In 1970, Bergmans demonstrated that single human motor axons could often be studied non-invasively by selective electrical stimulation . He defined the threshold of an axon as the lowest stimulus that would excite it reliably, and found that considerable information about the membrane properties of the axon could be inferred from measurements of the changes in threshold induced by impulse activity or by artificial membrane polarization. Threshold determination is a trial-and-error process. In 1979, Raymond described a feedback circuit for automatic determination of axonal thresholds . For single axons, ‘threshold' can be estimated as the stimulus current that activates the axon in 50% of the trials. In clinical practice, threshold is best determined using a computer to control the output of a current source, depending on the response (compound sensory or motor action potential) of the nerve axons stimulated. The computer is set to determine the stimulus current needed to produce a target potential of a defined percentage of the maximal compound action potential. It is not possible to measure membrane potential in intact human axons, but it is possible to obtain indirect evidence about membrane potential by studying excitability indices that are dependent on membrane potential [3,4].
Indices of membrane potential
Each of the indices below can be altered by factors other than membrane potential, but it is a reasonable conclusion that membrane potential is different when these indices undergo changes in the appropriate direction and to the appropriate extent.
During many acute manoeuvres, the stimulus current required to activate an axon or to produce a compound action potential of a defined size can be used as a marker of membrane potential. As the membrane depolarizes, the threshold current necessary to produce the target response decreases. If the membrane is hyperpolarized, the stimulation intensity to achieve the target response increases. Since threshold varies between subjects due to anatomical factors, the resting threshold does not provide information about resting membrane potential. Such information can instead be obtained by comparing the threshold before and after a conditioning nerve impulse, or before and during the application of depolarizing or hyperpolarizing current (see section Threshold electrotonus). It has to be added that changes in membrane excitability do not parallel changes in membrane potential when the membrane is strongly depolarized, since membrane depolarization not only reduces the voltage change to activate sodium channels but also inactivates sodium channels and therefore reduces the number available to pen during an action potential. Hence, progressive depolarization leads initially to a reduction in threshold, but beyond a level of maximal reduction the threshold increases, resulting finally in depolarizing block.
Absolute refractoriness cannot be measured in subjects because there is a limitation on the stimulus intensity that can be delivered to a subject. Relative refractoriness can be measured either by determining the increase in stimulus intensity required to produce the target response at a fixed conditioning-test interval, or as the duration of the relative refractory period [4,5]. Refractoriness changes with membrane potential because it alters sodium channel inactivation. It is generally assumed that, at resting membrane potential, some 30% of sodium channels are inactivated. Hyperpolarizing shifts in membrane potential remove this resting inactivation and decrease the extent of refractoriness. In contrast, nerve membrane depolarization will increase refractoriness. Refractoriness is extremely sensitive to temperature, which has to be taken into account for the interpretation of measurements .
When a node of Ranvier depolarizes to produce an action potential, current is stored on the internodal membrane and discharged through high-resistance pathways under or through the myelin. This produces the negative afterpotential that is responsible for the phase of supernormal excitability [7,8]. The extent of supernormality varies with membrane potential because this alters the resistance of the paranodal membrane (by voltage-dependent effects on paranodal potassium channels) . However, factors that alter myelin resistance (such as paranodal demyelination) should also alter the extent of supernormality. Hyperpolarization increases the internodal membrane resistance and therefore increases the extent of supernormality .
Strength-duration time constant
Strength-duration time constant is a measure of the rate at which the threshold current for a target potential declines as the stimulus duration is increased. Rheobase is the threshold for a stimulus that can be infinitely long. Both are properties of the nodal membrane. Depolarization of the node will produce a longer strength-duration time constant and lower rheobase. Persistent sodium currents make an important contribution to both indices .
The technique called ‘threshold electrotonus', in which excitability changes are measured during and after the application of 100-500 ms-duration subthreshold polarizing currents, provides evidence for slow potassium currents and hyperpolarization-activated currents in human axons in vivo [4,11]. During depolarization the changes in excitability are less at the end of polarizing currents (i.e. there is a ‘fanning-in' of threshold electrotonus waveforms), whereas in hyperpolarized fibres the changes in excitability are relatively greater (‘fanning-in'), mainly due to the voltage dependence of fast and slow potassium currents. Of all the excitability parameters tested by Kiernan and colleagues , the best indicator of changes in membrane potential was the threshold change at the end of a 100 ms depolarizing current that was set to 40% of the resting threshold current.
Assessing excitability parameters in human beings
A highly efficient computer program has been developed for measuring multiple excitability measures (MEM) of human motor axons in only 10 min  or of sensory axons in about 16 min [12,13]. MEM comprise the components of the recovery cycle after an impulse (refractoriness, superexcitability and late subexcitability), the strength-duration time constant and the changes in excitability induced by long-lasting subthreshold current pulses (threshold electrotonus, current-threshold relationship) (Fig. 1). This new technique has the potential to provide considerable information about the altered state of nerve membranes in disease, which cannot be obtained by any other technique. MEM have the advantage over conventional nerve conduction studies in that they are highly sensitive to changes in membrane potential , and they can also provide information about the altered function of different ion channels . The procedures are non-invasive and usually painless, allowing serial measurements to be made on each patient.
Detailed recording protocol
Nerve action potentials are recorded, e.g. from the abductor pollicis brevis muscle or from sensory nerve fibres of the median nerve, using surface electrodes, with the active electrode at the motor point and the reference electrode on the proximal phalanx. Stimulus waveforms generated by a computer are converted to current with an isolated linear bipolar constant current stimulator (maximum output ± 50 mA). The stimulus currents are applied via non-polarizable electrodes, with the active electrode over the median nerve at the wrist and reference electrode ˜10 cm proximal over muscle. Test current pulses of 0.2-1 ms are applied at 0.8 s intervals, and combined with suprathreshold conditioning stimuli or subthreshold polarizing currents as required. The polarizing, conditioning and test current pulses are all delivered through the same electrodes. The amplitude of the action potential is measured from baseline to negative peak. For all tracking studies, the target action potential is set to 40% of the maximal action potential. Skin temperature is monitored over the median nerve close to the site where axonal excitability is tested.
Stimulus-response curves are recorded for test stimuli of 1 ms duration. The stimuli are increased in 6% steps, with two responses averaged for each step, until three averages are maximal. A target response is then set at 40% of the maximum and the 1 ms test stimuli adjusted automatically by the computer to maintain this peak amplitude. The test stimulus amplitude required to excite the target response is regarded as the threshold current for axons recruited at this level of response. ‘Proportional tracking' is used whereby the change in stimulus amplitude from one trial to the next is made proportional to the ‘error', or difference between the last response and the target response . The slope of the stimulus-response curve is used to set the constant of proportionality and to optimize the tracking efficiency.
The strength-duration relationship for the nerve is measured by comparing the threshold current for a 1 ms test stimulus to the threshold current for the stimuli of 0.8, 0.6, 0.4 and 0.2 ms duration. A plot of stimulus charge (current × duration) against duration (Fig. 1d) gives a straight line, which crosses the x-axis where x = minus the strength-duration time constant. Threshold electrotonus  (Fig. 1a) is then measured by recording the changes in threshold induced by 100 ms polarizing currents, set to ±20% and ±40% of the control threshold current. Five stimulus conditions are tested in turn: test stimulus alone (to measure the control threshold current) and test stimulus plus each of the four levels of polarizing current. Threshold is tested at up to 26 time points (maximum separation 10 ms) before, during and after the 100 ms conditioning currents. The current-threshold relationship (Fig. 1b) is tested with 1 ms pulses at the end of 200 ms polarizing currents, which are altered in 10% steps from +50% (depolarizing) to −100% (hyperpolarizing) of the control threshold. Stimuli with conditioning currents are alternated with test stimuli alone. The recovery of excitability following a supramaximal conditioning stimulus (Fig. 1c) is tested at 18 conditioning-test intervals, decreasing from 200 ms to 2 ms in geometric progression. Three stimulus conditions are tested in turn: (i) unconditioned 1 ms test stimulus to track the control threshold; (ii) 1 ms supramaximal conditioning stimulus; and (iii) conditioning plus test stimuli. The response to (ii) is subtracted on-line from the response to (iii) before the test action potential is measured, to avoid contamination of the test action potential by the conditioning one when the conditioning-test interval is short.
Clinical studies using multiple excitability measurements
Initial clinical studies with MEM have shown the power of this new method to provide new information about neuropathies. The sensitivity to membrane potential has provided good evidence that axons in multifocal motor neuropathy are hyperpolarized distal to the lesion, as in a post-ischaemic nerve, and this unexpected finding suggests that the axons are depolarized at the site of block . In contrast, a study of patients with chronic renal failure showed that most had depolarized axons . The membrane depolarization was closely related to hyperkalemia, but not to serum levels of other electrolytes, urea or creatinine. Moreover, uraemic patients with normal serum potassium had normal nerve excitability properties. This study led to a new hypothesis that membrane depolarization due to hyperkalemia may be an under-appreciated cause of neuropathy in these patients . In another study, it was found that taxol/cis-platin anti-cancer chemotherapy caused changes in threshold electrotonus suggestive of membrane depolarization, well before any clinical signs or symptoms of neuropathy .
Furthermore, MEM can provide information about other pathological changes in nerve apart from changes in membrane potential. Kanai and colleagues  found an increase in strength-duration time constant in patients with Machado-Joseph disease who suffered from painful cramps. Since strength-duration time constant and nerve excitability are increased by persistent sodium currents, they treated the patients with the sodium channel blocker mexiletine. The cramps were abolished in all patients treated and the strength-duration time constants were partially normalized. Other qualitatively distinct changes in nerve excitability properties have been reported in amyotrophic lateral sclerosis [19,20], diabetic neuropathy , acquired neuromyotonia , Charcot-Marie-Tooth disease Type 1A  and in patients paralysed with puffer fish intoxication (tetrodotoxin) .
Nerve excitability changes in critical illness polyneuropathy
Using nerve excitability testing, we recently provided evidence that axons are depolarized in critical illness polyneuropathy patients , to a similar degree as was previously reported in patients with chronic renal failure . It seems reasonable to hypothesize that this membrane depolarization may lead to neuropathy in these patients, as it has previously been suggested in uraemic neuropathy [15,25]. The suggestion is that chronic membrane depolarization interferes with mechanisms of ionic homeostasis (e.g. Na+/Ca2+ exchange) essential for cellular viability. Altered nerve function with preserved nerve structure has been reported in early nerve biopsies, and altered structure and function in late biopsies . This finding would be consistent with ‘invisible' membrane depolarization preceding structural damage. The excitability measurements also provided some interesting clues as to the likely mechanisms underlying membrane depolarization: Correlations with serum factors suggest that this membrane depolarization is related to endoneurial hyperkalemia and/or hypoxia .
W. J. Z. was supported by a fellowship from the Swiss National Science Foundation.
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