The most direct point has long been obvious, namely that changes in the excitability of the spinal motoneurone pool can greatly affect the size of the EMG response evoked by a given cortical stimulus. The modelling, however, extends appreciation of the complex behaviour of the MNs as their mean level of activity varies. In particular, it emphasizes the role of stimulus size and this may already have led to confusion. Brouwer et al. (1989), for example, suggested that fine movements generating little force engage the motor cortex more strongly than cruder forcible contractions of the same muscle, because the cortical response in a unitary PSTH decreased when the contraction increased. Their control H reflex remained the same, but it unfortunately happened to be much smaller than the cortical responses; thus the MNs may have behaved in the way illustrated in Fig. 4 and responded differentially to different sized stimuli.
Much, however, can still be done using the gross EMG especially when an input-output plot of EMG response against cortical stimulus strength is determined for each condition studied, rather than relying upon a single observation (Devanne et al. 1997; Ridding & Rothwell, 1997). Unlike the unitary model (Fig. 3) the experimentally observed overall input-output curve shows a striking increase in slope with voluntary contraction, which can thus be attributed to population effects, presumably for the cortical as well as the motoneuronal pools. Imagine, for example, a population of MNs with regularly spaced thresholds, extending to infinity, all with the same stimulus and background drive. With the onset of firing the number of silent MNs responding to the stimulus will remain unchanged and give the same response as the quiescent pool, as fresh MNs are recruited within range of the stimulus; but to this must be added the response of the newly firing MNs, thereby producing an increase of slope. Different muscles will vary in the distribution of thresholds etc. of their constituent motor units so if population properties are responsible, then the increase of slope with contraction could be expected to vary between muscles as is indeed found, with elbow flexors showing much larger increases than hand muscles (Taylor et al. 1997; Abbruzzese et al. 1999). Devanne et al. (1997) likewise attributed the slope change to population effects, and surveyed the factors involved.
Next, given the behaviour of the MN, it becomes quite unjustifiable to assume that the overall descending response evoked by a given cortical stimulus (i.e. ‘excitability’) will always increase monotonically as the corticospinal neurones are brought by some manoeuvre (such as making a voluntary contraction) first to threshold and then to increase their firing rate. Any response evoked from an individual corticospinal neurone by excitation of its pacemaker, whether by presynaptic activity or extrinsic current, must be suspected to remain constant over part of the range or decrease, and for the effect of firing rate to vary with stimulus size. Like the motoneurone, the tonic firing of corticospinal neurones is regulated by a moderately prolonged post-spike recovery process (Takahashi, 1965; Reyes & Fetz, 1993a) so the present modelling of neuronal behaviour is potentially applicable. As discussed for the MN, the overall descending response evoked by transcranial stimulation will also depend upon the distribution of firing thresholds etc. of the population of excited neurones; given the difference in their ‘targets’, rate coding rather than recruitment may be suspected to be the relatively more important for corticospinal neurones which would stabilize the ‘excitability’ of the motor cortex as its activity increased.
It is, of course, already widely recognized that the level of cortical activity does not affect D wave responses evoked by electrical stimulation, since these normally depend upon the excitation of axons (Rothwell et al. 1991). However, most workers appear to assume that magnetically determined ‘excitability’ normally increases monotonically with increasing activation of corticospinal neurones, including when they are firing (Datta et al. 1989). Exceptionally, Baker et al. (1995) cautioned that their findings with transcranial magnetic stimulation (TMS) ‘implied that the period of maximum cortical susceptibility to TMS may not coincide with the period of maximum corticospinal cell activity’, since during precision grip the maximum size of the directly recorded D wave in the monkey failed to coincide with the highest rate of corticospinal firing as known from earlier recordings.
There are, however, two major complications about the behaviour of the individual corticospinal neurone. First, magnetic stimulation evokes a repetitive corticospinal discharge with an initial D wave followed by one or more sharply timed I waves. The I waves are probably due to subsequent synaptic excitation following direct excitation of interneurones and/or presynaptic terminals; they are notably absent on intracellular stimulation of a single neurone (Reyes & Fetz, 1993a), and so do not affect the modelling of the corticospinal neurone per se. Second, an intracellular stimulus delivered during the middle third of the interspike interval can initiate a slow regenerative process which may then trigger a delayed spike (Reyes & Fetz, 1993a), totally distinguishable from the I wave by its long and variable latency and contrasting with the synchronized spikes elicited by stimulation later in the cycle. Such delayed spikes will thus make no contribution to the initial peak in the PSTH as currently modelled or to the corresponding cortically evoked EMG response in life, though the underlying regenerative process might sensitize the neurone to subsequent I wave excitation. Thus detailed modelling of the overall response to cortical stimulation is not currently feasible. However, the view that the ‘excitability’ of corticospinal neurones does not increase with their firing rate is validated by findings of Reyes & Fetz (1993b) with intracellular stimulation of single neurones in cortical slices. This should apply to both D and I responses elicited by transcranial stimulation, presuming that any cortical interneurones involved with the I wave behave like those studied; I waves dependent upon stimulation of axons (as discussed below) simply re-test the excitability of neurones to a synaptic input shortly after conditioning them with a direct ‘magnetic’ stimulus.
The important work of Reyes & Fetz (1993a, b) requires further detailed comment as it seems to have been overlooked by those involved in cortical stimulation and its applicability is not immediately obvious. They themselves were unconcerned with such issues, never presented a PSTH, and tailored their analysis to their particular needs by computing an average ‘shortening-delay plot’. This clouds the situation for present purposes, particularly because with weak stimuli delivered near the end of the interspike interval (ISI) there can then be ‘an artificial lengthening of the ISI where there may have actually been an ISI shortening’ (1993a). Nonetheless, their Fig. 5 (1993b) clearly indicates that with a large stimulus the synchronized response remained the same for firing rates of 12, 28 and 49 Hz, while their Fig. 6D shows that the overall response (predominantly consisting of synchronized rather than delayed spikes) was likewise invariant. They specifically concluded that the average stimulus-induced increase in firing rate (synchronized + delayed spikes) ‘did not vary with the baseline firing rate’ for frequencies of 8-70 Hz.
Finite cortical threshold suggests magnetic stimulation excites axons
The final conclusion from the modelling is that the rather high threshold for magnetic stimulation applied during voluntary contraction has clear implications for its site of action. First, however, it is necessary to strip away any uncertainties about the relation between the output dial reading on a standard stimulator (such as those made by Magstim, UK) and the stimulus received by any individual element within the cortex, such as a corticospinal neurone. The dial reading simply gives the voltage applied to the element on a linear scale starting from zero (confirmed with Dr M. Polson of Magstim). The scaling factor will depend upon a variety of factors and will differ for every individual neurone and axon. This is physics, leaving the occurence of a threshold for excitation to physiology; the current does not spread deeper to reach new structures with increase of stimulus strength, it simply becomes larger everywhere.
Since this does not seem to be always recognized it becomes desirable to explain the underlying basis, so that the force of the present argument can be appreciated. The stimulator acts by discharging a capacitor through a coil to create a changing magnetic field which then induces a voltage gradient in the underlying brain tissue. The spatial distribution of the voltage field, and likewise the resulting current flow, is remarkably complex, largely because the brain is so electrically inhomogeneous. This makes it impossible to predict the absolute value of the stimulus at any point. However, the waveform of the discharge current that induces the magnetic field remains fixed when the output of the stimulator is changed (Barker et al. 1991), so that the waveform of the magnetic flux change and of the resulting induced voltage also remain the same. The maximum value of each is directly proportional to the output reading of the stimulator, which gives the initial voltage on the discharge capacitor as a percentage of the maximum available (Dr M. Polson, Magstim, personal communication). Thus any individual cortical neurone or axon receives an electrical stimulus of constant pulse shape and fixed spatial distribution; its magnitude is directly proportional to the stimulator reading, starting from zero. Of course, every cell body and axon will have its own constant of proportionality, relating degree of excitation to dial reading, and this will depend upon its shape, where it lies, how it is orientated and so on, as well as its chronaxie. Thus predicting the behaviour of a population is currently impossible, although the behaviour of every individual within it is basically simple.
The appreciable cortical threshold required to evoke a response from a non-contracting muscle tells one nothing about what is happening in the cortex, since the silent MN pool has a threshold and an appreciable descending volley is required to evoke a discharge; repetitive descending activity may be particularly effective. However, firing MNs should give a response to the weakest input (see Fig. 3), so even a weak stimulus should affect their discharge the moment they start firing, with the background noise level limiting the EMG detectability of the occurrence of an evoked corticospinal volley. Likewise, if the stimulus were to directly excite discharging corticospinal neurones which acted monosynaptically on the discharging motoneurones, then both should respond with the weakest input and the threshold should be close to zero. In fact, as numerous recordings testify, the threshold for cortical stimulation remains high during voluntary contraction, only slightly reduced from the value obtained with relaxation.
In the curves of Devanne et al. (1997), for example, the EMG response rises from zero to maximum on increasing the stimulus from 45 to 60 for tibialis anterior and from 30 to 40 for first dorsal interosseus (values = percentage maximum output during 40 % MVC; a similar threshold is observed for sample discharging single motor units). This mirrors the behaviour of the silent MN in Fig. 3 and strongly suggests that the stimulus is first acting on a cortical element which itself has a definite threshold. There seems little doubt that many of the relevant corticospinal neurones do discharge during voluntary contraction (Porter & Lemon, 1993), thereby excluding their pacemakers as the site of action of the stimulus. Different corticospinal neurones will, of course, have different scaling factors in relation to stimulator setting, but the input-output relation for their summed discharge should still start from zero and increase approximately linearly; recruitment of non-firing corticospinal neurones with an increase of stimulus strength would give an upward inflection to the plot. Likewise, the stimulus is unlikely to act via the cell bodies of nearby neurones whose terminals then excite the corticospinal neurones; many of these can also be expected to be firing during voluntary contraction. However, a variety of axons terminate on corticospinal and other cortical neurones and would have a definite threshold under all conditions, and one remaining unchanged during voluntary contraction. Thus the present modelling firmly suggests that transcranial magnetic stimulation acts on axons and their terminals rather than on the various pacemakers of the neurone.
It is notable that the originators of magnetic stimulation drew essentially the same conclusion (Barker et al. 1991), without particularly emphasizing its significance, when they investigated the effect of varying the time course of the magnetic stimulus. They used a complex variant of the classical strength-duration curve to estimate the ‘cortical membrane time constant’ for activation of the relaxed abductor digiti minimi. The particular value obtained (150 μs) may well be open to question. The important thing is that the value was the same as that obtained when the ulnar nerve was stimulated in the arm, evoking an EMG in the same muscle. If cortical stimulation directly activated neurones rather than axon terminals then the cortical value should have been appreciably larger, assuming that the pacemaker of the cortical neurone (presumably its initial segment) is sufficiently well-coupled electrically to the cell body for the neuronal rather than the axonal chronaxie (time constant) to apply.
In accordance with all this Di Lazarro et al. (1998) recently suggested that the I waves elicited by magnetic stimulation depend upon the activation of axons rather than cell bodies, when they found little or no change during contraction in I wave threshold in their epidural recordings of the massed descending I wave activity. However, the site of origin of any magnetically evoked D wave remains controversial. Its continued high threshold during contraction suggests that in conscious man it also arises from excitation of axons (whether pre- or post-synaptic). Likewise, the threshold for D wave induced facilitation of the H reflex also remains high during contraction, unchanged from its resting value (Mazzocchio et al. 1994), and there is no change with contraction in the small high-threshold D waves recorded epidurally (Di Lazarro et al. 1998). In the conscious monkey, however, the magnetically evoked and directly recorded D wave varies with the level of anaesthesia and during the course of a precision grip (Baker et al. 1994, 1995), and in unconscious humans reduction of anaesthesia can increase the D waves produced by magnetic stimulation (Burke et al. 1993). Thus it seems premature to generalize, since what happens may depend upon variants in the stimulating conditions and how the D wave is characterized.
In conclusion, the present model neglects the detailed complexity of the MN but has sufficed to emphasize that the apparently simple concept of ‘excitability’ needs to treated with extreme care when it is extrapolated from quiescent neurones to those that are already firing. The modelling was performed for spinal motoneurones, but corticospinal neurones can be expected to show related non-linearities. Study of real neurones under a comparably wide range of conditions would now seem highly desirable to check their actual behaviour and confirm the applicability of the modelling.