latency as that of the unconditioned test response), latency tracking was used (Serra et al. 1999): latency was measured within a small time window (adjusted between 1and 20 ms), which was automatically centred on the response after each recording, with the centring performed separately for the three stimulus conditions (Fig. 1A).

Figure 1.

Latency tracking of recovery cycles with one and two conditioning impulses

A, filtered and inverted action potential recordings from a single cold-specific C fibre. Top traces, responses recorded on Qtrac channel 1, to test stimulus alone. Middle traces, responses on channel 2 to test stimulus preceded by conditioning stimulus. Bottom traces, responses on channel 3 to test stimulus preceded by conditioning and pre-conditioning stimuli, 20 ms apart. Left traces recorded at ≈0.5 min elapsed time (arrowed in B), with interstimulus interval 500 ms, showing small increase in latency for each conditioning stimulus. Right traces recorded at ≈3.5 min elapsed time, with interstimulus interval 50 ms, showing reduced latency with single conditioning stimulus. Inset, schematic indication of timing of test (T), conditioning (C) and pre-conditioning (P) stimuli. Horizontal lines are the moving ‘windows’ in which latencies are measured, which are automatically centred on the action potentials. B, latencies to test stimuli, plotted as function of elapsed time during the recording, with first minute expanded on left to show that adding conditioning stimuli while keeping mean stimulation rate constant does not affect baseline latency. L0, L1 and L2, latencies to responses in top, middle and bottom traces in A, i.e. latencies to responses to test stimuli preceded by zero, one and two conditioning stimuli respectively.

Figure 2.

Recording of latency recovery cycle of sympathetic unit with pronounced supernormal period

Unit stimulated at mean rate of 1 Hz, with interstimulus interval of 1 s after single stimulus, 2 s after double stimulus and 3 s after triple stimulus. A, top, latencies to responses to unconditioned test stimulus (L0), to responses to test stimulus after single conditioning stimulus (L1), and to responses to test stimulus after conditioning and pre-conditioning stimuli (L2). Below, delays between (last) conditioning stimulus and test stimulus. B, latencies L0 and L1 as in A, and the latency (from the time of application of the test stimulus) to the response to the single conditioning impulse C1. C, latencies L0 and L2 as in A, and the latencies (from the test stimulus) to the responses to the conditioning impulses C2 and the pre-conditioning stimulus P2. NB, in A, the pre-conditioning impulse appears to accelerate the test impulse at short intervals but this is due to the effect of the pre-conditioning impulse in accelerating the conditioning impulse. The latency difference between time of arrival of the conditioning impulse and test impulse is always greater for two conditioning impulses (L2 − C2 in C) than for one (L1 − C1 in B).

A typical recovery cycle recording sequence with the RC500N protocol is illustrated in Fig. 1. A Type 2 (cold) unit was stimulated at 1 Hz on channel 1 until the latency to the unconditioned test stimulus (L0) stabilised. The first arrow in Fig. 1B (left) indicates the elapsed time at which the top trace in Fig. 1A was recorded. At this point, the single stimulus on channel 1 was rotated with double and triple stimuli on channels 2 and 3 respectively, and the first responses to the test stimuli on these channels are also illustrated in Fig. 1A (left). To keep the mean stimulation rate (and therefore the level of activity-dependent hyperpolarisation) constant, the double stimulus was followed by an interval of 2 s, and the triple stimulus by an interval of 3 s. By following each multiple stimulus with an appropriately longer interval (i.e. when stimulating at a mean rate of R Hz, a sweep containing n stimuli was followed by an interval of n/R s) the latency of the single stimulus was virtually unaffected (Fig. 1B), and the latencies were independent of the order in which the stimuli were delivered. (This invariance of L0 time course on introducing or removing conditioning stimuli, provided the mean stimulation rate was maintained, was a constant finding, and is also illustrated for 1A fibres at 0.5 m in Fig. 6, and for the 1B fibre in Fig. 4 at 19 and 29 m.) For a few recovery cycle recordings (7/85), a mean stimulation rate of 2 Hz was achieved by adding an extra stimulus at the end of the sweep (801 ms) on channel 1, omitting channel 3, and alternating channels 1 and 2 at intervals of 1 s.

Figure 6.

Relationship between supernormality and activity-dependent slowing

Supernormality was estimated continuously by alternating single and double pulses, with interstimulus interval of 50 ms. Mean baseline stimulation rate 0.25 Hz. Open bars indicate mean stimulation rate of 2 Hz. A and B, two mechanically responsive units recorded at the same time. Upper, L0 is latency unconditioned response; L1 is latency after single conditioning stimulus at interval of 50 ms; C1 is latency (relative to test stimulus) of response to conditioning stimulus. The interval between C1 and L1 never approaches the entrainment interval (≈10 ms), so supernormality was not limited by entrainment. Lower, latency change, calculated as (L1 − L0)/L0 × 100, where L0 at the time of the conditioned response was estimated by linear interpolation. C, relationship between percentage latency change (i.e. subnormality or supernormality), as in A (1) and B (2), and slowing of unconditioned test impulse. At the start of the train there is a linear relationship between supernormality and activity-dependent slowing, but this breaks down, especially for unit 2, for which supernormality reaches a maximum of ≈4 %.

Figure 4.

Recording effects of different stimulation rates on recovery cycles of CMR and CMI units

Modified raster plot of CMR (shorter latency) and CMI (longer latency) units, showing effects of 3 min pause in baseline stimulation at 0.25 Hz, 2 Hz tetanus, and recording of recovery cycles to single conditioning stimuli (open circles) at mean stimulation rates of 0.5, 1 and 2 Hz. The CMI was identified by the slowing at 0.25 Hz after the pause, and by the slower recovery after 2 Hz stimulation. The six corrected recovery cycles are plotted in Fig. 5A. Delay is the interval between conditioning and test stimuli. NB, starting at 19 min and in between recovery cycle recordings, a conditioning stimulus was delivered 50 ms before the test stimulus. This shows the graded transition from subnormality to supernormality as the fibres hyperpolarised (cf. Fig. 6).

When it was clear that the latencies on all three channels (i.e. L0, L1 and L2) were being recorded satisfactorily, the conditioning- test delay (D) was stepped through a sequence of 48 pre-determined values, in an approximately geometric series from 500 to 2 ms (or until the test stimuli failed to excite), as indicated in Fig. 1C (right), and the latencies of the test responses tracked automatically by computer (Fig. 1B, right). Cold fibres exhibit both late subnormality and supernormality, similar to large myelinated fibres, and the responses in Fig. 1A (right) correspond to a delay of 50 ms, when L0 and L2 were almost the same.

Recovery cycle correction for changes in interspike interval with distance

For a latency recovery cycle to be independent of conduction distance, it should describe how the velocity of an action potential depends on the interspike interval, whereas what is directly measured is how the latency depends on interstimulus interval. That these relationships can differ markedly is illustrated by the recordings in Fig. 2 and Fig. 3, from a sympathetic unit with pronounced supernormality. In Fig. 2A, it can be seen that the latency with two conditioning impulses (L2) becomes shorter than the latency with one conditioning impulse (L1) when the interstimulus intervals are short. The pre-conditioning impulse appears to accelerate the test impulse at short intervals, but this is misleading. In Fig. 2B and C are plotted the times of arrival of the conditioning as well as the test impulses for one and two conditioning stimuli. Although the conditioning stimulus in Fig. 2C is delivered 20 ms after the pre-conditioning stimulus, the corresponding impulses arrive only 10 ms apart. The latency difference between the time of arrival of the conditioning impulse and the test impulse is in fact always greater with a pre-conditioning impulse (L2 − C2 in Fig. 2C) than without (L1 − C1 in Fig. 2B). To adequately describe the effects of the conditioning and pre-conditioning impulses on conduction velocity, it is clearly essential to take into account the changes in interspike interval occurring between the stimulating and recording sites.

Figure 3.

Recovery cycle correction, allowing for changes in interspike intervals during conduction along the nerve

A, uncorrected recovery cycles, expressed as percentage increase in latency. Circles calculated from data points in Fig. 2 as (L1 − L0)/L0 × 100 (thick-walled circles) and (L2 − L0)/L0 × 100 (thin-walled circles). Lines were calculated from corrected recovery cycles below by simulation. B, corrected recovery cycles, with instantaneous change in velocity expressed as a function of interspike interval. (For correction method see text.) Thick lines, single conditioning impulse; thin lines, two conditioning impulses. C, simulation of relative latency changes along the length of the axon, for interstimulus interval of 8 ms (arrowed in A), to show how pre-conditioning stimulus can appear to accelerate test impulse. Latencies expressed relative to baseline latency of first impulse, assumed to conduct at constant velocity. Circles, latencies inferred from measurements (see text for explanation of x, y and z). Lines, latencies calculated from corrected recovery cycles in B by integration of slowing over distance. Upper, single conditioning impulse causes only slight relative slowing of test impulse at interval of 8 ms. Lower, pre-conditioning impulse accelerates second conditioning impulse, starting 20 ms later, towards the entrainment interval of ≈9 ms. This in turn accelerates the test impulse as interspike interval increases above its initial value of 8 ms.

Recovery cycle correction is illustrated in Fig. 3 for the same unit as in Fig. 2. Figure 3A shows the percentage increases in latency of the test stimulus when preceded by one or two conditioning stimuli, as a function of interstimulus interval. The circles are the experimental points, replotted from Fig. 2A. To estimate the continuous function, describing how the velocity changes as a function of interspike interval, for a single conditioning impulse, the following procedure was adopted. The interspike interval at the stimulation site is assumed to correspond to the interstimulus interval D (i.e. delay in Fig. 2A), while the interspike interval at the recording site is given by L1 − C1 (Fig. 2B). But C1 ≈ L0 − D, since C1 and L0 both depend on the velocity of an unconditioned action potential. (However, C1 is not identical with L0 − D, since the past history of the axon is not identical for the two conditions. The difference δ= C1 − L0 + D was measured for the example of Fig. 2 and Fig. 3 and varied from 1.5 ms at long delays to 0.5 ms for D < 150 ms.) The percentage slowing measured over the whole distance is the percentage increase in latency, (L1 − L0)/L0 × 100. This percentage slowing must correspond to an interspike interval (ISI) lying somewhere between that at the stimulation site (D) and that at the recording site (L1 − C1, or L1 − L0 + D −δ). We may therefore write that ISI = Df+ (D + L1 − L0 −δ)(1 −f), where the fraction f lies between 0 and 1, or ISI = D − (L1 − L0 −δ)f. The simplifying assumptions were then made that f would be the same for all ISI in a recording, and that δ could be neglected.

The best estimate for f was then obtained in the following way: for each estimate of f, a relationship of percentage slowing vs. ISI, as in Fig. 3B (thick line) was derived by calculating ISI = D − (L1 − L0)f for the experimental data points in Fig. 3A (thick-walled circles) and interpolating straight lines between these points. From this hypothetical relationship, the experimental data points were then reconstructed by simulating the movement of the conditioning and test impulses along the axon for each value of interstimulus interval D, adjusting the effect of the conditioning impulse on the test impulse for each small time step according to the instantaneous interspike interval. The value of f was then optimised to give the best least squares fit between the original data points and the results of the simulation (i.e. between the thick-walled circles and the thick continuous line in Fig. 3A). In this example, a value for f of 0.723 reduced the root mean square (RMS) discrepancy between original and reconstructed data points to 0.14 %. Without correction (i.e. with f= 0), the RMS discrepancy would have been 7.6 %.

To estimate the effect of the pre-conditioning stimulus, it was assumed that it caused an additional slowing s, over and above that caused by the first conditioning stimulus, and s was assumed to be constant for a given interstimulus interval. This assumption allowed the trajectories of all three impulses to be simulated for any interstimulus interval, and s to be optimised by minimising the sums of squares of the differences between the experimental and simulated recovery cycles, as for f. The thin line in Fig. 3B is the estimated continuous function for two conditioning stimuli, and the thin line in Fig. 3A shows how this function accounts for the L2 data points. The simulations are illustrated by the relative latency plots in Fig. 3C, for an interstimulus interval of 8 ms (arrowed in Fig. 3A). At the top, the single conditioning impulse has little effect on the velocity of the test impulse, because the 8 ms interval is close to entrainment interval, when relative slowing due to refractoriness gives way to relative speeding up in the supernormal period. At the bottom, however, the pre-conditioning impulse accelerates the conditioning impulse so much that the test impulse is now also accelerated. The simulated curves end up very close to the centres of the circles, which are calculated directly from the experimentally recorded relative latencies as follows: x= L1 − L0 + D, z= L1 − L0 + D when D = 20 ms, and y=z+ L2 − L0 + D.

The accuracy of the recovery cycle correction was attested by the satisfactory fits obtained between the simulations and the experimental data points, as illustrated in Fig. 3A. This was an extreme case, with the most pronounced apparent crossover of the latencies after single and double conditioning stimuli, and the greatest difference between the uncorrected recovery cycles (as in Fig. 3A) and the corrected ones (as in Fig. 3B). The same correction procedure was used to convert all the latency measurements in this paper to percentage slowing as a function of interspike interval. Values of f fell between 0.5 and 0.75 (mean 0.57). In all cases the correction produced a satisfactory correspondence between the uncorrected values for percentage slowing and those reconstructed by simulation from the corrected recovery cycles (mean RMS discrepancy 0.034 %).

Statistics

Distributions of refractory periods and time constants were normalised by logarithmic conversion before applying statistics, so that geometric means are given in place of means, and comparisons between different functional classes of C fibre were made by t-tests of differences in means of logarithms of the variables.

Results

Eighty-five recovery cycles were measured from recordings of 48 units from 15 subjects. Recordings were made at different mean stimulation rates (0.25, 0.5, 1 and 2 Hz) and from different types of C fibre (41 CMR, 22 CMI, 11 cold and 12 sympathetic recovery cycles), and with single and double conditioning pulses.

General form of the recovery cycles and relationship to stimulation frequency and fibre function

The dependence of recovery cycles on stimulation rate and on functional category of nerve fibre are illustrated in Fig. 4 and Fig. 5. Figure 4 shows a single experiment in which recovery cycles were measured simultaneously for a CMR (Type 1A) and a CMI (Type 1B) at mean stimulation rates of 0.5, 1 and 2 Hz, after the fibres had been categorised by the standard protocol involving a 3 min pause in stimulation followed after 6 min of stimulation at the baseline rate of 0.25 Hz by stimulation at 2 Hz for 3 min. In Fig. 5A, corrected recovery cycles are plotted for these two units and a cold and a sympathetic unit. The greater effect of stimulation rate on the recovery cycles of the nociceptor than on cold and sympathetic units is related to the greater activity-dependent slowing and hyperpolarisation in nociceptor fibres (Serra et al. 1999; M. Campero, J. Serra, H. Bostock & J. Ochoa, unpublished observations). At the same 1 Hz mean stimulation rate, CMI and sympathetic units consistently exhibited supernormality, as did most cold fibres, whereas CMR units were almost as likely to show long-lasting subexcitability as superexcitability, and the mean latency changes were small. For all fibre types, supernormality increased with activity-dependent hyperpolarisation, or subnormality was replaced by supernormality. In cold fibres, supernormality was shorter-lived than in the other fibre types, and gave way to a late subnormality, analogous to H1 in A fibres, which is attributed to a slow K+ current (Bergmans, 1970; Baker et al. 1987; Taylor et al. 1992). In cold and CMR fibres the velocity changes stabilised by about 300 ms, leaving a long-lasting slowing, analogous to H2 in A fibres, which is attributed to hyperpolarisation by Na+/K+-ATPase.

Figure 5.

Recovery cycle dependence on stimulation rate and fibre function

A, examples of corrected recovery cycles for four different types of C fibre recorded at 0.5, 1 and 2 Hz. The CMR and CMI units are those illustrated in Fig. 4. B, superimposed corrected recovery cycles for all units recorded at 1 Hz of the four types illustrated in A. The greater effect of stimulation rate on the recovery cycles of CMR and CMI than on cold and sympathetic units is related to the greater effect of stimulation rate on the unconditioned conduction velocity and membrane potential of the nociceptor fibres.

It might be objected that we have described recovery cycles of nociceptors stimulated at rates as high as 2 Hz, when we have previously noted that these fibres are characterised by progressive slowing during repetitive stimulation at this frequency, so that a steady state may never be reached. Thus in Fig. 4, although the CMR unit had more or less reached a plateau at the end of 5 min at 2 Hz, the latency of the CMI unit was still increasing. To test whether supernormality increases indefinitely with latency, in some experiments we alternated test stimuli with and without a conditioning stimulus at an interval of 50 ms, before, during and after repetitive stimulation at 2 Hz (Fig. 6). We found that supernormality did not increase indefinitely, but approached a limit (Fig. 6A) or even started to decline (Fig. 6B), while latency continued to increase. When recording over longer distances, Weidner et al. (2002) found that as stimulation rate was increased, supernormality increased linearly with ‘pre-existing slowing’ (i.e. linearly with the unconditioned latency L0) until the conditioning-test interspike interval (L1 − C1) approached the entrainment interval of about 10 ms, when supernormality became constant. For the units in Fig. 6, however, which had a conduction distance of 135 mm, the supernormality diverged from a linear relationship with the unconditioned slowing (Fig. 6C) even though L1 − C1 was always much longer than the entrainment interval. An actual decline in supernormality, while unconditioned latency continued to increase, as in Fig. 6B, was seen in four out of twelve CMR and one out of five CMI units during 3 min 2 Hz trains.

Effects of second conditioning impulse

The effect of a second conditioning impulse (i.e. the pre-conditioning impulse, excited 20 ms before the conditioning impulse) was tested to shed light on the mechanisms of the latency changes, on the basis that latency changes due to ion accumulation (like H2 in A fibres) should approximately double for a second impulse, whereas those due to passive cable responses to the action potential (like supernormality in A fibres) are almost unchanged by a second conditioning impulse. Latency changes due to slow K+ channels (like H1 in A fibres) are also increased, but by less than a factor of two, since they are activated too slowly to reach a steady state during a single action potential. The results in Fig. 7 are clear-cut. For the CMR fibres, whether stimulated at 0.5 or 1 Hz, the effect of the pre-conditioning impulse is to cause an additional slowing of approximately 0.7 % at all interspike intervals, an amount indistinguishable from the 0.68 ± 0.12 % (mean ±s.d., n= 15) caused by a single impulse at interspike intervals above 200 ms. For these fibres the effect of a second conditioning impulse seems to be almost entirely accounted for by ion accumulation, presumably the increase in intracellular Na+ that activates Na+/K+-ATPase. For the seven sympathetic units, the supernormality is evidently not increased by a second conditioning impulse. Instead there is again a small relative slowing at all intervals, consistent with increased activation of Na+/K+-ATPase. For cold fibres the effect of the pre-conditioning impulse is more complicated: additional slowing is time dependent, with a maximum at 60 ms. The time-dependent slowing is most likely to be due to the same mechanism, analogous to H1 in A fibres, which causes the late subnormality in cold fibres.

Figure 7.

A second conditioning stimulus never increases supernormality

Upper traces, corrected recovery cycles for single (thick lines) and double (thin lines) conditioning stimuli. Each trace is mean of indicated number of units. Lower traces, increase in slowing due to pre-conditioning stimulus; thick lines, mean; thin lines, mean ±s.d. Groups of units selected with differing degrees of supernormality. A and B, CMR units exhibit only subnormality at 0.5 Hz, and small supernormality at 1 Hz, but effect of pre-conditioning stimulus is always a small increase in slowing. C, pre-conditioning impulse induces characteristic peak in extra slowing of cold fibres at 50–60 ms. D, pronounced and long-lasting supernormality of sympathetic fibres is not increased by pre-conditioning impulse.

Refractory periods

The early parts of the recovery cycles, for different fibre types stimulated at 1 Hz, are plotted with a logarithmic time axis in Fig. 8A. There is considerable variability from fibre to fibre, but some trends are evident between fibre types. For fibres exhibiting supernormality, the relative refractory period is easily measured as the interstimulus or interspike interval at which the velocity first recovers to its unconditioned value, i.e. the entrainment interval (Weidner et al. 2002). For the many nociceptor fibres exhibiting only subnormality, however, this quantity is inappropriate as a measure of the short-lasting aftereffects of a spike, since entrainment does not occur and the ‘relative refractory period’ may be virtually infinite. To get round this difficulty, we arbitrarily defined an effective ‘refractory period’ at which the velocity was 2.5 % slower than that at an interspike interval of 50 ms, which could be estimated accurately for most fibres, whether they exhibited supernormality or not. Values of this ‘refractory period’ are compared in Fig. 8B for the four fibre types, normalised by plotting on a logarithmic axis. There was no significant difference between CMR and CMI fibres (geometric means 11.4 and 12.6 ms), but the nociceptor refractory periods were significantly longer than those of the cold fibres (6.9 ms) and shorter than those of the sympathetic fibres (16.8 ms) as indicated in the figure.

Figure 8.

Duration of refractoriness depends on fibre function

A, partial recovery cycles plotted with logarithmic interspike interval axis to show early parts more clearly. B, measurements of ‘refractory period’ (until velocity recovered to within 2.5 % of value at 50 ms) compared for four types of C fibre. Horizontal lines indicate geometric means, asterisks indicate statistical significance of differences between means (*P < 0.05, **P < 0.01, ***P < 0.001, unpaired t-test of difference in mean logarithmic refractory periods).

Time constants of recovery from supernormality or subnormality

According to the passive time constant hypothesis of C fibre afterpotentials (see Discussion) the time constant of recovery from supernormality, or the subnormality of similar duration, should correspond to the membrane time constant. To estimate this value, it is necessary to fit an exponential decay curve to the recovery cycle. Unfortunately, small deviations from exponentiality, which are evident in the recovery cycles of cold fibres and most nociceptor fibres, severely compromise curve-fitting procedures. It was observed, however, that the deviations from exponential behaviour of the CMR and CMI units were not much affected by stimulation rate, which affected the absolute amplitude of the exponentials but not their time constants (Fig. 5A). We were therefore able to obtain improved exponential decay curves, by subtracting the recovery cycle at 1 Hz from that at 0.5 Hz, for those units recorded at both stimulation rates (Fig. 9A). This operation also strikingly reduced the variability in absolute amplitudes of supernormality or subnormality, compared with the recovery cycles at a single frequency (Fig. 5B). Figure 9A also shows that the mean of these recovery cycle differences was well fitted with a single exponential of time constant 118 ms, whereas the relatively few CMI differences gave a figure of 128 ms. To assess the reliability of these estimates, exponentials were also fitted to each recovery cycle difference separately, and the time constant distributions normalised by plotting on a logarithmic axis (Fig. 9B). The recovery from supernormality of the cold fibres was much quicker (Fig. 5), but because of the conspicuous late subnormality, which was not independent of stimulation rate, it was not justifiable to fit single exponentials. In contrast to the cold fibres, the recovery curve of sympathetic fibres were well fitted by single exponentials, and in contrast to the nociceptor fibres, the recovery cycles of sympathetic fibres were strongly rate dependent: the three fibres tested at 0.5 and 1 Hz all had much longer time constants at the lower stimulation rate (Fig. 9B). The nociceptor time constants (geometric mean 109 ms) were significantly shorter than the sympathetic fibres, both at 1 Hz (178 ms) and at 0.5 Hz (337 ms), as detailed in the figure.

Figure 9.

Time constants of recovery from supernormality or subnormality

A, approximately exponential components of nociceptor recovery cycles obtained by subtracting recovery cycle at 1 Hz from recovery cycle of same unit at 0.5 Hz: left, data for 13 CMR units superimposed; centre, same data averaged and fitted with an exponential decay curve; right, similar data for four CMI units measured at 1 Hz and 0.5 Hz. B, time constants fitted to mean recovery cycles of CMI, cold and sympathetic units which exhibited supernormality at 1 Hz. C, time constants for individual units of different types compared. CMR and CMI unit time constants were not significantly different, but recovery from superexcitability of cold units was faster and of sympathetic units was slower, especially at 0.5 Hz. Three lines to the right connect time constants of same unit tested at different stimulation rates.

Discussion

This is the third study of recovery cycles of single human C fibres recorded in vivo by microneurography. The present study was undertaken independently of the other two studies (Weidner et al. 2000, 2002) and the experimental approach differed in several respects. Nevertheless, there has been a degree of overlap, generally with good agreement, and the emphasis in this report has been on results that were not anticipated by the previous studies. Thus we have included the first recovery cycle data from specific cold C fibres and sympathetic fibres, which differ in several respects from the nociceptor fibres. We have made the first recovery cycle measurements over sufficiently short conduction distances, and at sufficient interstimulus intervals, to allow conversion of latency changes as a function of interstimulus interval to velocity changes as a function of interspike interval. We have used two conditioning impulses to test the role of ion accumulation, and we have fitted exponentials to recovery cycles (or differences in recovery cycles) to provide the first time constant estimates. Before discussing the implications of our results for C fibre membrane properties, some comparisons with the previous studies are appropriate. Weidner et al. (2000, 2002) recorded from the same superficial peroneal nerve but at the knee, with considerably longer conduction distances (means 363 and 307 mm respectively, as against our 108 mm), and they expressed latency changes in milliseconds rather than as percentage changes in velocity. This makes direct comparisons with their numerical values difficult. Thus Weidner et al. (2000) found 76 mechano-sensitive units (equivalent to our Type 1A) had a mean CV of 0.98 m s−1 and a mean slowing at long delays of 0.66 ms per impulse. Assuming a mean latency of 363/0.98 = 370 ms, this gives a mean slowing of 0.66/370 × 100 = 0.18 %, which is much lower than our mean value of 0.68 % for a single impulse. This apparent discrepancy suggests that most of the slowing occurred in the distal portion of the axon.

Although we agree with Weidner et al. (2000) that mechano-insensitive units are more likely to show supernormality (relative speeding) than mechano-responsive units, we have not confirmed their report that all mechano-insensitive units exhibit supernormality at a baseline stimulation rate of 0.25 Hz, or that they can therefore be distinguished reliably from mechano-responsive units, which only exhibit subnormality (relative slowing) by a conditioning impulse at 50 ms. Whereas all our CMI units had a supernormal period at 1 Hz, only one out of eight exhibited supernormality at 0.25 Hz, and CMI units were on average slowed at an interspike interval of 50 ms. The reason for this discrepancy is unclear. Since the amount of slowing seems to vary along the length of the axons, it is conceivable that the shape of the recovery cycle also varies along the length of the axons, but our sample of units was too small to test this. Weidner et al. (2002) noted that CMR and CMI units did not differ in several recovery parameters, when allowance was made for the level of pre-existing slowing. We also found no evidence for differences between these nociceptor types in refractory period and time constant (Fig. 8 and Fig. 9), although the number of observations was relatively small.

Mechanism of the depolarising afterpotential in myelinated and unmyelinated axons

A study of afterpotentials in lizard myelinated axons by Barrett & Barrett (1982) led to a profound revision of our understanding of the electrical equivalent circuit of myelinated axons and the repolarising phase of the action potential (Baker et al. 1987; Ritchie, 1995). They demonstrated that the depolarising afterpotential behaves like a passive electrotonic potential, and is best understood as being due to depolarisation of the internodal axolemma during the action potential. The internodal axolemma under the myelin sheath has a large membrane capacitance and long membrane time constant, and it is connected electrically to the nodal axolemma by conduction paths through and under the myelin (i.e. by the ‘Barrett & Barrett resistance’ (Ritchie, 1995)). During the nerve impulse, current in this pathway acts both to repolarise the nodal membrane and to depolarise the internodal axolemma. After the impulse, the depolarised internode keeps the node depolarised during the period of the depolarising afterpotential. The depolarising afterpotential results in a period of increased excitability (the superexcitable period) and increased conduction velocity (the supernormal period). In mammalian myelinated axons the depolarising afterpotential and superexcitability are followed by a hyperpolarising afterpotential and late subexcitability, due to activation of slow K+ channels by the impulse (Bergmans, 1970; Baker et al. 1987; Bostock et al. 1998).

Whereas Barrett & Barrett's (1982) hypothesis for the mechanism of the depolarising afterpotential in myelinated axons is now widely accepted (Ritchie, 1995; Baker, 2000), their proposal that unmyelinated axons may behave similarly has until very recently received less attention. They wrote ‘It is conceivable that the depolarising afterpotential postulated in unmyelinated axons might, like the depolarising afterpotential in some myelinated axons, represent a passive capacitative discharge. Unmyelinated axons would show a long passive depolarising afterpotential if the axonal membrane has a high specific membrane resistance, and hence a long passive time constant, and if activation of axonal K+ channels requires relatively large depolarisations, so that most of the K+ channels activated during the action potential close before the axons has completely repolarised. If this model is accurate, then the time course of the depolarising afterpotential in unmyelinated axons would, as in some myelinated axons, reflect a passive time constant of the axonal membrane.’Weidner et al. (2002) argued that their findings supported this radical concept, and our findings in this paper provide further strong confirmation. The passive time constant hypothesis of supernormality can also be extended to the complementary phenomenon of the period of subnormality, of similar time course to the supernormality and presumably related to a hyperpolarising afterpotential that occurs most conspicuously in CMR units at low frequency. This hypothesis is supported first by the fact that supernormality (unlike H2) is not at all additive for a second impulse at an interstimulus interval of 20 ms, so that any explanation in terms of ion accumulation or altered ion channel properties extending over hundreds of milliseconds is untenable. Secondly, like Weidner et al. (2002). we have shown that supernormality is strongly dependent on stimulation rate, presumably because, as in A fibres, it is enhanced by membrane hyperpolarisation. There is, however, an interesting difference from A fibres, namely that at relatively depolarised membrane potentials the supernormality is not simply reduced, but reverses and is replaced by subnormality with a similar time course. This phenomenon is readily accounted for by Barrett & Barrett's (1982)‘passive time constant’ hypothesis, whereas neither the ‘K+ accumulation’ nor the ‘Na+ conductance’ hypotheses (see Introduction) can provide any convincing explanation.

Our interpretation is that during the action potential, Na+ channels allow a quantity of Na+ ions (and also some Ca2+ ions, Quasthoff et al. 1995) to flow into the axon, applying a certain depolarising charge (QNa) on the capacitance (C) of the membrane. The depolarisation activates fast K+ channels, which in turn apply a certain hyperpolarising charge (QK) on the same capacitance to return the membrane potential approximately to its resting value. As Barrett & Barrett (1982) foresaw, the K+ channel activation requires relatively large depolarisation, so that QK, like QNa, does not change very much after the spike. An afterpotential is therefore generated, corresponding to (QNaQK)/C. This voltage decays according to the membrane time constant RC. As the membrane undergoes activity-dependent hyperpolarisation, QNa increases (since the electrochemical gradient for Na+ influx is enhanced and Na+ channel inactivation is reduced) and also QK decreases (since the electrochemical gradient for K+ efflux during the action potential is reduced). Therefore (QNaQK) and the depolarising afterpotential increase rapidly with hyperpolarisation. Conversely, membrane depolarisation, unless induced by raising extracellular K+ concentration, reduces QNa and increases QK, so that a depolarising afterpotential gives way to a hyperpolarising afterpotential, which also decays with the membrane time constant RC. In CMR and CMI fibres, for which we have recorded both supernormality and subnormality at different stimulation rates, these two time constants have been remarkably similar, so that the subtracted recovery cycles have resembled single exponentials (Fig. 9A). The range of recovery cycles for CMR units in Fig. 5B, which includes both supernormal and subnormal velocity changes with similar time course, is likewise accounted for by variation around zero in the balance of (QNaQK). This finding nicely confirms Barrett & Barrett's (1982) conjecture, quoted above, that mammalian C fibres, unlike A fibres, do not have a large voltage-dependent K+ conductance active at normal resting potentials. Whereas A fibre depolarising afterpotentials become shorter and smaller with membrane depolarisation, C fibre supernormality reverses in amplitude with little change in duration. Finally, we note that all afterpotentials and post-spike velocity changes due to the ‘passive time constant’ mechanism are absent when QNa=QK, and some recovery cycles are remarkably flat. The main residual effects are the refractoriness attributable to Na+ channel inactivation, and the long-lasting hyperpolarisatioin (H2) due to increased Na+/K+-ATPase activity.

The C fibres with recovery cycles least well described by the ‘passive time constant’ mechanism are the cold fibres (Fig. 5 and Fig. 9). In addition to a brief supernormality, they have a marked, time-dependent subnormality, comparable with the delayed hyperpolarising afterpotential (H1) or late subexcitability in myelinated fibres (Baker et al. 1987). Similar to H1 in A fibres (Kiernan et al. 1996), the late subnormality in cold C fibres is enhanced by a second conditioning impulse (Fig. 7C), consistent with it being generated by a slowly activating K+ current that is incompletely activated during one action potential (cf. Schwarz et al. 1995). As the fibres hyperpolarise at higher frequencies, not only does supernormality increase, but also the late subnormality becomes larger and later (Fig. 5A). This suggests that the late subnormality is activated in part by the depolarising afterpotential, as well as by the spike, as has been observed for the late subexcitable period in A fibres during post-ischaemic hyperpolarisation (Kiernan & Bostock, 2000). The resemblance between cold fibre and A fibre recovery cycles is interesting in view of the possibility that the cold C fibres may represent long unmyelinated terminal portions of fibres that are thinly myelinated over most of their length (Campero et al. 2001). In cold fibres and A fibres with subexcitability, H1 brings the supernormality to a premature end, so the its decay time course does not provide a useful estimate of the passive membrane time constant.

In the above discussion it was implied that the latency changes during repetitive stimulation were due to hyperpolarisation by the electrogenic Na+ pump, and there is little doubt that that is the dominant factor for short trains. However, the failure of the progressive latency increases during 2 Hz stimulation of nociceptors to be matched by a continued increase in supernormality (Fig. 6) suggests that a second factor becomes involved, which does not have the same effect on supernormality that hyperpolarisation has. The progressive accumulation of intracellular Na+ must slow conduction by reducing the electrochemical gradient for Na+ ions (and therefore reducing QNa) as well as by activating hyperpolarisation by the Na+ pump (which increases QNa). The continuous supernormality estimation in Fig. 6 suggests that the former effect becomes progressively more important during the long 2 Hz trains, so that there can even be a net reduction in QNa.

In conclusion, this study of human C fibre recovery cycles has shown how the recorded latency changes can be corrected for the changes in interspike interval with distance, and documented their dependence on stimulation rate, axonal functional type and a second conditioning impulse. In agreement with Weidner et al. (2002). these data strongly support Barrett & Barrett's (1982)‘passive time constant’ hypothesis for the generation both of supernormality and of the component of subnormality with a similar time course as supernormality that is seen in some less hyperpolarised fibres. According to this hypothesis the membrane time constants of CMR and CMI nociceptors are close to 100 ms, and are not much affected by membrane potential, whereas sympathetic unit time constants can be much longer at low impulse rates. The marked tendency of sympathetic unit time constants to shorten with hyperpolarisation (Fig. 5A and Fig. 9B), contrasts with the behaviour of A fibres, and is probably due to activation of a hyperpolarisation-activated current (IH), that limits activity-dependent hyperpolarisation and slowing in these axons.

Acknowledgement

This work was supported by NIH grant RO1 NS-39761.

Ancillary