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Brain, Vol. 123, No. 7, 1459-1470, July 2000
© 2000 Oxford University Press

Coherence between cerebellar thalamus, cortex and muscle in man

Cerebellar thalamus interactions

J. F. Marsden1, P. Ashby3, P. Limousin-Dowsey1, J. C. Rothwell1 and P. Brown1,2

1 MRC Human Movement and Balance Unit, Institute of Neurology, London, 2 National Hospital for Neurology and Neurosurgery, London, UK and 3 Playfair Neuroscience Unit, Toronto Western Hospital, Canada

Correspondence to: Dr P. Brown, MRC Human Movement and Balance Unit, Institute of Neurology, Queen Square, London WCIN 3BG, UK


    Abstract
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
Local field potentials (LFPs) were recorded in seven unanaesthetized patients between the four adjacent contacts of a macroelectrode stereotactically implanted for the treatment of tremor. The LFPs were presumed to arise predominantly from the nucleus ventralis intermedius (Vim) of the thalamus, the implantation target. They were recorded simultaneously with the ipsilateral EEG and contralateral EMG during an isometric contraction or at rest. The patients had a history of either isolated tremor (essential tremor, n = 2; benign tremulous Parkinson's disease, n = 1) or tremor with signs of a cerebellar syndrome (multiple sclerosis, n = 3; essential tremor and ataxia, n = 1), although clinical tremor was absent at the time of recording because of a temporary microthalamotomy effect in four patients. In patients with isolated tremor, oscillatory activity picked up by contacts in Vim (cerebellar thalamus) was invariably coherent with that in the sensorimotor cortex or contracting muscle in the 8–27 Hz range. Such coherence was absent in two of the four subjects with tremor associated with a cerebellar syndrome. Coherence between LFPs recorded from more caudally placed contacts and the sensorimotor cortex or contracting muscle was negligible in all patients. These caudally placed contacts demonstrated the highest sensory evoked potential in response to median nerve stimulation. Oscillatory activity in the cerebellar thalamus (Vim) lagged behind that in both cortex and muscle. Coherent activity between the cerebellar thalamus (Vim) and the cortex persisted at rest. It is suggested that rhythmicities in the 8–27 Hz range could provide the basis for a temporal framework that is widely distributed within the motor system.

motor thalamus; thalamic stimulation; coherence; essential tremor; multiple sclerosis

BTPD = benign tremulous Parkinson's disease; FDI = first dorsal interosseous; LFP = local field potential; MVC = maximum voluntary contraction; Vc = thalamic nucleus ventrocaudalis; Vim = thalamic nucleus ventralis intermedius


    Introduction
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
In recent years there has been increasing interest in oscillatory activity within the human sensorimotor system. Oscillations that are coherent between the contralateral sensorimotor cortex and muscle can be recorded in humans making voluntary muscle contractions (Conway et al., 1995Go; Salenius et al., 1997Go; Brown et al., 1998Go; Halliday et al., 1998Go), and during motor tasks functionally active areas of cortex are themselves coherent with each other (Classen et al., 1998Go; Gerloff et al., 1998Go; Andres et al., 1999Go).

The precise function and genesis of these cortical rhythms remain elusive. Their reflection in the pattern of spinal motor neuron discharge raises the possibility that the same rhythmicities may be conducted to other subcortical projection sites, and thus perhaps provide a timing mechanism that is widely distributed within the motor system. In view of the hypothesized role of the cerebellum in timing (Llinas, 1991Go; Ivry, 1996Go), we looked for a linear relationship between oscillatory activity recorded in the cerebellar system, the motor areas of the cortex, and muscle. Such a motor study necessarily requires an alert and cooperative subject. Activity within the motor cortex can be non-invasively picked up as the EEG, or inferred indirectly from the pattern of the EMG during voluntary contraction. To record from the nucleus ventralis intermedius (Vim) of the cerebellar thalamus, we took advantage of the recent emergence of deep-brain stimulation to treat tremor. The subjects, therefore, had tremor as at least one symptom. The recordings were made while the leads were exposed externally, in the interval between the stereotactic implantation of stimulating electrodes and the subsequent subcutaneous rerouting of leads to an internal stimulator. Thus, we were able to record local field potentials (LFPs) from the cerebellar thalamus in cooperative, awake humans during natural movements while simultaneously recording from active muscle and the sensorimotor cortex. The recording of thalamic LFPs, as opposed to the action potentials of individual neurons, as performed previously (Lenz et al., 1988Go, 1990Go; Hua et al., 1998bGo), has the advantage that the detection of both subthreshold and suprathreshold oscillatory activity affecting populations of neurons is facilitated, and consequently also has the advantage of detecting possible coherence with other sites. The results show that coherence within a band from 8 to 27 Hz may occur between the cerebellar thalamus (Vim), the sensorimotor cortex and muscle, suggesting that coherent activity may represent a common element in coding activity in simultaneously active motor centres.


    Methods
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
Patients were recruited from the Toronto Western Hospital, Canada, and the National Hospital for Neurology and Neurosurgery, London, UK. Their clinical features are summarized in Table 1Go. Patients 1–3 had tremor as their only symptom (with the exception of epilepsy in patient 3). Patients 4–7 had tremor associated with signs of cerebellar ataxia. All subjects participated with informed consent and the approval of the local ethics committee according to the Declaration of Helsinki.


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Table 1 Clinical details of subjects
 
Thalamic target, anatomical considerations and definitions
The target for thalamic stimulation was Vim, which is considered to be the projection zone of the fibres from the deep cerebellar nuclei (Macchi and Jones, 1997Go; Strafella et al., 1997Go). The electrodes were positioned stereotactically (Leksell model G, Elektra Instrument, Atlanta, Ga., USA or Radionics CRW frame, Radionics, Burlington, Mass., USA) after registration of MRI or CT scans with the Schaltenbrand and Bailey (1977) atlas. At Toronto Western Hospital, Canada, the border between the ventrocaudal nucleus (Vc), which receives lemniscal input, and the Vim was also identified by the response to tactile stimuli. The target site was anterior to this border, and here activity was recorded in response to kinaesthetic stimulation and/or active movement (for a discussion on defining the borders of Vim, see Macchi and Jones, 1997; Strafella et al., 1997). In both groups, stimulation of the target site arrested tremor. The microelectrode used for target localization was replaced with a macroelectrode once the target area had been localized. The macroelectrode (model 3387DBS; Medtronic, Minneapolis, Minn., USA) ran in a rostrodorsal-to-caudoventral direction and had four platinum–iridium cylindrical surfaces (contacts). Each was 1.27 mm in diameter and 1.52 mm long, with a centre-to-centre separation of 3 mm. The four wires from the macroelectrode were led out temporarily through the scalp.

Although the electrodes were positioned stereotactically, it was impossible to confirm the position of each macroelectrode contact with respect to Vim ante mortem. The Vim in humans is wedge-shaped with its base laterally. Its dimensions are estimated as 3–3.5 mm rostrocaudally in its lateral part and 1.5–2.0 mm rostrocaudally in its medial part. The dorsoventral height and the mediolateral width are 8–9 and 1.5–2.0 mm, respectively (Hirai et al., 1989Go). Therefore, as the total contact-to-contact separation of the macroelectrode was 9 mm, some contacts may have been sited outside this nucleus. We therefore broadly classified the site of electrode contact pairs as `cerebellar thalamus' (Vim) if low-intensity electrical stimulation led to the suppression of tremor and/or ongoing tonic voluntary activity (Ashby et al., 1995Go). Furthermore, the site where low-intensity electrical stimulation evoked paraesthesiae and/or gave the highest-amplitude sensory evoked potentials following median nerve shocks was defined as Vim-s. In all subjects, Vim-s was the most caudal–ventral recording site. The exact location of Vim-s cannot be determined; it may reside in the sensory thalamus (Vc), which lies posterior to Vim, within the shell lying anterior to Vc and receiving muscle and joint afferent input, or within Vim itself, where neurons also respond to sensory stimulation (Ohye et al., 1989Go; Macchi and Jones et al., 1997).

Recording procedure
Each subject was seated and recorded during an unconstrained or manually resisted isometric contraction involving the wrist or hand muscles contralateral to the thalamic electrode, with the forearm supported. In four cases (subjects 1, 3, 5 and 6) recordings were also made whilst the subject was at rest. Periods of muscle activity were exported using the SPIKE 2 programme prior to analysis and separate records gathered under the same condition were pooled as described by Amjad and colleagues (Amjad et al., 1997Go).

Bipolar thalamic recordings were made from adjacent contacts of the macroelectrode. The deepest and most caudal contact was contact 0. In patient 3, it was possible to make recordings only between contacts 0–2 and 2–3. The thalamic field potentials were amplified and pass-band-filtered (2.5 Hz to 0.5/1 kHz at Toronto Western Hospital, Canada, and 0.16 Hz to 1 kHz at the National Hospital for Neurology and Neurosurgery, London, UK, with the exception of one patient, in whom the pass band was 0.16–300 Hz). EMG activity contralateral to the site of thalamic stimulation was recorded using Ag–AgCl surface electrodes placed over the muscle belly. Distal muscles were recorded preferentially as these show the largest cortical representation (Porter and Lemon, 1993Go). It was hoped that this would improve the chances of detecting coherence between EEG and muscle. Such coherence has been found in healthy human subjects using similar non-invasive surface EMG recordings (Halliday et al., 1998Go). Muscles recorded were the first dorsal interosseous (FDI), the abductor digiti minimi or the wrist extensors/flexors. The EMG signal was amplified and pass-band-filtered (10 Hz to 0.5/1 kHz at Toronto Western Hospital, Canada, and 56 Hz to 1 kHz at the National Hospital for Neurology and Neurosurgery, London, UK).

In five patients (patients 1, 3, 4, 6 and 7) the EEG was recorded simultaneously using bipolar Ag–AgCl scalp electrodes ipsilateral to the thalamic macroelectrode in positions FC3/F3–C3 or FC4–C4 depending on the site of stimulation, and in patient 5 in position C3–P3. Sites C3 and C4 overlie the sensorimotor cortex (Homan et al., 1987Go; Steinmetz et al., 1989Go). Other electrode positions (FP1–F3 and Cz-C4,C3–P3) were recorded ipsilaterally or contralaterally to the side of stimulation depending on the access given by surgical dressings. The signals were amplified and pass-band-filtered (0.16–0.5 Hz to 0.5/1 kHz). EMG, EEG and thalamic LFPs were sampled at either 1 or 2 kHz, digitally converted with 12-bit resolution (CED 1401, Cambridge Electronic Design, Cambridge, UK) and stored using the SPIKE 2 program for off-line analysis, except for patient 3, who was sampled at 2.5 kHz.

Analysis
The cerebellar thalamic (Vim) LFP, denoted by subscript a, and the rectified EMG and EEG, denoted by subscripts b and c, respectively, were assumed to be realizations of stationary zero mean time series. The principal statistical tool used for data analysis in this study was the discrete Fourier transform and parameters derived from it. These were estimated by dividing the records into a number of disjoint sections of equal duration (512, 1024 or 2048 data points with sampling rates of 1, 2 and 2.5 kHz, respectively), and estimating spectra by averaging across these discrete sections (Halliday et al., 1995Go). In the frequency domain, estimates of the autospectrum of the LFP, faa({lambda}), and EMG, fbb({lambda}) or EEG, fcc({lambda}), and their cross-spectrum, for example fab({lambda}), were constructed. The frequency resolution of all spectra was 1.95 Hz (except for patient 3, for whom it was 1.22 Hz). The coherence, |Rab({lambda})|2, was also estimated, where:

Coherence is a measure of the linear association between two signals. It is a bounded measure taking values from 0 to 1, where 0 indicates that there is no linear association (i.e. process B is of no use in linearly predicting process A) and 1 indicates a perfect association. Confidence limits for autospectra and coherence were calculated as described previously (Halliday et al., 1995Go). Coherence was considered to be significant if it exceeded the 95% confidence level.

The phase, defined as the argument of the cross-spectrum, may be estimated by:

Often, peaks of significant coherence were discrete and comprised only one or two data points, making assessment of the phase relationship unreliable (Gotman, 1983Go). Phase was assessed formally if the significant coherence peak met the following empirically derived criteria. First, the peak had to comprise four or more data points. A line was then fitted to the relevant data points using linear regression analysis, and if the standard error of the estimate did not exceed 0.3 the phase was calculated using the equation:

The 95% confidence limits for the phase were calculated as described previously (Halliday et al., 1995Go).


    Results
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
Coherence between cerebellar thalamus, muscle and EEG activity
Coherence between cerebellar thalamic LFPs and the contralateral EMG or ipsilateral Rolandic EEG fell into two bands (Table 2Go). There was a low-frequency band that corresponded to the frequency of the clinically evident tremor, and a higher-frequency band from 8 to 27 Hz.


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Table 2 Summary of the presence of significant coherence between muscle and the cerebellar thalamus (Vim) or cerebellar thalamus and EEG (sensorimotor cortex) at either tremor frequency or between 8 and 27 Hz
 
Coherence at tremor frequency
Coherence between the cerebellar thalamus and EMG at tremor frequency was clearly present only during isometric contraction in patient 1, who had essential tremor, and at rest in patient 3, who had benign tremulous Parkinson's disease (BTPD). The latter patient had a rest tremor but no clinical tremor upon voluntary muscle activity. The absence of coherence at tremor frequency in other subjects may have been due to the effect of microthalamotomy, i.e. abolition of or decrease in tremor due to a minor lesion in the target area during surgery. Such an effect was seen in patients 2, 4, 5 and 7. Low-frequency coherence corresponding to the tremor frequency was also observed between EEG and the cerebellar thalamus in patient 6 (multiple sclerosis with action and postural tremor) (Fig. 6FGo).



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Fig. 6 (A) Raw data in patient 6, who had a cerebellar syndrome due to multiple sclerosis (action and postural tremor). Recordings were made from the right Vim-s (contact 0–1) and cerebellar thalamus (Vim contacts 1–2 and 2–3), the left FDI and right somatosensory cortex (C4–CF4) during a moderate isometric contraction. Autospectra of cerebellar thalamic LFPs (B, contact 1–2), rectified EMG in FDI (C) and EEG over the somatosensory cortex (D) are shown, together with coherence between the cerebellar thalamus and FDI (E) and the somatosensory cortex (F) and between FDI and the somatosensory cortex (G). Note the absence of coherence between EMG and the cerebellar thalamus or EEG.

 
High-frequency coherence in patients with isolated tremor
All of the patients with a history of isolated tremor (patients 1–3) showed coherence between cerebellar thalamic LFPs and EEG or EMG in the 8–27 Hz band. Raw data from patient 1 (essential tremor) during both maximal and moderate [~30–50% maximum voluntary contraction (MVC)] isometric contraction of FDI are illustrated in Fig. 1A and BGo.



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Fig. 1 Raw data from patient 1 with essential tremor during moderate (30–50% MVC) (A) and maximal (B) isometric contractions of the right FDI. Local field potentials were recorded from the left cerebellar thalamus between macroelectrode contacts 1–2 and 2–3. Autospectra of left LFPs recorded between contacts 1–2 (C, E) and the rectified right FDI EMG (D, F) during moderate (C, D) and maximal (E, F) contractions, and coherence between thalamic LFPs (contact 1–2) and the rectified FDI EMG during moderate (G) or maximal (H) contractions are also illustrated. The peak in LFP–EMG coherence at tremor frequency is arrowed in G. Note also the coherence in a band from 8 to 27 Hz (G and H). The peak at 12 Hz in G may be related to physiological tremor and/or be a harmonic of that at 6 Hz. In these and subsequent figures, vertical lines in autospectra and horizontal dotted lines in coherence spectra indicate the 95% confidence limits.

 
The autospectra of cerebellar thalamic LFPs recorded from the left cerebellar thalamus (Vim, contact 1–2) and right FDI and the coherence between these signals are also shown (Fig. 1C–HGo). During moderate contraction, the pathological 6 Hz tremor was evident in the raw EMG (Fig. 1AGo) and as a peak in the FDI autospectrum (Fig. 1DGo). Coherence at this tremor frequency was also seen between the cerebellar thalamus (Vim) and FDI (arrowed in Fig. 1GGo). Essential tremor was much less marked during maximal contraction (Fig. 1B, F and HGo). In addition, coherence was also found, regardless of contraction strength, in the 8–24 Hz range (Fig. 1G and HGo). Coherence between the cerebellar thalamus and sensorimotor EEG followed a similar pattern, with coherence both at tremor frequency and between 8 and 24 Hz during moderate isometric contraction (Fig. 2AGo) and at rest, although the peak at tremor frequency was reduced at rest (Fig 2BGo). Note that with the hand at rest we cannot rule out muscle activity in other muscles.



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Fig. 2 Patient 1 (essential tremor). Coherence between the left thalamic LFPs (contact 1–2) and FC3–C3 during moderate contraction (A) and at rest (B). Note that coherence within the 8–24 Hz band was present during moderate contraction and at rest. In addition, a peak was seen at tremor frequency; the peak was larger during activity (arrowed) than rest. Coherence estimates in Figs 1G and 2AGoGo were derived from the same thalamic LFP signal.

 
Coherence between cerebellar thalamic LFPs and EMG or EEG was greatly reduced when signals were recorded from Vim-s, i.e. between those macroelectrode contacts picking up the largest response to sensory stimulation (see Methods). This is illustrated for patient 2 (essential tremor) in Fig. 3Go. This patient had a microthalamotomy effect and no clinically evident pathological tremor during the study period. The raw EMG (Fig. 3AGo) and EMG autospectrum (Fig. 3BGo), however, revealed the presence of presumed physiological tremor at ~10 Hz. EMG activity was also coherent at this frequency at contacts 1–2 and 2–3 in Vim (Fig. 3G and HGo). In contrast, coherence between contact 0–1 (defined as Vim-s) and EMG was low across all frequencies (Fig. 3FGo).



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Fig. 3 (A) Raw data during moderate isometric contraction of the right FDI in patient 2, who had essential tremor. Contact 0–1 was in left Vim-s and contacts 1–2 and 2–3 were in the cerebellar thalamus (Vim). Autospectra of the rectified FDI EMG (B), Vim-s LFP (C) and cerebellar thalamus LFP (D and E) and coherence between FDI and Vim-s (F) or cerebellar thalamus (Vim) (G, contact 1–2; H, contact 2–3) are also shown. Physiological tremor at ~11 Hz is evident in the rectified EMG in A, in the peak at this frequency in the power spectrum of EMG in B and in the EMG–cerebellar thalamus LFP coherence spectrum in G and H. The small peaks in the autospectra at 60 Hz are due to mains artefact. Note that significant coherence occurred only between muscle and the cerebellar thalamus.

 
The above pattern of coherence between cerebellar thalamic LFPs and EMG or EEG was not limited to patients with isolated essential tremor, but was also found in patient 3, who had BTPD and rest tremor. Here, coherence between 10 and 18 Hz was seen between the right wrist flexors and either the contralateral sensorimotor cortex (Fig. 4AGo) or the contralateral cerebellar thalamus (Vim, Fig. 4BGo) and also between the cerebellar thalamus (Vim) and the cortex (Fig. 4CGo). The coherence between muscle or thalamus (contact 0–2) and cortex was highest between F3–C3 as opposed to FP1–F3 or C3–P3. Note that EEG was recorded in only six patients, and consistent EMG–EEG coherence was seen only in patient 3.



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Fig. 4 Coherence and associated phase calculated in patient 3, who had BTPD and rest tremor, during a tonic isometric contraction between (A and D) the right wrist flexors (WF) and left sensorimotor cortex (FC3–C3), (B and E) the right WF and left thalamus (contact 0–2) and (C and F) the left thalamus and FC3–C3. All signals were recorded simultaneously. The phase between the rectified EMG and EEG (D) did not reach our criterion for measurement. The latency between the right WF and the thalamus and between FC3–C3 and the thalamus was 90 ± 9.4 ms (95% confidence limit) and 31.3 ± 2.2 ms, respectively. The thalamus phase-lagged behind both the muscle and the EEG signal. Phase is shown only over frequencies at which coherence was significant.

 
High-frequency coherence in patients with cerebellar pathology
The presence of coherence within the 8–27 Hz band was seen in only two patients with tremor and clinical evidence of a cerebellar syndrome (patients 4 and 5, with postural and action tremor). Figure 5AGo shows the significant coherence between EMG (left abductor digiti minimi) and the right cerebellar thalamus (Vim) between 10 and 25 Hz in patient 4. Significant coherence was also observed between the right cerebellar thalamus (Vim) and right sensorimotor cortex but not the left sensorimotor cortex (Fig. 5C and DGo). Coherence between the VIM-s and muscle was small.



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Fig. 5 (A) Coherence between the left abductor digiti minimi EMG and the right cerebellar thalamus LFP (contact 2–3) in patient 4, who had cerebellar syndrome due to multiple sclerosis (action and postural tremor). (B) Phase relationship between muscle and cerebellar thalamus over the significant portion indicated in A. The latency between muscle and the thalamus was 23.9 ± 2.5 ms, the thalamic LFP phase lagging behind the muscle signal. (C and D) Coherence between the right thalamus (contact 2–3) and FC4–C4 (C) and FC3–C3 (D). Note that significant coherence in the 8–27 Hz band was seen only between the thalamus and the ipsilateral sensorimotor cortex.

 
Significant coherence between the cerebellar thalamus and muscle at ~18 Hz was also found in patient 5, but this coherence was low. The remaining two patients (patients 6 and 7), who had prominent cerebellar syndromes and associated action and postural tremor, showed negligible coherence between the cerebellar thalamus and EMG at any frequency, and coherence only at low frequencies between cerebellar thalamus and cortex. This is illustrated for patient 6 in Fig. 6Go.

Phase relationship between oscillatory activities
The phase between separate oscillatory activities met our criteria for measurement (see Methods) in patients 1–4. Examples of phase spectra are given in Figs 4D–FGo and 5BGo and the results are summarized in Fig. 7Go. As indicated in Fig. 7Go, there was a large spread in the latencies recorded in different subjects for separate combinations of the sensorimotor cortex, muscle and cerebellar thalamus. Part of this inter-individual variation may have been due to differences in the muscles recorded, the site of the EEG electrodes and the exact frequency band analysed. However, the general trend (i.e. which structure led or lagged) was consistent between subjects. Oscillatory activity within the muscle phase led that recorded within the cerebellar thalamus (Vim), whilst oscillatory activity within the cortex phase led that within the cerebellar thalamus (Fig. 7Go). The phase-lead of the sensorimotor cortex over the cerebellar thalamus was also seen during rest (not shown). The phase between the sensorimotor cortex and muscle did not meet the criteria for measurement in any subject.



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Fig. 7 Mean latencies between EMG and cerebellar thalamus and cerebellar thalamus and EEG for patients 1 (filled circles) and 2 (filled squares), who had essential tremor (postural tremor), patient 3 (filled triangles), who had BTPD (rest tremor) and patient 4 (crosses), who had cerebellar tremor due to multiple sclerosis (action and postural tremor). The latency was calculated only if the phase met our criteria for measurement and the frequency lay within the band 8–26 Hz. Error bars indicate the 95% confidence limits. Negative values indicate that thalamic activity lagged behind either the EMG or the EEG signal. Latencies were calculated by linear regression analysis as described in Methods. The forearm and hand muscles and EEG electrodes from which recordings were made varied in some of the subjects.

 

    Discussion
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
The main finding in the present study was the presence of oscillatory activity of high frequency in the cerebellar thalamus, which was coherent with activity in both contralateral muscle and the ipsilateral sensorimotor cortex. Coherence was found in a broad band from 8 to 27 Hz in the three patients with isolated tremor and in two of the four patients with tremor and signs of cerebellar disease.

Coherence at the frequency of clinical tremor
Coherence between cerebellar thalamic LFPs and rectified EMG at tremor frequency was seen in patient 1. Coherence between spike trains and the rectified EMG has also been reported in subjects with essential tremor (Hua et al., 1998aGo) and subjects with Parkinson's disease (Lenz et al., 1988Go, 1994Go). However, previous cross-correlation analysis of LFPs and EMG in subjects with Parkinson's disease has also revealed a lack of the coherence at tremor frequency (Alberts et al., 1965Go), and Lenz and colleagues have reported that thalamic spike trains and thalamic LFPs are often uncorrelated (Lenz et al., 1988Go). Therefore, it may be that spike trains, rather than LFPs, are more effective in the detection of coherence at tremor frequency. The absence of coherence at the tremor frequency in the majority of our subjects may also have been due to the temporary microthalamotomy effects still present at the time of study, although a more extensive sampling of muscles, as in previous studies, may have revealed coherence at tremor frequency (Lenz et al., 1994Go). A temporary reduction in tremor in the absence of stimulation immediately after functional neurosurgery is common. In one retrospective study, such a microthalamotomy effect was observed in 10 of 19 patients (Tasker, 1998Go).

Coherence in the 8–27 Hz range
LFPs recorded from the cerebellar thalamus (Vim) were coherent with ipsilateral EEG and contralateral EMG in the 8–27 Hz band in five of the seven subjects. Significant coherence between spike trains and rectified EMG within the frequency band 8–27 Hz is apparent in published coherence spectra from patients with essential tremor, although it has not been commented upon previously (Hua et al., 1998aGo). The 8–27 Hz band includes two frequency ranges in which oscillations that affect the motor system have been detected in healthy subjects. The firing time of motor units, for example, is modulated by an 8–12 Hz rhythm (Elble and Randall, 1976Go; Kakuda et al., 1999Go) and coherence between muscle and contralateral peri-Rolandic magnetoencephalographic activity can be detected at this frequency range (J. F. Marsden and P. Brown, unpublished observations). Similarly, motor unit pairs in distal hand muscles can be modulated by a descending 15–30 Hz drive, and there is evidence that this drive is mediated via corticospinal pathways (Datta et al., 1991Go; Farmer et al., 1993aGo, bGo). Further, studies recording magnetoencephalographic and scalp EEG activity in humans, and those in which cortical activity has been directly recorded in animals, show that oscillations within the 15–30 Hz (beta) band occur in the sensorimotor cortex and that these are coherent with contralateral muscle (Conway et al., 1995Go; Salenius et al., 1997Go; Halliday et al., 1998Go; Kilner et al., 1999Go). It is therefore suggested that the coherence detected in the 8–30 Hz band in the present study is physiological and similar to that seen in healthy subjects. This is supported by previous evidence suggesting that the descending 15–30 Hz drive from the sensorimotor cortex and the 8–12 Hz drive are preserved in patients with essential tremor (Lakie et al., 1992Go; Halliday et al., 1997Go) and in treated parkinsonian patients who do not have bradykinesia (Brown, 2000Go).

Two possible methodological issues should be highlighted. First, we rarely found coherence between the sensorimotor cortex and muscle in the beta range, although in the majority of patients it was detected between the cerebellar thalamus and contralateral muscle or the ipsilateral sensorimotor cortex. We were limited in our sampling of EEG sites by surgical dressings. Previous studies using EEG have used either more medially placed electrode positions and have found that the degree of coherence varies with the laterality of the bipolar recording electrodes (Halliday et al., 1998Go), or Laplacian derivations (Mima et al., 1999Go). Secondly, the loss of pathological tremor due to microthalamotomy effects in patient 2 meant that we could only presume that coherence between activity in cerebellar thalamus and EMG at ~11 Hz was related to physiological tremor rather than pathological tremor. This is not an unreasonable assumption, given that essential tremor is usually of lower frequency and that the survival of physiological tremor after thalamotomy has been described previously (Lakie et al., 1992Go), but future studies should include the electrophysiological recordings of preoperative tremor.

Phase relationships between the cerebellar thalamus and EEG and EMG
The phase relationships between the three different signals recorded in the present study varied considerably between subjects, although variability within subjects was small and in every instance except one both the EMG and the EEG signals phase-led the signals recorded from the cerebellar thalamus.

This general phase-lead of EMG and EEG over the cerebellar thalamus (Vim) is important in interpreting the coherence between these signals. Coherence could arise in one of two major ways. First, it might result from peripheral reafference, given the likelihood that the pyramidal tract tends to synchronize motor unit activity in line with cortical rhythmicity (see above). Against this explanation is the absence of coherence between LFPs in Vim-s and either EMG or EEG; Vim-s demonstrated the largest response to peripheral or median nerve stimulation. Further, coherence was present between the cerebellar thalamus (Vim) and the sensorimotor cortex at apparent rest, when reafference should be greatly diminished, and the thalamus phase-lagged behind the EEG.

Alternatively, coherence between the cerebellar thalamus and EMG and between the cerebellar thalamus (Vim) and EEG might be due to the simultaneous driving of both spinal and supraspinal projection areas by the sensorimotor cortex. The sensorimotor cortex could drive the cerebellar thalamus (Vim) either directly, via corticothalamic projections involving short delays (Sawyer et al., 1994Go), and/or indirectly, via a corticopontine–cerebellar–thalamic loop. The pontine nuclei have recently received attention as important nodal points in both the transmission and the modification of descending oscillatory drives (Schwarz and Thier, 1999Go). The lag of the cerebellar thalamus with respect to the cortex was, with one exception, >20 ms, and perhaps therefore more in keeping with a long transcerebellar rather than a direct corticothalamic loop. This would also be consistent with the finding that coherence in the 8–26 Hz band was less apparent in multiple sclerosis patients with prominent cerebellar syndromes. Here it is tempting to speculate that coherence between the cerebellar thalamus and the sensorimotor cortex was lost due to demyelination-related conduction block, desynchronization or secondary axonal loss in corticocerebellar or cerebellothalamic projections.

What is the role of coherence between Vim, sensorimotor cortex and muscle in the 8–27 Hz range?
One possible role of oscillations within the motor system is to promote synchronous neural firing between neuronal populations that differ in spatial distribution but are functionally related. The arrival of synchronous action potentials at common postsynaptic sites may be more effective than uncorrelated firing of the same inputs (Gray et al., 1989Go), so that coherent activities are emphasized at subsequent levels of processing (Singer et al., 1993). Coherent activity may, therefore, provide a means of linking different neuronal populations. The timing of neuronal discharge is closely related to fluctuations in LFPs, which can therefore be used (as here) as a surrogate marker of the synchronization of neuronal discharge (Creutzfeld et al., 1966; Frost, 1968Go). The binding potential of neuronal synchronization has received particular attention in the sensory system (Singer,1993; Gray, 1994Go). However, evidence is also accumulating from both animal and human studies showing that disparate cortical areas involved in the same motor task may be coherent with each other (Gerloff et al., 1998Go; Classen et al., 1998Go; Andres et al., 1999Go; Marsden et al., 2000Go). Similarly, coherent oscillations between cortical and subcortical structures, as shown here, may serve to bind functionally related activities in these structures (Schwarz and Thier, 1999Go).

An alternative view, but one that is not necessarily mutually exclusive with the above interpretation, is that the oscillations may represent some temporal aspect of movement. This has been suggested by Nicolelis and colleagues (Nicolelis et al., 1995Go), who observed 7–12 Hz oscillations between the sensorimotor cortex and the ventral posterior medial nucleus in the rat during active whisker exploration of the environment. Interestingly, the thalamic activity lagged cortical oscillations by up to 50 ms (Nicolelis et al., 1995Go), similar to that seen in the present study. Nicolelis and colleagues proposed that the oscillations were an internally generated temporal representation of exploratory movements in the sensorimotor domain (Nicolelis et al., 1995Go). Therefore, it is possible that the coherent activities demonstrated here provide a common mechanism for the temporal sampling of movement-related activities within the sensorimotor cortex and cerebellar systems. One major advantage of this putative temporal framework is the potential for the systematic modulation of gain at different phases of the sampling cycle. As the period of the sampling cycle matches that of the rhythmic motor output, afferent input can be weighted according to the phase of motor output. In this hypothetical mechanism, the sensorimotor cortex would be continuously digitizing activity in the cerebellar thalamus, perhaps via a corticocerebellar–thalamic loop, explaining why coherence was present between the cortex and the cerebellar thalamus at rest as well as during activity. These oscillations may then interact with and entrain afferent input routed through the cerebellum during activity.

We have focused on the 8–27 Hz range, but in animals (Nicolelis et al., 1995Go; Timfeev and Steriade, 1997) and in other clinical reports (Lenz et al., 1994Go) there is evidence for important oscillations within the cerebellar thalamus that are coherent with the cortex and muscle at lower and higher frequencies. The differing frequencies of these oscillations imply that they represent activity in other functionally distinct pathways, and provide a further example of how plurality in the frequency domain can add another dimension to the organizational capacity of a given nucleus.


    Acknowledgments
 
We wish to thank Professors A. Lozano, D. Thomas and A. J. Thompson for letting us study their patients, and Dr D. Halliday and Mr D. Buckwell, whose computer programs were used in the analyses.


    References
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
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Received November 14, 1999. Revised January 20, 2000. Accepted February 21, 2000.


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