Negative myoclonus induced by cortical electrical stimulation in epileptic patients

doi:10.1093/brain/awh661 Brain (2005) of 17

Negative myoclonus induced by cortical electricalstimulation in epileptic patients

Guido Rubboli,1 Roberto Mai,2 Stefano Meletti,1 Stefano Francione,2 Francesco Cardinale,2

Laura Tassi,2 Giorgio Lo Russo,2 Michelangelo Stanzani-Maserati,1 Gaetano Cantalupo1

and Carlo Alberto Tassinari1

1Department of Neurological Sciences, Bellaria Hospital, University of Bologna, Bologna, and 2Epilepsy Surgery Center‘C.Munari’, Niguarda Hospital, Milan, Italy

Correspondence to: Guido Rubboli, MD, Department of Neuroscience, Bellaria Hospital, Via Altura, 3–40139 Bologna, ItalyE-mail: [email protected]

Negative myoclonus (NM) is a motor disorder characterized by a sudden and abrupt interruption of muscularactivity. The EMG correlate of NM is a brief (<500 ms) silent period (SP) not preceded by any enhancement ofEMG activity (i.e. myoclonus). This study investigated the role of premotor cortex (PMC), primary motorcortex (MI), primary somatosensory area (SI) and supplementary motor area (SMA) in the pathophysiology ofcortical NM by means of intracerebral low frequency (1 Hz) electrical stimulation. In three drug-resistantepileptic patients undergoing presurgical evaluation, we delivered single electric pulses (stimulus duration: 3 ms;stimulus intensity ranging from 0.4 to 3 mA) to PMC (2 patients), MI (1 patient), SI and SMA through stereo-EEG electrodes; surface EMG was collected from both deltoids. The results showed that (i) the stimulation ofPMC or MI could evoke a motor evoked potential (MEP) either at rest or during contraction, in this latter casefollowed by an SP; however, in two patients, at the lowest stimulus intensities (0.4 mA), 50% of stimuli couldinduce a pure SP, i.e. not preceded by an MEP; raising the intensity of stimulation (0.6 mA), the SPs showed anantecedent MEP in >80% of stimuli; (ii) the stimulation of SI at low stimulus intensities (from 0.4 to 0.8 mA)induced in two patients only SPs, never associated with an antecedent MEP, whereas in the third subject the SPscould be inconstantly preceded by an MEP; by incrementing the stimulus intensity (up to 3 mA), in all threepatients the SPs tended to be preceded, although not constantly, by an MEP; stimulus intensity affected SPduration (i.e. the higher the intensity, the longer the SP), without influencing the latency of onset of the SPs;(iii) the stimulation of SMA induced only pure SPs, at all stimulus intensities up to 3 mA; as for SI, increment ofstimulus intensity was paralleled by an increase in SP duration, without influencing the onset latency of SPs. Weconclude that single electric pulse stimulation of PMC, MI, SI and SMA through stereo-EEG electrodes caninduce pure SPs, not preceded by an MEP, which clinically appear as NM, suggesting therefore that thesecortical areas may be involved in the genesis of this motor phenomenon. However, it must be pointed out thatSMA stimulation induced only pure SPs, regardless of the stimulus intensity, whereas occurrence of pure SPsfollowing stimulation of PMC, MI, and SI depended mainly on the intensity of stimulation.

Keywords: negative myoclonus; silent period; supplementary motor area; primary somatosensory cortex; intracerebralelectrical stimulation

Abbreviations: DCR = direct cortical response; MEP = motor evoked potential; NM = negative myoclonus; NMA = negativemotor area; MI = primary motor area; PMC = premotor cortex; PNP = primary negative potential; SI = primary somatosensoryarea; SMA = supplementary motor area; SP = silent period; TMS = transcranial magnetic stimulation

Received December 2, 2004. Revised July 18, 2005. Accepted September 19, 2005

IntroductionSudden, irregular lapses in the maintenance of postural tone

were described in patients with hepatic encephalopathy by

Adams and Foley (1949) under the term of asterixis. Lance

and Adams (1963) reported lapses of postural control in the

post-anoxic intention myoclonus syndrome as a result of a

muscular silent period (SP), preceded or not by myoclonus,

in relation to a spike and slow wave complex. Periods of

muscular inhibition, strictly and only related to a diffuse or

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focal spike, without preceding myoclonia, were defined as

‘spike-related epileptic silent periods’ (Tassinari et al.,

1968; Tassinari, 1981). The catching term ‘negative

myoclonus’ (NM), introduced by Shahani and Young

(1976), encompass all the above-mentioned phenomena,

and extends this definition to any brief, jerky interruption

of tonic muscular activity, which causes a sudden postural

lapse. As such, NM is an aspecific motor disorder that can be

observed in a variety of physiological as well as pathological

conditions. The EMG correlate of NM is a brief (<500 ms)

muscular SP not preceded by any enhancement of EMG activ-

ity (Blume et al., 2001). Epileptic NM is defined as an inter-

ruption of tonic muscular activity, time-locked to a spike on

the EEG, without evidence of an antecedent myoclonia

(Tassinari et al., 1995). Although pathophysiology of NM

is still incompletely understood, cortical as well as subcortical

mechanisms are admitted (Obeso et al., 1995; Toro et al.,

1995; Tassinari et al., 1995, 1998; Shibasaki, 2002). Regarding

the cortical areas mediating NM, some evidences suggest a

role of the perirolandic cortex (Ugawa et al., 1989; Artieda

et al., 1992; Aguglia et al., 1995), whereas studies on epileptic

NM showed that this phenomenon may be associated with

epileptic activity in premotor cortex (PMC), including the

supplementary motor area (SMA) (Rubboli et al., 1995;

Baumgartner et al., 1996; Meletti et al., 2000), or in post-

central somatosensory cortex (Tassinari et al., 1995;

Noachtar et al., 1997).

Negative motor areas (NMA) have been identified in

the lateral aspects of the frontal lobe (primary NMA) and

in the frontomesial regions encompassed in the SMA

(‘supplementary NMA’) (Luders et al., 1987, 1995; Lim

et al., 1994). In epileptic patients undergoing presurgical

evaluation, high frequency (50 Hz) cortical electrical stimu-

lations of NMA through subdural electrodes produced

sustained negative motor responses such as motor arrest,

inability to perform a voluntary movement or to maintain

a voluntary muscular contraction (Penfield and Welch, 1949,

1951; Luders et al., 1987, 1995; Fried et al., 1991; Lim et al.,

1994; Hanakawa et al., 2001). On the basis of these findings, it

has been hypothesized that NMA can play a role in the patho-

physiology of cortical NM (Tassinari et al., 1995; Baumgartner

et al., 1996). This view has been challenged by other authors

(Werhahn and Noachtar, 2000), who pointed out that the

negative motor responses elicited by high frequency cortical

stimulation were sustained and developed gradually over sec-

onds, at variance with NM, which is a brief (<500 ms) (Blume

et al., 2001) and sudden event; on the other hand, at present,

no evidence that either repetitive (50 Hz) or single electric

shock stimulation of NMA can induce brief, phasic SP such

as in NM has been reported.

The aim of our study was to investigate the possible role of

the PMC, the primary motor cortex (MI), the primary soma-

tosensory area (SI) and the SMA in the generation of NM

by delivering single electric pulses intracortically through

intracerebral stereotaxic EEG (stereo-EEG) electrodes, during

low frequency (1 Hz) electrical stimulation (Munari et al.,

1993; Kahane et al., 1993), performed in drug-resistant epi-

leptic patients undergoing functional cortical mapping for

presurgical evaluation. We report evidences showing that sin-

gle electric shocks delivered to PMC, MI and SI can induce

brief contralateral ‘pure’ SPs, i.e. not preceded by a motor

evoked potential (MEP), depending mainly on the intensity of

stimulation: in fact, by increasing stimulus intensity,

the SPs tended to be preceded by an MEP. On the contrary,

single pulse stimulation of the SMA produced only pure

SPs, i.e. never preceded by an MEP, regardless of stimulus

intensity. We discuss the implications of our findings in the

pathophysiology of cortical NM.

Materials and methodsWe studied three patients (two females and one male; age range

13–32 years) with drug-resistant partial epilepsy undergoing presur-

gical evaluation for epilepsy surgery. Clinical features of the patients

are reported in Table 1. Brain MRI (1.5 T) was unremarkable in

Patients 1 and 3; in Patient 2, who suffered from post-traumatic

epilepsy, it showed atrophy of the right frontal pole, extended to the

right frontal horn, and gliosis of the corresponding white matter.

All three patients first underwent long-term video-EEG monitor-

ing to record their spontaneous seizures. The data provided by video-

EEG recordings were not considered sufficient to proceed to surgery;

therefore, a video-stereo-EEG evaluation was judged necessary to

define the cerebral structures involved in the onset and propagation

of seizure activity. Furthermore, the video-stereo-EEG procedure, in

addition to recording intracranially spontaneous seizures permits

Table 1 Clinical features of the patients

Patient 1 (30/F) Patient 2 (32/M) Patient 3 (13/F)

Age (years) at epilepsy onset 13 22 9Seizure type Non-convulsive status 6 SG Left focal motor 6 SG Speech arrest, left limbs

tonic-dystonic posturingSeizure frequency Weekly 4–6/month DailyInterictal scalp EEG Vertex theta activity

associated with spikesRight frontocentral slowwaves and spikes

Right frontocentral slowwaves and spikes

Brain MRI Unremarkable Atrophy and gliosis of theright frontal pole extendedto the right frontal horn

Unremarkable

Neurological examination Unremarkable Unremarkable UnremarkableCurrent treatment CBZ, PB CBZ, PB, CNZ CBZ, TPM

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performance of high frequency, (50 Hz) electrical stimulation and

low frequency (1 Hz) electrical stimulation whose purposes are,

respectively, to elicit some or all of the electroclinical seizures,

and to map functionally eloquent cortical areas. Informed consent

was obtained from all patients after the type and the purposes of the

procedures were explained.

The stereo-EEG procedures were performed according to the

Sainte-Anne School in Paris (Bancaud et al., 1965; Talairach et al.,

1974; Munari et al., 1994) at the ‘C.Munari’ Epilepsy Surgery Center

at Niguarda Hospital in Milan. All three patients were chronically

implanted with semi-rigid platinum/iridium depth electrodes

(0.8 mm in diameter) (DIXI, Besancon, France), featuring 5–15

contacts, 2 mm long and 1.5 mm apart. The number of the

electrodes, their entry points and the target cerebral structures,

were established on the basis of the clinico-EEG features of the

seizures recorded during long-term video-EEG monitoring; anatom-

ical landmarks (i.e. cerebral vessels) might represent additional con-

straints partially influencing the choice of the electrode entry point

and trajectory to reach a specific target structure. For the aim of this

study, we selected those patients in whom the stereo-EEG evaluation

required the exploration of motor areas (either MI or PMC), SI and

SMA. Patient 1 was studied with 20 electrodes exploring bilaterally

homologous lateral and mesial frontoparietal cortices (Fig. 1).

Patient 2 was implanted with 14 electrodes that explored both the

convexity and the mesial aspects of the right frontal and parietal

lobes, and the anterior portion of the right temporal lobe (Fig. 2).

Fig. 1 Stereotaxic schemes of Patient 1 and MRI images illustrating the trajectories of the electrodes N, Q and K. The upper panels showthe stereotaxic schemes (right lateral and frontal views of the skull) showing the bilateral implantation (10 electrodes on each side).Upper left axial MRI slice: it shows the location of: electrode contacts N 5–6 in the precentral gyrus exploring PMC; electrode contacts Q7–8, in the post-central gyrus, exploring SI; electrode contact K1, at the tip of electrode K, obliquely inserted, exploring SMA; CS:central sulcus. Upper right coronal MRI slice: the trajectory of electrode Q (featuring 15 contacts) is displayed; contacts 7–8 are located inthe grey matter of the dorsal portion of the post-central gyrus. Note that the last four outer contacts are outside of the cortex. Lowerleft coronal MRI slice: it shows the trajectory of electrode K (featuring 10 contacts); the couple of contacts K 1–2 is placed in the greymatter of SMA. Lower right coronal MRI slice: it illustrates the trajectory of electrode N (featuring 15 contacts). Contacts 5–6 arepositioned in the cortex of the precentral gyrus. The last four outer contacts are outside of the cortex.

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Patient 3 was studied with 13 electrodes that recorded EEG activity

from the convexity and the mesial aspects of the right frontal and

parietal cortices (Fig. 3).

Significant interindividual anatomical variability has been repor-

ted in human brains, particularly in the precentral motor areas

(Rademacher et al., 2001); furthermore, the exact boundaries

between MI and PMC in the lateral aspects of the frontal lobe are

still uncertain (Freund, 1996; Rizzolatti et al., 1998). Indeed, recent

data indicate that most of the surface of the precentral gyrus belongs

to area 6 and not to area 4 (Geyer et al., 1996; Rizzolatti et al., 1998).

To determine the precise sites of the recording/stimulating elec-

trodes, as well as the locations of the discharges elicited by electrical

stimulations, we first identified the cerebral structures explored by

each stereo-EEG electrode through their entry point and target

point as defined in the three-dimension proportional grid system

devised by Talairach and Tournoux (1988). Then, to visualize with

higher accuracy the exact locations of the electrode contacts we

reconstructed the trajectories of the stereo-EEG electrode on the

MRI images in each patient (Figs 1–3). Finally, we calculated the

Talairach coordinates of the couple of electrode contacts of interest

for this study, by superposing the X-ray of the skull of the patient

with the electrodes implanted on the Talairach proportional grid

system with a grid scale of 1 mm; the position of each couple of

contacts was defined by the three axis coordinates (x = anteropos-

terior axis ; y = lateral axis; z = vertical axis) (see Table 2). For each

electrode, the lowest numbers indicate the inner contacts whereas the

highest numbers the outer contacts; electrodes on the left side are

labelled with letters with apostrophe. In Patient 1, who underwent a

Fig. 2 Stereotaxic schemes of Patient 2 (upper panels; right lateral and frontal views of the skull) and MRI images illustrating the trajectoriesof the electrodes M, P and N. Upper left MRI sagittal slice: the anteroposterior location of electrodes M, N and P is shown. Upper rightcoronal MRI slice: the trajectory of electrode M (featuring 15 contacts) is illustrated; contacts 1–2 explore the SMA. Lower left coronalMRI slice: it displays the trajectory of electrode P (featuring 15 contacts), with contacts 8–9 positioned in the grey matter of the dorsalportion of the post-central gyrus. Lower right coronal MRI slice: the location of contacts 4–5 of electrode N (featuring 15 contacts)in the cortex of the dorsal part of the precentral gyrus is shown.




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Fig. 3 The upper panels illustrate the stereotaxic schemes in Patient 3 (right lateral and frontal views of the skull). Upper right coronal MRIslice: it shows the trajectory of electrode Z (featuring 10 contacts) obliquely inserted. Contacts 1–2 are located in the cortex of SMA.Contacts 6–7 explore the upper portion of the precentral bank of the central sulcus belonging to MI, whereas contacts 8–9 are locatedin the dorsal part of post-central bank of the central sulcus, belonging to SI. In the scheme (modified from Talairach and Tournoux’s atlas)on the left of the coronal MRI image, we reconstructed on the axial plane the trajectory of the electrode Z, which crosses, from lateral tomesial, at first the post-central bank (SI), then the precentral bank (MI) of the central sulcus (CS), to reach with its tip the SMA. Lower axialMRI slices: they illustrate, on the left, the location of electrode contact Z 9 just on the cortical surface of the dorsal part of the postcentralgyrus; on the right, the location of electrode contact Z 6, more mesial with respect to Z 9, due to the oblique trajectory of electrode Z.




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bilateral stereo-EEG exploration, we report the data obtained from

stimulation of the right side electrodes, because they were more

constant and replicable than their counterparts on the left side.

For the aim of our study, we identified which electrodes explored

MI or PMC, SI and SMA. PMC was explored in Patients 1 and 2,

MI in Patient 3, SI and SMA in all three patients. Based on the

Talairach and Tournoux’s atlas and on the reconstruction of the

stereo-EEG electrodes trajectories on the MRI, PMC was explored:

in Patient 1, by the middle contacts of electrodes N and H (Fig. 1); in

Patient 2, by the middle contacts of electrodes N, H and M (Fig. 2).

MI was explored in Patient 3 by the middle contacts of electrodes Z

and by the outer contacts of H (located in the precentral operculum)

(Fig. 3). SI was explored: in Patient 1, by the outer contacts of

electrode Q (Fig. 1); in Patient 2, by the outer contacts of electrode

P (Fig. 2); and in Patient 3, by the outer contacts of electrodes Z and S

(Fig. 3). The SMA was investigated: in Patient 1, by the inner contacts

of electrodes K and M (Fig. 1); in Patient 2, by the inner contacts of

electrodes M and Z (Fig. 2); and in Patient 3, by the inner contacts of

electrodes K, F, M, J and Z (Fig. 3).

Stereo-EEG recordings were obtained with a bipolar montage

from pairs of nearby contacts. As part of our standard procedure

to detect possible motor phenomena induced by electrical stimula-

tion, we collected EMG activity from both deltoids, other muscles

were not recorded; therefore, we cannot provide information on

the somatotopy of the motor effects. EKG was monitored applying

two electrodes on the patients’ chest. Electrophysiological signals

were recorded and digitized with a sampling frequency of 800 Hz

with a 128 channel computerized video-EEG system for long-term

monitoring (Telefactor Corp, West Conshohocken, PA). Bipolar

high frequency electrical stimulation was performed by delivering

50 Hz trains of rectangular electrical stimuli of alternating polarity

(IRES 600 CH electrical stimulator, Micromed, Italy) with pulse

width of 1 ms through pairs of nearby contacts to reproduce ictal

phenomena, in order to assess the participation of the stimulated

brain structures in seizure semiology. Stimulation intensity ranged

from 0.4 to 3 mA; the duration of the stimulation trains varied

from 1 to 9 s. In Patient 1, analysis of one recorded episode of

non-convulsive status and results of high frequency electrical stimu-

lation were not unequivocal in defining the epileptogenic zone,

therefore the patient is still under evaluation and has not been oper-

ated yet. In Patient 2, the analysis of one spontaneous and seven

seizures induced by high frequency stimulation indicated that the

epileptogenic zone extended from the right frontal pole to the

orbital cortex, gyrus cinguli and mesial frontal regions (without

involvement of the SMA), with a rapid spread of the epileptic

discharge to the ipsilateral motor cortex. In Patient 3, based on

10 spontaneous seizures and on the results of high frequency

electrical stimulation, we concluded that the epileptogenic zone

involved the right posterior frontomesial cortex (including SMA),

the middle portion of the gyrus cinguli and extended to the right

dorsolateral superior frontal gyrus.

Low frequency (1 Hz) electrical stimulationLow frequency electrical stimulation for functional mapping of elo-

quent areas was performed by delivering monophasic rectangular

electrical stimuli of alternating polarity (IRES 600 CH electrical

stimulator, Micromed, Italy) with pulse width of 3 ms, at a frequency

of 1 Hz for 5–25 s; the intensity could vary from 0.2 to 3 mA (Munari

et al., 1993; Kahane et al., 1993, 1999). The stimulus marker was

recorded in an additional channel included in the recording mont-

age. For each stereo-EEG electrode, all contiguous couples of con-

tacts were tested using a bipolar montage. Intensity of stimulation

was raised with 0.2 mA steps. Data analysis was performed on a

computerized polygraphic system (Scan 4.1, Neuroscan, Herndon,

VA). Analysis window of the EMG activity was set from 100 ms pre-

stimulus to 350 ms post-stimulus. Bandpass filters for analysis were

set to 50–400 Hz. Rectification and average of the EMG activity,

triggered from the intracerebral electrical stimulus, were performed.

Number of averaged stimuli ranged from 5 to 20. For most of the

stimulus intensities, once a motor phenomenon was noted for a

given couple of contacts, at least two sessions of stimulation at

the same intensity, delivering 5–20 stimuli for each session, were

performed to replicate the observation. In Results, we report the

findings obtained from the couple of contacts that, for each cortical

area examined, provided the most constant and replicable results.

In Table 2, we report the Talairach coordinates and the correspond-

ing Brodmann areas of the most effective couple of contacts (see

Results). The stimulation procedure started with the patient at rest,

lying supine; after at least five stimuli were delivered with the patient

in a relaxed condition, he/she was asked to raise both upper limbs

while the stimulation continued, with the administration of at least

five other stimuli. In both conditions of stimulation (relaxed/upper

limbs raised), the patient was also asked to count aloud (to detect any

modification of speech induced by stimulation).

Throughout both high frequency and low frequency electrical

stimulation procedures, stereo-EEG was continuously monitored

to detect any after-discharge or seizure activity.

StatisticsComparison of the durations of the SPs at different intensities of

stimulation was performed by two-tailed one sample t-tests. Pearson

correlation analysis was used to correlate stimuli intensities and

the durations of the SPs. Statistical Package for Social Sciences

(Version 8.0) was employed for computation.

ResultsLow frequency electrical stimulation ofPMC and MI (Table 3)Low frequency electrical stimulation of PMC and MI induced

an MEP in the contralateral deltoid, either at rest or during

Table 2 Anatomical sites of the most effective electrodecontacts in inducing SPs

Patient Electrode/contacts

Talairachcoordinates

Brodmannarea

Gyrus Side

x y z

1 N/5–6 36 �12 56 6 Precentral RightQ/7–8 33 �35 60 3 Postcentral RightK/1–2 4 12 48 6 Superior

frontalRight

2 N/4–5 34 �12 65 6 Precentral RightP/8–9 32 �35 59 2 Postcentral RightM/1–2 6 8 47 32 Medial frontal Right

3 Z/6–7 16 �20 58 4 Precentral RightZ/8–9 45 �21 56 3 Postcentral RightZ/1–2 6 �22 53 6 Medial frontal Right




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contraction; we did not observe any detectable change on the

ipsilateral deltoid (Fig. 4). During contraction, the MEPs

showed increased amplitude and were followed by an SP

(Figs 4 and 5). In Patients 1 and 2, the most effective couples

of contacts for PMC stimulation were N 5–6 and N 4–5,

respectively, both couples located in Brodmann’s area 6,

in the precentral gyrus (see Figs 1 and 2 and Table 2). In

Patient 3, MI stimulation was achieved through electrode

contacts Z 6–7, located on the precentral bank of the central

sulcus (see Fig. 3 and Table 2). In Table 3, the results obtained

with stimulation of PMC and MI during contraction of the

upper limbs are reported. We consistently obtained MEPs at

low stimulus intensities (i.e. 0.4 and 0.6 mA), which con-

firmed that we were stimulating PMC or MI, therefore we

did not deliver stimuli at higher intensities (apart from

Patient 2, to whom we delivered few stimuli at 0.8 mA;

not reported in Table 3). Clinically, each single electric

shock caused a muscle jerk that involved proximally the

left upper limb. In Patient 2 (PMC stimulation), 100% of

stimuli, at stimulation intensities of 0.4 and 0.6 mA, elicited

Table 3 Results obtained by cortical stimulation of PMC, MI, SI and SMA

Stimulationintensity (mA)

No of stimuli MEP no (%) MEP latency (ms) SP no (%) SP latency (ms) SP duration (ms)

PMC/MI stimulation*Pt.1 (N;5–6/PMC) 0.4 10 5 (50) 18 6 7 10 (100) 37 6 10 36 6 7

0.6 13 11 (85) 15 6 6 13 (100) 40 6 10 42 6 19Pt.2 (N;4–5/PMC) 0.4 28 28 (100) 16 6 2 28 (100) 52 6 6 155 6 12

0.6 8 8 (100) 15 6 4 8 (100) 53 6 4 190 6 31Pt.3 (Z 6–7/MI) 0.4 10 5 (50) 8 6 4 10 (100) 32 6 6 61 6 23

0.6 6 5 (83) 8 6 4 6 (100) 34 6 5 50 6 8SI stimulation*

Pt.1 (Q;7–8) 0.5 18 – – 3 (17) 48 6 10 32 6 30.6 13 – – 10 (77) 48 6 16 61 6 80.8 47 – – 1 (2) 40 601.6 12 1 (8) 15 2 (17) 38 6 18 65 6 142 12 1 (8) 35 3 (25) 58 6 10 61 6 122.6 13 – – 8 (62) 43 6 7 93 6 193 13 2 (15) 10 6 0 7 (54) 54 6 13 100 6 20

Pt.2 (P;8–9) 0.6 32 10 (31) 22 6 5 17 (53) 73 6 19 72 6 190.8 10 4 (40) 29 6 11 8 (80) 77 6 11 134 6 121 6 4 (67) 19 6 6 4 (67) 64 6 11 140 6 121.2 8 2 (25) 15 4 (50) 93 6 4 138 6 113 8 4 (50) 13 6 4 6 (75) 73 6 13 165 6 9

Pt.3 (Z;8–9) 0.4 10 – – 4 (40) 48 6 5 34 6 50.6 6 1 (17) 10 5 (83) 45 6 5 33 6 61 5 2 (40) 20 6 0 2 (40) 45 6 0 50 6 141.6 17 2 (12) 13 6 4 3 (18) 43 6 10 42 6 201.8 6 2 (33) 15 6 (100) 40 6 5 53 6 232 13 1 (8) 20 6 (46) 44 6 11 77 6 172.2 8 4 (50) 14 6 3 4 (50) 43 6 6 98 6 12

SMA stimulation*Pt.1 (K;1–2) 0.4 8 – – 4 (50) 54 6 19 38 6 6

0.6 8 – – 4 (50) 63 6 5 45 6 40.8 10 – – 2 (20) 63 6 11 45 6 01 10 – – 5 (50) 58 6 7 54 6 51.2 11 – – 6 (55) 57 6 9 57 6 81.6 13 – – 13 (100) 59 6 12 62 6 102 26 – – 9 (35) 57 6 10 62 6 162.6 20 – – 9 (45) 69 6 20 62 6 133 25 – – 5 (20) 62 6 8 60 6 4

Pt.2 (M;1–2) 1.4 51 – – 16 (31) 58 6 17 50 6 132 114 – – 35 (31) 58 6 10 68 6 283 12 – – 12 (100) 58 6 11 77 6 18

Pt. 3 (Z;1–2) 0.6 9 – – 2 (22) 63 6 25 70 6 350.8 8 – – 5 (63) 45 6 13 74 6 211 23 – – 5 (22) 47 6 9 76 6 191.4 8 – – 4 (50) 40 901.6 8 – – 6 (75) 62 6 3 107 6 32.2 8 – – 8 (100) 38 6 4 120 6 72.6 10 – – 10 (100) 56 6 6 113 6 12

*The data reported refer to stimulation during contractions of both deltoids.




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an MEP followed by an SP. In Patients 1 (PMC stimulation)

and 3 (MI stimulation), at 0.4 mA, 50% of stimuli were

effective in inducing an MEP, followed by an SP; the remain-

ing 50% of stimuli could induce only a pure SP, not preceded

by an MEP. In these two patients, at 0.6 mA, the percentage of

stimuli effective in inducing an MEP was raised to 85% in

Patient 1 and to 83% in Patient 3, constantly followed by an

SP, whereas the remaining stimuli induced an isolated SP.

Therefore, in Patients 1 and 3, single electric pulses delivered,

respectively, to PMC and MI at intensities of 0.4 and 0.6 mA

could elicit either an MEP followed by an SP, or an isolated

SP, not preceded by an MEP; by increasing the stimulus

intensities, SPs showed more frequently an antecedent

MEP. The latency of the MEPs ranged from �15 ms (at

0.4 mA) to �18 ms (at 0.6 mA) in Patient 1 whereas

it was �15 ms in Patient 2; in Patient 3, it was shorter,

Fig. 4 EMG tracing of both deltoids, at rest (left panel) and during muscular contraction (right panel) (the patient held his upper limbs raisedand outstretched) during electrical stimulation of the right PMC (at 0.4 mA), SI (at 0.6 mA) and SMA (at 3.0 mA). The markers for eachelectrical stimulus at 1 Hz are shown above. PMC stimulation induced MEPs at rest, that increased in size during contraction, and werefollowed by an SP. SI stimulation did not evoke any MEPs at rest, but could induce an SP during muscular contraction, inconstantly precededby an MEP. SMA stimulation did not induce any EMG phenomenon at rest, but evoked brief SPs, not preceded by an MEP, during muscularactivation. These motor responses were observed only in the left deltoid, either at rest or during contraction; no effect was observed in theright one, ipsilateral to the stimulation. Asterisks indicate SPs not preceded by an MEP.




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being �8 ms. Latencies of SPs ranged from �37 (at 0.4 mA) to

�40 ms (at 0.6 mA) in Patient 1, whereas in Patient 2 they

were �52 ms. In Patient 3, as for the latencies of MEPs,

latencies of SPs were shorter, �32–34 ms. On the whole,

the only difference between MI and PMC stimulation was

regarding latencies of MEPs and SPs, which were shorter

for MI stimulation.

Low frequency electrical stimulationof SI (Table 3)In Patient 1 and 3, low frequency electrical stimulation of SI at

low stimulus intensities could evoke SPs not preceded by

MEPs in the contralateral deltoid; no change of the EMG

activity was visible on the ipsilateral deltoid (Fig. 4). The

most effective contacts were located in Brodmann’s area 3,

in the right post-central gyrus in Patient 1 (electrode contacts

Q 7–8) (Fig. 1; Table 2) and in the post-central bank of the

central sulcus in Patient 3 (electrode contacts Z 8–9) (Fig. 3;

Table 2). SPs not preceded by MEPs were observed for

intensities ranging from 0.4 to 0.8 mA in Patient 1, and at

0.4 mA in Patient 3. The optimal stimulus intensities for

evoking pure SPs, never preceded by an MEP, were 0.6 mA

in Patient 1, which was effective in 77% of stimuli, and 0.4 mA

in Patient 3, effective in 40% of stimuli. Average of the EMG

activity triggered from the stimulus did not show any

enhancement of EMG activity that could indicate the occur-

rence of an antecedent MEP (Fig. 6). Raising the stimulation

intensity, the SPs were preceded, although not constantly, by

an MEP; these responses were observed in the contralateral

deltoid, whereas in the ipsilateral one no clear modification of

EMG activity was detectable. Indeed, for each stimulation

intensity that we tested, the number of evoked SPs exceeded

consistently the number of MEPs. Only in Patient 3, at the

highest intensity of stimulation (2.2 mA), each SP was

associated with an antecedent MEP. The latency of the SPs

did not change across the different stimulation intensities,

regardless of the presence or not of an antecedent MEP. It

was �45 ms in both patients. On the contrary, the increment

of the intensity of the stimulus was paralleled by an increase of

Fig. 5 Effects of different intensities of electrical stimulation of PMC, SI and SMA in Patient 2. By increasing the stimulus intensity,stimulation of PMC evoked MEPs of increasing amplitudes followed by SPs of increasing duration. SI stimulation at low stimulus intensitiescould induce pure SPs, not preceded by an MEP; the increment of the stimulus intensity increased the probability to obtain an MEP,preceding the SP. Stimulation of the SMA induced only SPs, not preceded by an MEP, up to the highest stimulus intensity delivered (3 mA).




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Fig. 6 Average of the rectified EMG activity from the left deltoid, triggered from the electrical stimulus. The results obtained fromstimulation of SI and SMA in the three patients are illustrated. The tracings related to SI stimulation were obtained averaging only those SPsnot preceded by an antecedent MEP. The superposition of two averaged trials (number of averaged SPs ranged from 5 to 15) are shown.No evidence of an antecedent MEP, preceding the SP was observed, confirming that stimulation of SI and SMA could induce pure SPsnot preceded by an MEP.




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the duration of the SP, showing a positive correlation (Patient

1: r = 0.795, P < 0.001; Patient 3: r = 0.772, P < 0.001) (Fig. 7).

In Patient 2, at all stimulation intensities that we tested,

SPs in the contralateral deltoid could be preceded, although

not constantly, by an MEP; no changes were observed in

the ipsilateral deltoid. The electrode contacts (P 8–9) that

provided the most replicable results were located in Brod-

mann’s area 2, in the right post-central gyrus (see Fig. 2

Fig. 7 Relationship between stimulus intensity and duration of the induced SPs. A statistically significant positive correlation(see text for details) was observed for stimulation of both areas in all the three patients.




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and Table 2). We did not detect contact pairs that could elicit

only pure SPs. As in the other patients, for each stimulation

intensity, a number of evoked SPs were not preceded by

MEPs, however, by incrementing the stimulus intensity, the

probability to obtain an MEP preceding the SP tended to

increase (Fig. 5). Average of the EMG activity triggered

from the stimulus failed to show any MEP preceding the

SP (Fig. 6). Latency of onset of SPs was not affected by stimu-

lus strength, and was longer than in the other two patients

(�75 ms). The duration of the SPs showed a linear correlation

with the stimulation intensity (r = 0.636, P < 0.001) (Fig. 7).

Low frequency electrical stimulation ofSMA (Table 3)Low frequency electrical stimulation of SMA did not produce

any effect at rest, either in the EMG tracing or in the descrip-

tion by the patients (Fig. 4). During contraction, 1 Hz electric

pulses elicited, in the contralateral deltoid, brief SPs not

preceded by MEPs; no interruptions or enhancements of

the EMG activity were observed in the ipsilateral deltoid

(Fig. 4). Clinically, they appeared as small twitches at the

left upper limb proximally, which the patients themselves

described as ‘small jerks’ or ‘loss of muscle tone’. The most

effective couple of contacts were located in the mesial part of

the superior frontal gyrus, corresponding to Brodmann’s

area 6, in Patients 1 (electrode contacts K 1–2) and 3 (elec-

trode contacts Z 1–2)(Figs 1 and 3; Table 2), and in the most

caudal portion of Brodmann’s area 32, in the mesial part of

the superior frontal gyrus, in Patient 2 (electrode contacts

M 1–2) (Fig. 2; Table 2). SPs started to appear at stimula-

tion intensity of 0.4 mA in Patient 1, 1.4 mA in Patient 2

and 0.6 mA in Patient 3. In Patient 1, the most effective

intensity of stimulation was 1.6 mA, which evoked an SP

in 100% of stimuli; higher intensities of stimulation were

less effective. In Patients 2 and 3, the progressive increase

of stimulus intensities was associated with an increment of

the percentage of effective stimuli; indeed, in both patients,

at the highest intensities employed, i.e. 3 mA in Patient 2

and 2.6 mA in patient 3, 100% of stimuli evoked an SP.

Remarkably, in all patients, regardless of the stimulation

strength, SPs were never preceded by MEPs (Fig. 5). Average

of the EMG activity triggered from the stimulus failed to

show any enhancement of EMG activity, consistent with an

MEP, preceding the SP onset, even at the highest and most

effective intensities of stimulation (Fig. 6). Latency of onset

of SPs did not show statistically significant differences at the

different stimulation intensities. Furthermore, it was quite

similar in the three patients, resulting �60 ms in Patient 1,

�58 ms in Patient 2, and a little more variable in Patient 3,

ranging from �45 ms (at 0.8 mA) to �62 mA (at 1.6 mA).

Duration of SPs was affected by stimulus strength. Indeed,

there was a positive correlation between the stimulus intensity

and the duration of the induced SPs (Fig. 7): in Patient 1,

ranged from 45 6 4 ms (at 0.6 mA) to 60 6 4 ms (at 3 mA)

(r = 0.458; P < 0.01); in Patient 2, ranged from 50 6 13 ms

(at 1.4 mA) to 77 6 18 ms (at 3 mA) (r = 0.346; P < 0.05); in

Patient 3, varied from 74 6 21 ms (at 0.8 mA) to 113 6 12 ms

(at 2.6 mA) (r = 0.731; P < 0.001).

DiscussionIn our study, we could obtain pure SPs by stimulating PMC

and MI in the precentral gyrus (Brodmann’s area 6 in

Patients 1 and 2, and Broadmann’s area 4 in Patient 3)

and SI in the post-central gyrus (Brodmann’s area 3 in

Patients 1 and 3, and Brodmann’s area 2 in Patient 2);

the same couple of contacts could produce either pure SPs

or MEPs associated with SPs, depending on the stimulus

intensity, i.e. the higher the intensity the higher the probab-

ility that the SP was preceded by an MEP. Stimulation of

the SMA induced in all three patients only pure SPs, never

preceded by an MEP, regardless of the intensity of stimula-

tion. A role of the primary sensorimotor cortices in the genesis

of NM has been previously suggested by recording pure

SPs evoked by single electric shocks delivered through sub-

dural electrodes to a cortical area, located immediately

posterior to the central sulcus, in a region that roughly

corresponded to the SI portion that we stimulated (Ikeda

et al., 2000); in the same report, stimulation of the SMA

was ineffective in producing any SP.

Electrical stimuli applied directly to the cerebral cortex

elicit a potential (the ‘direct cortical response’, DCR)

(Adrian, 1936; Ochs, 1968) in the immediate vicinity of

the site of stimulus application. Taking into account that

DCR characteristics depend significantly on a variety of

parameters (such as stimulus frequency, electrode size,

physiological state of the cortex, anaesthesia and absence or

presence of epileptogenicity) (Goldring et al., 1994), stimulus

strength is a crucial factor in influencing DCR components.

In fact, at weak stimulus intensities, DCR is essentially com-

posed of an initial negative potential (the ‘primary negative

potential’ , PNP) followed by a longer lasting positive deflec-

tion. PNP represents excitatory post-synaptic potentials

(EPSPs) of apical dendrites (Li and Chou, 1962; Sugaya

et al., 1964); it is likely to reflect inhibition occurring in

deep cortical layers (Ochs and Clark, 1968; Barth et al.,

1989; Barth and Sutherling, 1988; Harding, 1992). At pro-

gressively stronger stimulus intensities, PNP increases in

amplitude; moreover, in motor and primary sensory cortex,

it is preceded by short-latency bursts of positive potentials

(BPP) (Stohr et al., 1963; Barth and Sutherling, 1988), which

have been demonstrated to be correlated with motor output

(Adrian, 1936). Indeed, Mingrino et al. (1963) showed that

BPP were related to the I waves of Patton and Amassian’s

pyramidal response (1954). In humans, DCRs have been

recorded from PMC, MI and SI, with distinguishable char-

acteristics among these different cortical areas (Goldring et al.,

1994). We can speculate that the pure SPs that we observed

at low intensity stimulation might depend on a cortical inhib-

itory process possibly related to the PNP of the DCR. By

increasing stimulus intensities, the appearance of BPPs,




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preceding the PNP, might be responsible for a descending

volley of I-waves resulting in an MEP; in addition, the incre-

ment of the duration of the SP following the MEP might be

related to the increment of PNP amplitude occurring with

stronger stimuli. Since electrophysiological studies showed

that DCR and interictal epileptic spikes are produced by

the same neuronal circuits (anatomically represented by

two neuronal populations, one in the supragranular layer,

the other in the infragranular layer) (Barth et al., 1989,

1990), we can postulate that a single epileptic spike is suffi-

cient to induce cortical inhibition resulting in NM. This hypo-

thesis may be supported by experimental data in a penicillin

model of focal epilepsy demonstrating that epileptic activity

confined to the superficial cortical layers can be associated

with hyperpolarization of neurons in deep cortical layers,

including pyramidal tract neurons, causing a suppression

of the background descending activity on the spinal moto-

neurons. This phenomenon, called ‘vertical inhibition’,

was not observed when epileptic activity involved all cortical

layers: in this case, each epileptiform potential was associated

with neuronal discharges descending to the spinal cord

(Elger and Speckmann, 1983).

The modulatory effect of the stimulus intensity on the

probability of obtaining either SPs or MEPs has been

described also in transcranial magnetic stimulation (TMS)

studies (Wassermann et al., 1993; Davey et al., 1994). These

findings have been explained admitting that low intensity

TMS can induce brief pure SPs by activating selectively intra-

cortical inhibitory interneurons, whereas at higher stimulus

intensity intracortical cells synapsing on corticospinal

neurons would be enrolled (Wassermann et al., 1993;

Davey et al., 1994). However, the analogies between the SP

obtained by TMS both in normal and epileptic patients and by

intracerebral electrical stimulation, as in our cases, should be

cautiously evaluated owing to the topographic limits of TMS,

variabilities among different groups of epileptic patients,

antiepileptic treatment, and above all to the complexity of

the cortical SPs induced by TMS (Hallett, 1995).

Our findings are in agreement with previous data suggest-

ing that activation of the perirolandic cortex can produce

pure SPs (Ikeda et al., 2000); in addition they provide the

first evidence of the capability of non-primary motor areas,

such as PMC and SMA, to generate SPs. It is conceivable,

therefore, that the areas that we investigated can be involved

in the genesis of cortical NM. As reported above, the prob-

ability of obtaining pure SPs following PMC, MI and SI

stimulation was higher at low intensity of stimulation. Cor-

tical SPs may result from the activation of low threshold

inhibitory neurons, widely located in cortical areas, project-

ing onto the pyramidal cells of the motor cortex (Krnjevic

et al., 1964). A scattered distribution of excitatory and inhib-

itory responses, the latter consisting of transient inhibition

lasting �40–100 ms, has been observed with microstimula-

tion studies of MI (Schmidt and McIntosh, 1990). Inhibitory

motor phenomena induced by PMC stimulation might be

mediated by the corticofugal projections that PMC sends

to regions of medullary reticular formation (Kuypers and

Brinkman, 1970; Wise, 1985) whose activation might be

responsible for motor inhibition (Magoun and Rhines, 1946).

By increasing stimulus intensity, the SPs tended to be pre-

ceded more frequently by MEPs. In Patients 1 and 2, latencies

of MEPs recorded in the deltoid muscle by stimulation of

PMC were �15–18 ms, longer than those obtained in the

same muscle by direct cortical stimulation of MI with sub-

dural grids (Ikeda et al., 2000) and by TMS (Rossini et al.,

1994), and in keeping with recent data reporting longer laten-

cies of the deltoid MEPs elicited by TMS stimulation of

PMC (Fridman et al., 2004). PMC stimulation can conceiv-

ably evoke MEPs by itself through direct projections to spinal

interneurons and alpha motoneurons (Murray and Coulter,

1981; Dum and Strick, 1991; He et al., 1993) or by engaging

directly the motor cortex through corticocortical connections

to the MI (Civardi et al., 2001; Munchau et al., 2002). In

Patient 3, the MEP latency was �8 ms (she was a small sized,

young girl) consistent with the MEP latencies reported in the

deltoid with MI stimulation by direct cortical electrical stimu-

lation (Ikeda et al., 2000) and by TMS (Rossini et al., 1994).

Low intensity stimulation of SI produced exclusively pure

SPs in two patients, whereas in the third an MEP could incon-

stantly precede the SPs. These observations may be supported

by experimental data in monkeys that demonstrate an inhib-

itory action of SI on the motor system by showing mainly

inhibitory, or extremely weak, effects of electrical microstimu-

lation of SI neurons on muscular activity as compared with

MI neurons, even at high stimulus intensities (Widener and

Cheney, 1997). Additional studies have emphasized the dif-

ferent functional properties of movement-related neurons in

motor and sensory cortex concluding that SI neurons have a

significantly lower motor output capacity with respect to MI

neurons (Wannier et al., 1986, 1991). In our SI stimulation

session, the increment of stimulus intensity resulted in the

progressive appearance of an MEP preceding the SP. Motor

responses induced by electrical cortical stimulation of the

post-central somatosensory cortex were reported since the

pioneering works by Penfield and Boldrey (1937), and

Woolsey (1958), and later replicated by electrical cortical

stimulation with subdural grids (Uematsu et al., 1992; Nii

et al., 1996). However, because of the stimulation methods

used in these studies (macroelectrodes or subdural grid elec-

trodes, relatively high current levels), it cannot be ruled out

that the observed results might depend on a current spread to

adjacent motor areas. In fact, Uematsu et al. (1992) acknow-

ledged the possibility that their stimulation procedure could

activate a somewhat broad region, although, with low current

densities. In our stereo-EEG stimulation procedure, the short

distance (1.5 mm) between the two stimulating contacts

should limit the spread of current; however, at the highest

intensities of stimulation with a stimulus duration (3 ms)

longer than the one usually employed in other studies, we

cannot exclude that the appearance of MEPs might be related

to a diffusion of current to the precentral cortex, or altern-

atively, to the activation of the corticocortical connections




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between SI and the adjacent, functionally related, MI (Jones

et al., 1978; Asanuma and Bornschlegl, 1988).

In our study, stimulation of SMA with increasing stimulus

intensities produced only pure SPs. This finding substantiates

the hypothesis of a role of the SMA in the genesis of NM

(Rubboli et al., 1995; Tassinari et al., 1995; Baumgartner et al.,

1996), based on the evidence of a circumscribed NMA encom-

passed in the SMA, labelled as ‘supplementary NMA’ (Luders

et al., 1987, 1995; Lim et al., 1994; Hanakawa et al., 2001), and

on reports of patients with strokes in the mesial aspects of

anterior frontal lobes showing non-epileptic NM in the

contralateral upper limb (Degos et al., 1979; Santamaria-

Cano et al., 1983; Young and Shahani, 1986; Kim, 2001).

High frequency (50 Hz) trains of electrical stimuli delivered

directly to the supplementary NMA can produce sustained

negative motor responses, such as behavioural arrest, motor

slowing and inability to maintain a tonic contraction (Luders

et al., 1987, 1995; Lim et al., 1994). We can speculate that the

pure SPs that we recorded by stimulating SMA may depend

on a transient, stimulus-related activation of the same mech-

anisms that underlie the more prolonged negative motor

responses induced by repetitive 50 Hz stimulation. Interest-

ingly, by SMA stimulation, we obtained only pure SPs, never

preceded by an MEP, even at the highest intensity of stimu-

lation, suggesting that the portion of SMA that we investig-

ated exerted mainly an inhibitory action on the motor system.

A subdivision of the SMA in two separate areas, the pre-SMA

and the SMA proper, with distinct functional properties

(Rizzolatti et al., 1998) has been delineated; the supplement-

ary NMA described by Luders et al. (1987, 1995) is roughly

encompassed in the pre-SMA. In our study, the sites of the

electrode contacts that resulted more effectively in inducing

SPs varied from a position that could be consistent with

the SMA proper (electrode M in Patient 2 and electrode Z

in Patient 3) to a position that might correspond to the

pre-SMA (electrode K in Patient 1). Although in humans

the distinction between pre-SMA and SMA proper is still

under debate, our findings may suggest that it is possible

to elicit inhibitory responses by stimulating more caudally

with respect to the supplementary NMA, in a region possibly

pertaining to the SMA proper.

Epilepsy has been shown to modify cortical excitability

in response to direct electrical stimulation of the cortex

(Goldring et al., 1961, 1994; Wyler and Ward, 1981). In a

penicillin model of focal epilepsy, the neuronal populations

participating in the genesis of the DCR may pathologically

synchronize depolarization, triggering interictal spikes in the

neocortex (Barth et al., 1989, 1990). Goldring et al. (1961)

reported an increased duration of the PNP of DCR. This

finding might relate to TMS data showing a prolonged cor-

tical SP in the epileptic hemisphere when the epileptogenic

area included MI, suggesting an up-regulation of inhibitory

mechanisms (Classen et al., 1995; Cincotta et al., 1998;

Tassinari et al., 2003). On the other hand, the inability of

the epileptic hemisphere, as compared with the unaffected

one, to produce a linear progression of the SP duration in

parallel with the progressive increment of the stimulus intens-

ity has been explained admitting a failure of recurrent inhibi-

tion from the excited pyramidal neurons at higher stimulus

intensity (Cicinelli et al., 2000). In our study, SP duration

increased linearly with the increment of stimulus intensity,

as it occurs in normal condition, suggesting that in our

cases cortical inhibitory mechanisms were preserved, at

least at the stimulus intensity that we used. We could not

verify asymmetries of SP duration between the two hemi-

spheres since, in the only patient with bilateral exploration

(Patient 1), contralateral stimulation provided less constant

findings possibly due to a certain degree of asymmetry in the

implantation of the stereo-EEG electrodes, in the homologous

cerebral structures.

In epileptic patients, motor system excitability can be

modified by antiepileptic treatment (Michelucci et al.,

1996; Ziemann et al., 1996; Tassinari et al., 2003). Cortical

SP duration mainly reflects GABAB-mediated inhibitory

mechanisms (McCormick, 1992). Phenobarbital, clonaze-

pam, and topiramate have multiple mechanisms of action,

that include modulatory functions on the GABAergic system;

these effects, however, are mediated by GABAA receptors. In

fact, recent data showed no effect of topiramate on cortical SP

induced by transcranial magnetic stimuli (Reis et al., 2002).

Carbamazepine, that acts on sodium channel conductance

can leave unchanged (Inghilleri et al., 2004) or slightly incre-

ment (Schulze-Bonhage et al., 1996; Ziemann et al., 1996)

cortical SP duration as evaluated by TMS.

The discrepancies between our results and those reported

by Noachtar et al. (1997) and Ikeda et al. (2000), who failed

to obtain NM by stimulating, respectively, SI and SMA,

might depend on technical reasons. Direct cortical stimula-

tion by means of subdural electrodes activates only the cor-

tical surface just beneath the electrodes with a significant

dispersion of the current due to a shunting effect through

the CSF (Nathan et al., 1993). On the contrary, bipolar

electrical stimulation with stereo-EEG electrodes tends to

activate a limited amount of tissue, close by the two electrode

contacts, using lower currents, with the significant yield of

allowing the exploration of areas of cortex deeply situated

inside cerebral sulci, providing, therefore, a more complete

and accurate investigation of cortical functions (Yeomans,

1990).

AcknowledgementsThis research was partially supported by ex-40% research

funds of the Italian Ministry of University and Research

(Grant no. 2004060530) and by a Research Grant provided

by Cassa di Risparmio di Bologna. We thank Mrs Clementina

Giardini for editorial assistance. This work was inspired by a

keen observation by Professor Claudio Munari to whom this

paper is dedicated.

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