Changes in excitability indices of cutaneous afferents produced by ischaemia in human subjects

Abstract

1. The present study was undertaken to determine whether mechanisms other than membrane depolarization contribute to the changes in excitability of cutaneous afferents of the median nerve under ischaemic conditions.

2. In six healthy subjects, axonal excitability was measured as the reciprocal of the threshold for a compound sensory action potential (CSAP) of 50% maximal amplitude. Refractoriness and supernormality were measured as threshold changes 2 and 7 ms, respectively, after supramaximal conditioning stimuli. The strength-duration time constant (τ_SD) was calculated from the thresholds for unconditioned CSAPs using test stimuli of 0·1 and 1·0 ms duration. Changes in these indices were measured when subthreshold polarizing currents lasting 10 or 100 ms were applied, before, during and after ischaemia for 13 min.

3. At rest, the change in supernormality produced by polarizing currents was greater with the longer polarizing current, indicating that it took up to 100 ms to charge the internodal capacitance.

4. Refractoriness and its dependence on excitability increased more than expected during ischaemia. Supernormality was abolished during ischaemia, and reached a maximum after ischaemia but was then barely altered by polarizing current. τ_SD had a similar relationship to excitability before, during and after ischaemia.

5. By contrast, during continuous depolarizing current for 8 min to mimic the depolarization produced by ischaemia, the relationship between excitability and refractoriness was the same during the depolarization as before it.

6. It is suggested that the large increase in refractoriness during ischaemia might be due to interference with the recovery from inactivation of transient sodium channels by an intra-axonal substrate of ischaemia. The post-ischaemic increase in supernormality and the lack of change with changes in axonal excitability can be explained by blockage of voltage-dependent potassium channels.

Relatively brief periods of ischaemia paralyse the electrogenic Na⁺-K⁺ pump, increase [K⁺]_o and produce membrane depolarization. In sensory axons, the axonal depolarization can lead to hyperexcitability sufficient to result in ectopic activity. This is less likely in motor axons, probably because the former express a threshold conductance, thought to be mediated by persistent Na⁺ channels (Bostock & Rothwell, 1997). Following release of ischaemic compression, heightened activity of the electrogenic Na⁺-K⁺ pump leads to axonal hyperpolarization. Paradoxically, ectopic activity can then be quite intense, particularly in sensory axons, and this is probably due, in part, to activation of an inwardly rectifying conductance that is again expressed more on sensory axons than on motor axons (Bostock et al. 1994).

The changes in axonal excitability during ischaemia and after its release can be reproduced reasonably well by long-lasting depolarizing and hyperpolarizing currents (Baker & Bostock, 1989), suggesting that the change in membrane potential is largely sufficient to explain some of the effects of ischaemia. However, it is likely that there is more to the excitability changes produced by ischaemia than the change in membrane potential. In a short communication on voltage-clamped rat axons, Brismar (1981) reported that anoxia decreased maximal Na⁺ permeability and shifted the relationship between Na⁺ channel inactivation and membrane potential to more negative potentials, so that more Na⁺ channels were inactivated at rest. In addition, ischaemia can have complex effects, both direct and indirect, on other processes that could affect axonal excitability. For example, it will affect energy-dependent processes within the axon (e.g. Na⁺-K⁺-ATPase, Ca²⁺-ATPase), and may have secondary effects due to abnormal ion accumulation (e.g. reverse action of the Na⁺-Ca²⁺ exchanger, see Stys et al. 1991; activation of Na⁺-dependent K⁺ channels, see Koh et al. 1994). The switch to anaerobic glycolysis could lead to intracellular acidosis, and ultimately to secondary effects on ion channel function (e.g. inactivation of fast K⁺ channels), particularly in the presence of hyperglycaemia (Schneider et al. 1993). Finally, some conductances are sensitive to intracellular ATP (K_ATP channels, see Jonas et al. 1991; inward rectification, see Kusaka & Puro, 1997).

The present studies were undertaken to determine whether ischaemia and its release have demonstrable effects on axonal excitability other than those that would be expected from the resulting changes in threshold, as measured using brief test pulses. The effects of graded depolarizing and hyperpolarizing currents on different indices of axonal excitability were measured before, during and after ischaemia produced by inflation of a sphygmomanometer cuff around the limb. The relationships between excitability (expressed as the reciprocal of threshold, as measured using brief test pulses) and refractoriness, supernormality and strength-duration time constant (τ_SD) were determined under these conditions, when the ischaemic and post-ischaemic changes in threshold were stable. These relationships are near-linear at rest (Burke et al. 1998), and they are assumed to reflect dependence of each measure on membrane potential (hence ‘voltage dependence’), though it must be stressed that there may be no direct relationship between threshold (or its reciprocal, excitability) and membrane potential. The rationale for the studies was that, if the effects of ischaemia and its release on these indices could be explained by the change in threshold, their relationships to excitability would not change: the data would merely be displaced in either direction along the appropriate regression line. The major findings were that ischaemia produced a disproportionate increase in refractoriness and that, following its release, supernormality was increased, as expected, but varied less with applied currents, as if it had become relatively independent of threshold. On the other hand, τ_SD maintained the same relationship to the reciprocal of threshold, as if the manoeuvre did not alter its voltage dependence. In addition, it was found that polarizing currents of > 10 ms duration are required to produce maximal changes in supernormality, behaviour consistent with the equivalent circuit model of the electrical properties of axons proposed by Barrett & Barrett (1982), as modified by Bostock et al. (1991b).

METHODS

Four series of experiments were performed, each involving six healthy adult volunteers of both sexes, all of whom had given informed written consent for the experimental procedures, which had the approval of the Committee on Experimental Procedures Involving Human Subjects of the University of New South Wales.

Antidromic recordings of compound sensory action potentials (CSAPs) were made using ring electrodes around the index finger of the right hand, as previously described (Kiernan et al. 1996; Mogyoros et al. 1996, 1997). The cathode was placed over the median nerve at the wrist and the anode over the forearm muscle, 15-20 cm proximal to the cathode. Using the QTRAC threshold tracking program (copyright, Institute of Neurology, Queen Square, London, UK; see Bostock et al. 1998), stimuli were delivered at 2 Hz through a single output from a current source, driven by the computer, rotating through a sequence of seven different test stimuli (stimulus ‘channels’), alone or following a conditioning pulse, with or without a polarizing current, as described in detail below. A fixed supramaximal stimulus of 0.2 ms was delivered on channel 1 to produce a CSAP of maximal amplitude. On channels 2-6, the threshold current needed to elicit a CSAP with an amplitude of 50% of the maximal CSAP was tracked by an IBM compatible computer. Stimulus current was increased or decreased automatically proportional to the error between the recorded CSAP and the target (see Bostock & Rothwell, 1997; Bostock et al. 1998). The threshold current required to produce the target CSAP using a test pulse of 1.0 ms duration was recorded on channel 2 and was used as the reference for the polarizing current applied on channels 3-7 (see below). Channels 3 and 4 recorded the thresholds using unconditioned test stimuli of 0.1 and 1.0 ms duration, and these were used to calculate the strength-duration time constant (τ_SD) according to Weiss’ Law (see Bostock & Bergmans, 1994; Mogyoros et al. 1996, 1997):

where I_0.1 and I_1.0 were the threshold currents using 0.1 and 1.0 ms test stimuli, respectively.

To test refractoriness and supernormality, stimuli of 0.1 ms duration were preceded by supramaximal conditioning stimuli of 0.2 ms duration with conditioning-test intervals of 2 and 7 ms on channels 5 and 6, respectively. These intervals were chosen to sample excitability during the relatively refractory period and during the supernormal period, when the latter was maximal (Kiernan et al. 1996). The conditioning stimuli were identical to that on channel 1. On channels 5 and 6 the conditioned response was measured after on-line subtraction of the maximal CSAP produced by the conditioning stimulus. The subtracted CSAP was recorded on channel 7 using a fixed stimulus, identical to that on channel 1, except that the stimulus was superimposed on the polarizing current. Refractoriness was measured as the increase in current required to produce the target CSAP when the conditioning-test interval was 2 ms, and was normalized to the unconditioned threshold. Supernormality was measured similarly but as the decrease in current required to produce the target potential when the conditioning-test interval was 7 ms, again normalized to the unconditioned control.

In order to determine the threshold dependence of refractoriness, supernormality and τ_SD, threshold was altered on channels 3-7 using long-lasting subthreshold DC current pulses. The strength of the DC current was a percentage of the threshold current tested using the 1.0 ms stimulus on channel 2, and was changed every minute in steps of 10% from +50% (depolarizing) to -50% (hyperpolarizing) or vice versa, as illustrated in Figs 1 and 2. The duration of the polarizing current was 30 or 120 ms, with the test stimuli timed to occur either 10 or 100 ms after the onset of the current. The changes in threshold induced by polarization were normalized so that the unpolarized value before ischaemia was unity.

Figure 1. Threshold data from an entire experiment.

Polarizing steps were begun at 1 min, initially 50% depolarizing, changing to 40% depolarizing at the first vertical arrow. Ischaemia was applied during the period indicated by the horizontal bar, starting at 14 min. Traces a, b and c represent thresholds using a 0.1 ms test pulse, unconditioned (a) and conditioned using conditioning-test intervals of 2 ms (b) and 7 ms (c). Traces d and e are thresholds in response to a 1 ms test pulse, with and without polarization. Polarizing current was applied during traces a-d, the strength of the current being a percentage of the threshold of trace e. Accordingly, trace e shows the (unmodified) threshold changes produced by ischaemia and its release. The double-headed arrow shows the interval over which threshold-dependence relationships were assessed during ischaemia. The open vertical bar indicates the ‘resting’ state during ischaemia, when the polarizing current was zero. Data from one experiment.

Figure 2. Threshold dependence of excitability indices prior to ischaemia.

Polarizing steps proceeded from 50% hyperpolarization to 50% depolarization. Traces in A show the original thresholds and are labelled as in Fig. 1. The open vertical bar indicates zero polarization. B illustrates the polarizing current, initially set to 50% of the current in A trace e. C illustrates the excitability indices, calculated from the threshold data in A. ‘Excitability’ is the reciprocal of the unconditioned threshold (i.e. trace a in A). For refractoriness (b) and supernormality (c), the change in threshold is expressed as a fraction (rather than a percentage). τ_SD (d) is in milliseconds. Data from one experiment.

In two subjects the effects of continuous depolarizing current were studied using an 8 min current ramp designed to mimic the depolarization that occurs during ischaemia. The depolarizing current ramp was set to produce a decrease in threshold of approximately twice that which occurs during ischaemia. The relationship between refractoriness and axonal excitability was followed before and during the depolarizing current ramp using polarizing current lasting 10 or 100 ms, set at +50, +30, 0, -30 or -50% of I_1.0.

The amplitude of the CSAP was measured peak to peak. In all experiments, temperature was monitored continuously by skin sensors at the first metacarpophalangeal joint and at the wrist, and was kept constant (33.4 ± 0.8°C, mean ±s.d., prior to ischaemia; 32.9 ± 0.7°C prior to release of ischaemia) by wrapping the arm in blankets and applying radiant heat if necessary. Ischaemia was induced by inflating a sphygmomanometer cuff around the upper arm to 200 mmHg for 13 min.

Data are expressed as means ±s.e.m. The significance of changes in absolute values or in the slope of the relationships with excitability was assessed using Student's paired t tests with Bonferroni correction for multiple tests. All quoted probabilities are given after this correction.

RESULTS

Depolarizing and hyperpolarizing currents of graded intensity were used to change membrane potential, and the induced change was measured as the change in threshold for a compound sensory action potential (CSAP) of 50% maximum. The effects of the change in membrane potential on refractoriness, supernormality and strength-duration time constant (τ_SD) were determined using the reciprocal of threshold (hereinafter termed ‘excitability’) as an indirect (and possibly non-linear) indicator of membrane potential. These studies were performed before ischaemia (control), and then during ischaemia and again after its release, at times when the ischaemic and post-ischaemic threshold changes were stable (Fig. 1, trace e). Refractoriness was measured during the relatively refractory period as the change in current required to produce the target CSAP when the test stimulus was delivered 2 ms after a supramaximal conditioning stimulus, and supernormality was measured as the change in current required to produce the target potential when the conditioning-test interval was 7 ms. τ_SD was calculated from the thresholds determined using unconditioned test stimuli of 0.1 and 1.0 ms duration.

During ischaemia, the steps of polarizing current proceeded in the opposite direction to that before ischaemia, and after release of ischaemia they proceeded in the same direction as before ischaemia (Fig. 1). For this reason, separate experiments were performed on each subject reversing the direction of the step changes in polarizing current from that seen in Fig. 1: i.e. hyperpolarizing to depolarizing prior to ischaemia, depolarizing to hyperpolarizing during ischaemia, and hyperpolarizing to depolarizing after release of ischaemia. In addition, separate studies using polarizing currents lasting 10 and 100 ms were performed for each step direction. Accordingly, subjects underwent four separate experiments.

Figure 1 illustrates the data for a single experiment. Traces a, b and c represent channels for which the test stimulus was of 0.1 ms duration, unconditioned (a) and conditioned using conditioning-test intervals of 2 ms (b) and 7 ms (c). Traces d and e illustrate thresholds for the target CSAP using unconditioned test stimuli of 1.0 ms duration. Polarizing currents were applied 10 ms before the test stimuli with traces a-d but not trace e. At 1 min, depolarizing current steps of 50% of the threshold on trace e were commenced and, when thresholds had stabilized after 2 min (first vertical arrow), the applied current was changed in steps of 10% every minute from 50% depolarizing to 50% hyperpolarizing. At 14 min, the sphygmomanometer cuff was inflated (horizontal bar), and after 3 min the polarization was stepped from 50 to 40% hyperpolarizing current (second vertical arrow), and then, in steps of 10% each lasting 1 min, to a 50% depolarizing current. The cuff was then deflated and, after the thresholds had stabilized, the current steps were recommenced (third vertical arrow), proceeding from 50% depolarizing to 50% hyperpolarizing. In Figs 4, 7 and 8, D-H shows the sequences for which polarization started with depolarizing currents and ended with hyperpolarizing currents, using the data from the two complementary experiments. Similarly, H-D illustrates the sequences beginning with hyperpolarizing current.

Figure 4. Effects of the duration of the polarizing current and the direction of the step changes on excitability indices.

When the polarizing current lasted 100 ms (right panels), the relationships for refractoriness and τ_SD were the same as those with 10 ms polarizing currents (left panels), but the relationships for supernormality differed significantly (D-H, P = 0.003; H-D, P = 0.001) There were no differences in the relationships whether the polarizing steps started with 50% depolarizing and ended with 50% hyperpolarizing current (D-H, ⋄) or the reverse (H-D, ▴). Data are mean values for six subjects ±s.e.m.

Figure 7. Changes in refractoriness and its relationship to excitability.

A and B present the mean data for the six subjects ±s.e.m. for each of the four experiments. The data have been normalized so that the threshold in the absence of polarization before ischaemia produced an excitability of unity. The intra-ischaemic threshold with zero polarization is indicated by the vertical arrows. As in other figures, D-H represents sequences in which the polarizing current started with depolarization and ended with hyperpolarization. For H-D the polarization was stepped from hyperpolarization to depolarization. C shows the absolute values of refractoriness when polarization was zero (means and s.e.m.). The displacement of the relationships during ischaemia was significant (for 10 ms currents: D-H, P = 0.011 and H-D, P = 0.005; for 100 ms currents: D-H, P = 0.011 and H-D, P = 0.001).

Figure 8. Changes in supernormality and its relationship to excitability.

Data are for six subjects (means ±s.e.m.) displayed using the same format as in Fig. 7 (⋄, before ischaemia; •, during ischaemia; ▴, after ischaemia). Thus A and B illustrate the mean threshold change at the 7 ms conditioning-test interval for the six subjects for the two polarizing current durations and the two directions of step change in polarizing current. The data have been normalized so that the pre-ischaemic threshold in the absence of polarizing current equals an excitability of unity. The vertical arrows indicate the intra-ischaemic values when polarization was zero. C illustrates the absolute values when the polarizing current was zero for each experiment (means and s.e.m.). The slopes for the post-ischaemic relationships are significantly less than those prior to ischaemia (for 10 ms currents, P = 0.003 and 0.023; and for 100 ms currents, P = 0.017 and 0.032; for the D-H and H-D sequences, respectively).

Excitability values prior to ischaemia

Prior to ischaemia, the step changes in polarizing current from 50% hyperpolarizing to 50% depolarizing (Fig. 2B) produced a progressive reduction in threshold as measured with both 0.1 ms test stimuli (Fig. 2A, trace a) and 1.0 ms test stimuli (trace d). Trace e represents an unpolarized channel on which threshold was measured using 1.0 ms test stimuli, and the point where the two 1.0 ms thresholds overlap represents the resting state, during which the polarizing current was zero. The upper three traces in Fig. 2A represent thresholds measured using 0.1 ms test stimuli: trace a, unconditioned; trace b, conditioned using a 2 ms conditioning-test interval; and trace c, conditioned using a 7 ms conditioning-test interval.

From the threshold data in Fig. 2A, refractoriness, supernormality and τ_SD were calculated as detailed in Methods. The changes in these indices with step changes in polarizing current were much as previously described (Burke et al. 1998): depolarizing currents produced clear step changes in threshold (expressed in Fig. 2C, trace a, as its reciprocal, excitability), increased refractoriness (trace b), decreased supernormality (trace c) and increased τ_SD (trace d). From the traces in Fig. 2C, it can be seen that refractoriness was replaced at the 2 ms conditioning-test interval by supernormality as hyperpolarization increased (left of traces), and that supernormality was replaced by refractoriness at the 7 ms interval with extreme depolarization (right of traces). As noted above, supernormality is a negative value (i.e. the threshold reduction produced by the conditioning stimulus), such that a less negative value represents less supernormality.

When threshold was tested 10 ms after the onset of the polarizing currents, there were, in each subject, near-linear relationships between excitability and the three indices (Fig. 3), with mean r² values of 0.995 for refractoriness, 0.881 for supernormality and 0.839 for τ_SD. The relationships presumably reflect the voltage dependence of the axonal properties that contribute to each index, and were quantified by calculating the value for each index at rest (i.e. when there was no polarizing current, excitability of 1, open vertical bars in Figs 2 and 3) and the slope of the regression equation. At rest, refractoriness was 26 ± 3% (mean ±s.e.m.), indicating that the test stimulus had to be increased by 26% of the control value when delivered 2 ms after a supramaximal conditioning stimulus. Resting supernormality was -12 ± 2% (i.e. the test stimulus could be decreased by 12% when delivered 7 ms after a supramaximal conditioning stimulus), and resting τ_SD was 515 ± 36 μs. Doubling excitability would have increased refractoriness to 118 ± 7%, abolished supernormality, replacing it by refractoriness of 4 ± 3% at the 7 ms conditioning-test interval, and increased τ_SD to 894 ± 72 ms. There was no significant difference in these values whether the steps of polarizing current proceeded from 50% hyperpolarizing to 50% depolarizing or the reverse (Fig. 4).

Figure 3. Relationships between excitability and refractoriness, supernormality and τ_SD.

The reciprocal of threshold measured using an unconditioned 0.1 ms test pulse is used as an indicator of axonal excitability (x-axis). The unpolarized (resting) state is indicated by the vertical open bar. There are near-linear relationships between excitability and the other indices. Same data as in Fig. 2C. Data from one experiment.

There was no significant difference in refractoriness or τ_SD, whether threshold was tested 10 or 100 ms after the onset of the polarizing currents, or whether the current steps started with hyperpolarization or depolarization (Fig. 4). This suggests that the 10 ms polarizing currents were sufficient to produce maximal changes in indices dependent on nodal properties. However, the slope of the relationship between excitability and supernormality was greater with 100 ms polarizing currents (0.36 ± 0.02, as against 0.15 ± 0.02 with 10 ms currents; Fig. 4, middle panels; D-H, P = 0.003; H-D, P = 0.001), indicating that the 10 ms polarizing current was insufficient to charge the internodal capacitance fully. There were accompanying changes in the intercept value, the value for a theoretical excitability of zero (-50 ± 2% with 100 ms currents; -27 ± 1% with 10 ms currents).

Excitability properties during and after ischaemia

During ischaemia the polarizing current was first applied after the initial fall in threshold had occurred and ended 11 min later, before conduction block had started to develop. The threshold changes during this 11 min period were calculated from the unpolarized channel on which threshold was measured using test stimuli of 1.0 ms duration (Fig. 1, trace e). The data from four experiments for each subject were averaged for the following measurements. During ischaemia, there was no significant change in threshold over the period of polarization: 76.7 ± 3.0% of the pre-ischaemic level at the beginning of the steps; 79.5 ± 3.4% at the end of the steps (P = 0.130). After release of ischaemia, the polarizing current was applied after the increase in threshold had stabilized. Again, there was no significant change in threshold during this 11 min period: 109.4 ± 5.9% of the pre-ischaemic level at the beginning of the steps; 103.8 ± 4.8% at the end of the steps (P = 0.129). Accordingly, excitability indices were measured when threshold was reasonably stable, such that differences in their relationship with axonal excitability were probably due to metabolic changes in function independent of excitability. Possible bias introduced by the trend for less depolarization at the end of the polarization sequence during ischaemia and for less hyperpolarization at the end of polarization after the release of ischaemia will be considered later. Importantly, the resting values (i.e. the threshold value in the absence of polarizing current) occurred at equivalent times into ischaemia and recovery therefrom, whether the steps proceeded from hyperpolarization to depolarization, as in Fig. 1, or vice versa.

Figure 5A (Refractoriness) illustrates the rationale for the study. If the effects of ischaemia and its release could be attributed to depolarization and hyperpolarization, respectively, refractoriness would have the same relationship with axonal excitability before, during and after ischaemia, the only change being displacement of the relevant data towards the depolarized or hyperpolarized ends of the regression line. In Fig. 5A, the data for refractoriness during ischaemia are displaced upwards, away from the pre-ischaemic data, there being greater refractoriness than would be expected at all levels of excitability (P = 0.013). On the other hand, the post-ischaemic data are superimposed on the pre-ischaemic data, suggesting that, after release of ischaemia, refractoriness behaved appropriately for the change in excitability. The three plots for supernormality (Fig. 5B) differ significantly (before-during ischaemia, P = 0.007; before-after ischaemia, P = 0.028), suggesting that factors other than the excitability change are important in determining supernormality during and after ischaemia. However, the relationships between time constant and excitability (Fig. 5C) are similar before, during and after ischaemia (before-during, P = 0.353; before- after, P = 0.139), suggesting that the time constant follows the excitability change in much the same way before, during and after ischaemia.

Figure 5. Effects of ischaemia and its release on the relationships of refractoriness, supernormality and τ_SD to excitability.

Data from one experiment using 10 ms polarizing currents, the polarization cycle starting with hyperpolarizing steps before ischaemia, with depolarizing steps during ischaemia and with hyperpolarizing steps after release of ischaemia. A, for refractoriness the data before and after ischaemia fall along the same regression line, but during ischaemia the relationship is shifted upwards and towards higher excitability, and the slope is reduced (the overall change being significant, P = 0.013). B, for supernormality the relationships with excitability differ before, during and after ischaemia (P = 0.007 and 0.028, before-during and before-after, respectively). However, during ischaemia, the threshold change was probably dominated by refractoriness. C, for τ_SD the three relationships do not differ significantly.

Strength-duration time constant

During ischaemia τ_SD increased and after release of ischaemia τ_SD decreased (Fig. 6), much as described previously (Mogyoros et al. 1997). However, the relationship with axonal excitability was similar before ischaemia, during ischaemia and after its release (Figs 5 and 6). There were no significant differences in the slopes of these relationships related to the duration of the polarizing steps or their direction (Fig. 6). Accordingly, the nodal mechanisms that underlie τ_SD behaved as if they were dependent solely on the properties that determine threshold.

Figure 6. τ_SD and its relationship to excitability before, during and after ischaemia.

The left panels in A and B illustrate the absolute values for τ_SD before, during and after ischaemia in the absence of polarizing current, for experiments in which the polarizing current lasted 10 ms (A) and 100 ms (B). The right panels illustrate the slope of the relationships with excitability. The data are mean values and s.e.m. for six subjects. The direction of the polarizing steps did not affect the values, and the data for the two experiments for each subject were averaged.

Refractoriness

The relationships between refractoriness and axonal excitability before and after ischaemia were identical regardless of the direction of the polarizing sequence (i.e. hyperpolarizing then depolarizing or vice versa) and the duration of the polarizing current (Fig. 7).

Refractoriness when the polarizing current was zero (i.e. at the middle of the polarizing sequences) increased during ischaemia by a factor of ∼3 (Fig. 7C). The vertical arrows in Fig. 7A and B indicate the mean refractoriness during ischaemia when polarization was zero. The equivalent values before ischaemia are aligned to an excitability of 1. One would expect greater refractoriness during ischaemia merely because of the increase in excitability due to ischaemic depolarization. However, the relationships with excitability were displaced upwards, with a greater slope when the polarization sequence commenced with 50% hyperpolarization and a smaller slope when it commenced with 50% depolarization (Fig. 7B). With Bonferroni correction for multiple tests, the upward displacement of each regression line during ischaemia from its pre-ischaemic control was significant (P = 0.011 -0.001). There was also a significant change in slope (P = 0.039) for the sequence hyperpolarizing to depolarizing current using 100 ms currents.

The differences in the relationships in Fig. 7A and B dependent on polarizing direction provide additional support for the view that ischaemia has effects on refractoriness other than those due to the ischaemic increase in axonal excitability. Refractoriness was less dependent on excitability when the polarizing sequence began with 50% depolarizing currents and more so when it began with 50% hyperpolarizing currents. Such behaviour is consistent with a gradually developing ischaemic metabolic disturbance.

As noted earlier, the polarizing sequences were commenced when the ischaemic decrease in threshold had reached a plateau, but threshold was not perfectly steady during the subsequent 11 min. Over the 11 min, threshold increased from 76.7% of the pre-ischaemic level to 79.5%, a change that was not statistically significant. This small threshold change is not sufficient to explain the directional difference in slopes of the relationship with excitability. Using the regression equations for the pre-ischaemic data, this difference in threshold could account for a difference in refractoriness of only 4%.

Supernormality

During ischaemia, supernormality was reduced, refractoriness appeared at the 7 ms conditioning- test interval (Fig. 8C), and there were significant changes in the relationship with axonal excitability. These changes were similar to those that occurred with refractoriness (Fig. 8A and B); it is likely that, during ischaemia, the voltage-dependent behaviour at the 7 ms conditioning-test interval was determined more by processes that underlie refractoriness than by those that contribute to supernormality.

This was not the case following release of ischaemia. The expected increase in resting supernormality occurred (Fig. 8C), presumably because the axons had hyperpolarized. The slope of the relationship with excitability was significantly reduced, particularly with the 10 ms polarizing currents, which had negligible effects on supernormality (Fig. 8A; D-H, P = 0.003; H-D, P = 0.023). With 100 ms polarizing currents, the dependence on excitability was more clear, though still less than that prior to ischaemia (Fig. 8B; D-H, P = 0.017; H-D, P = 0.032). Accordingly, there appeared to be an increase in overall supernormality, associated with a marked reduction in its dependence on excitability, a reduction that could be partially overcome by longer polarizing currents.

In the post-ischaemic period the polarizing sequences were commenced some 2-3 min after the rapid changes in threshold had subsided. As noted earlier, threshold did change slightly over the 11 min sequence, being on average 109.4% of the pre-ischaemic level at the beginning of the polarizing steps and 103.8% at the end of the sequence. Using the regression equations for the pre-ischaemic data, the difference in these threshold levels would account for a 1.7% difference in supernormality, insufficient to explain the post-ischaemic relationship with excitability.

Refractoriness during a continuous depolarizing current ramp

To determine whether long-lasting membrane depolarization alters the relationship between refractoriness and axonal excitability sufficient to explain the marked increase in refractoriness during ischaemia, the effects of continuous depolarizing current were studied in four experiments on two subjects. A current ramp was chosen because, in a parallel study (J. Grosskreutz, C. Lin, I. Mogyoros & D. Burke, unpublished observations), the waveform of the current required to keep threshold constant during ischaemia was found to resemble a continuous ramp more closely than the inverse of the threshold change (Fig. 9A and B). The depolarizing current ramp was applied for 8 min, and decreased threshold by 40-50% (Fig. 9C), about twice the threshold change produced by ischaemia (Fig. 9A). To document the relationship between refractoriness and axonal excitability, polarizing currents (-50, -30, 0, +30 and +50% of I_1.0) were applied for 10 ms (2 experiments) and 100 ms (2 experiments) prior to the conditioned and unconditioned test stimuli used to measure refractoriness (Fig. 9C).

Figure 9. Continuous depolarizing current.

A shows mean data for six subjects in whom a hyperpolarizing current lasting 10 ms was injected to balance the depolarization produced by ischaemia for 13 min. The mean threshold change produced by ischaemia is shown in the upper trace and the current required to offset the threshold change is shown in the lower trace. Note that while threshold reached a plateau, the current required to return threshold to the pre-ischaemic level continued to increase. B, plot of the data in A, showing the non-linearity. C, changes in unconditioned threshold (middle traces) and refractoriness (upper traces) produced by a prolonged depolarizing current ramp (lower trace). In the upper and middle traces, depolarizing and hyperpolarizing currents lasting 30 ms were delivered 10 ms before the test stimuli. Data from one subject.

The findings were the same in all four experiments. Figure 9C illustrates the data for one subject using 10 ms polarizing currents superimposed on the continuous depolarizing current ramp, and Fig. 10 plots the 100 ms data for the second subject. The symbols in the upper panel of Fig. 10 represent the five levels of brief polarizing current, each gradually displaced upwards and to the right as axonal excitability increased due to the continuous depolarizing current ramp. In the lower panel, the two sets of open symbols illustrate the relationship between refractoriness and excitability at rest and the filled symbols the relationships recorded at intervals during the development of the depolarizing ramp current. Axonal depolarization did not change the slope of the relationship.

Figure 10. Effects of continuous polarizing current on refractoriness.

The relationships between refractoriness and excitability tested using brief polarizing currents lasting 100 ms before and during a prolonged depolarizing current ramp lasting 8 min. Data for one subject. The symbols in the upper panel indicate data for the different polarization levels. The lower panel plots the relationship between refractoriness and excitability using the five levels of polarization. The vertical arrows indicate the data at rest (○) for the five levels of polarization; the equivalent data points 2, 4, 6 and 8 min into the prolonged depolarizing current are shown (▴). Each data point represents the mean over a 1 min interval.

DISCUSSION

This study presents evidence that the relationship between threshold and its reciprocal, excitability, and some excitability indices is distorted when measured during ischaemia and after its release. The findings suggest that the effects of these manoeuvres cannot be attributed simply to depolarization and hyperpolarization, respectively, a conclusion supported by the data in Fig. 10. Of the three excitability indices measured in this study, only the strength-duration time constant maintained much the same relationship to excitability under control, ischaemic and post-ischaemic conditions.

One notable finding, even if it could have been anticipated, is that, at rest, the true extent of the voltage-dependent change in supernormality was not revealed using polarizing currents lasting 10 ms. This finding would have been expected given that the first slow phase of electrotonus is largely passive, due to the dissipation of current stored on the internodal membrane, and that the accompanying changes in threshold last some 20-30 ms in human subjects (Bostock & Baker, 1988; Baker & Bostock, 1989). The mechanisms responsible for this phase of electrotonus are essentially the same as those that underlie the depolarizing after-potential and the supernormal period of increased excitability following a single conditioning discharge (Barrett & Barrett, 1982; David et al. 1995; Ritchie, 1995). The present findings are therefore consistent with the model of electrical excitability of myelinated axons proposed by Barrett & Barrett (1982), as modified by Bostock et al. (1991b).

Does threshold reflect membrane potential?

Under many circumstances, threshold varies appropriately with membrane potential: threshold rises and its reciprocal (excitability) falls when axons are hyperpolarized; threshold decreases and excitability increases when they are depolarized (as in Fig. 2C, trace a). However, ischaemia changes the accommodative properties of axons (Kugelberg, 1944; Bostock et al. 1991a) and, following its release, the pattern of threshold change varies with the type of test stimulus (brief, long or triangular; see Bostock et al. 1991a). To a large extent, these changes in accommodation are due to internodal mechanisms. The data in Fig. 9A and B also suggest a non-linearity in the relationship between threshold and membrane potential during ischaemia. Clearly, the near-linear relationship between the excitability indices and the reciprocal of threshold (Fig. 3) does not imply a similar relationship to membrane potential. These reservations need to be kept in mind when extrapolating from ‘threshold dependence’ to ‘voltage dependence’. Accepting this, there were unexpected findings, not readily explained on the basis of existing data, as discussed below.

Effects of polarizing currents on strength-duration time constant

The strength-duration time constant is a nodal property, dependent only on threshold measurements using test stimuli of different duration, and its relationship to excitability is due to a threshold conductance, probably mediated through ‘persistent’ Na⁺ channels (Bostock & Rothwell, 1997). That the relationship between time constant and excitability did not change during and after ischaemia suggests that the voltage dependence of these channels was not altered by ischaemia. Importantly, it provides an unaltered control which supports the view that the changes in the relationships for the other indices involved factors additional to the change in membrane potential.

Effects of polarizing currents on refractoriness

Ischaemia enhanced refractoriness by much more than would be expected for the increase in axonal excitability. This disproportionate increase in refractoriness could not be reproduced using a continuous depolarizing current ramp to change membrane potential (Fig. 10). Accordingly, it cannot be attributed to a voltage-dependent slow process, such as slow Na⁺ channel inactivation.

Refractoriness is generally accepted to represent recovery from Na⁺ channel inactivation (Hodgkin & Huxley, 1952), and the present results raise the possibility that ischaemic processes or metabolites interfere with the process of recovery from inactivation. It is therefore relevant that the inactivation gate is located on the intracellular side of the Na⁺ channel, where it would be more vulnerable to an intracellular metabolic disturbance (Patlak, 1991). In addition to increasing ‘resting’ refractoriness, ischaemia altered the slope of the relationship with excitability. The change in slope depended on the direction of the polarizing sequence, and again this is consistent with the accumulation of a voltage-sensitive product of ischaemia interfering with the processes responsible for refractoriness.

Ischaemia increases [Ca²⁺]_i in both optic nerve and peripheral axons (Stys et al. 1992; Wachtler et al. 1996), and this could affect Ca²⁺-dependent K⁺ channels, which have been identified in human axons (Scholz et al. 1993). Similarly, a reduction in intracellular ATP during ischaemia would allow opening of ATP-sensitive K⁺ channels (Jonas et al. 1991), and an increase in [Na⁺]_i would activate Na⁺-dependent K⁺ channels. These effects would increase K⁺ fluxes and might help compensate for failure of the pump during ischaemia, but it is difficult to see how this would alter the relationship between refractoriness and excitability. However, in voltage-clamped anoxic axons, Brismar (1981) reported a shift of the relationship between Na⁺ channel inactivation and membrane potential to more negative values, a finding that could explain the greater refractoriness during ischaemia in the present study. The mechanism of this shift was not elucidated, but presumably it reflects susceptibility of the inactivation mechanism of the Na⁺ channel to intracellular disturbances.

Post-ischaemic effects of polarizing currents on supernormality

The data for ‘supernormality’ during ischaemia probably reflect not the processes that normally underlie supernormality but instead the growth of refractoriness into conditioning-test intervals which, at rest, are associated with supernormality. On the other hand, supernormality was enhanced in the post-ischaemic period, as would be expected when axons are hyperpolarized by the electrogenic Na⁺-K⁺ pump, driven to restore ionic balance across the axonal membrane. With hyperpolarization, voltage-dependent channels in the paranodal region will close, increasing membrane resistance and the size of the depolarizing after-potential (Barrett & Barrett, 1982). The relationship between supernormality and excitability is largely due to the voltage dependence of these channels, particularly fast K⁺ channels (Baker et al. 1987; David et al. 1995; see Ritchie, 1995). The decreased slope of the relationship between supernormality and excitability after release of ischaemia would be consistent with decreased voltage dependence of paranodal K⁺ channels. This, with the enhanced resting supernormality, is consistent with these channels being rendered relatively ineffective, requiring a longer polarizing current than usual to restore their voltage dependence.

Ischaemia can block K⁺ channels, but this has been demonstrated only when axons are hyperglycaemic as well as hypoxic (Schneider et al. 1993; Grafe et al. 1994). The block is due to intracellular acidosis, and a comparable phenomenon would explain the present findings, despite the fact that the subjects were not hyperglycaemic and that the effects were seen following release of ischaemia rather than during ischaemia.

Conclusions

In summary, the present study provides support for the view that the changes in axonal excitability during ischaemia and after its release are not due solely to changes in membrane potential. During ischaemia, there is disproportionately greater refractoriness and, after release of ischaemia, the slope of the relationship between supernormality and excitability is flatter. The former could be due to interference with the recovery from inactivation of Na⁺ channels by some intracellular metabolic disturbance created by ischaemia. The latter could be due to blockage of paranodal K⁺ channels, which limit the depolarizing after-potential and thereby determine the voltage dependence of supernormality. In addition, there was evidence that charging of the internodal capacitance can take many tens of milliseconds, a finding consistent with the Barrett-Barrett model of electrical excitability of myelinated axons and the mechanisms responsible for the depolarizing after-potential and supernormality.