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ABSTRACT |
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 TopAbstract IntroductionMethodsResultsDiscussionReferences |
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INTRODUCTION |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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Physiological tremor in man comprises both mechanical and neurogenic components. The frequency range of neurogenic tremor is classically described as occurring between 7 and 12 Hz. However, because it overlaps with the frequency range of mechanical-reflex tremor the relative contributions of each to the overall tremor signal cannot be easily determined (Halliday & Redfearn, 1956; Elble & Randall, 1976, 1978; Halliday et al. 1995, 1999; McAuley et al. 1997).
The mechanical component of tremor arises because perturbation of a limb originating either externally or internally produces a damped oscillatory movement. The frequency components of mechanical tremor are primarily influenced by two factors that may be modelled by a mass-spring resonant system, namely inertia and stiffness (Robson, 1959; Stiles & Randall, 1967). Thus the mechanical component of tremor differs for different limbs, may be lowered by addition of a load to the limb and may be influenced by changes in stiffness both of joints and of muscles and by the nature of the resisting force (see Elble & Koller, 1990 for review). This component is commonly termed mechanical-reflex tremor because under conditions of high load, fatigue and drug stimulation, the spinal reflex arc may also make a contribution (Stiles, 1976; Hagbarth & Young, 1979).
The neurogenic component of human physiological tremor is detected in the frequency range of approximately 7-12 Hz (Elble & Randall, 1976; Findley & Gresty, 1984), although it is most commonly termed the 8-12 Hz neurogenic tremor. It has been found to be largely insensitive to changes in inertial load and stiffness (Elble & Randall, 1978; Homberg et al. 1987). Elble & Randall (1976) reported the first direct demonstration of the relationship between motor unit discharge and neurogenic tremor. They showed that during conditions of high inertial load, finger extensor motor units may fire at approximately 20 Hz yet be modulated at ~8-12 Hz. Recently these results have been confirmed and the frequency range of load- independent tremor has been extended to approximately 40 Hz (McAuley et al. 1997; Halliday et al. 1999). During steady muscle contraction different single motor units are commonly modulated at frequencies between 1 and 40 Hz, with maxima at 1-12 Hz and 16-32 Hz (Farmer et al. 1993). Coherence in similar ranges and with similar maxima can be detected between finger tremor and surface EMG (Halliday et al. 1999).
It has long been suggested that the 8-12 Hz neurogenic component of tremor is of central origin (Elble & Randall, 1976; Lamarre, 1979; Llinás & Yarom, 1986; Halliday et al. 1999). Koster et al. (1998) in their study of patients with pathological mirror movements provided evidence to support this hypothesis for enhanced 8-12 Hz physiological tremor. It has also been postulated that higher frequencies of tremor (15-40 Hz) may be produced by oscillation in the central motor command (Conway et al. 1995).
Abnormal bilateral fast conducting corticospinal pathways are known to be present in subjects with pathological mirror movements including those with Klippel-Feil syndrome (Farmer et al. 1990), congenital mirror movements (Cohen et al. 1991) and XKS (Danek et al. 1992; Mayston et al. 1997). In XKS subjects, short-latency cutaneous and spinal stretch reflexes are confined to the stimulated side. However, the long-latency components of cutaneomuscular reflexes (CMRs) can be recorded bilaterally from homologous left and right upper limb muscles (Mayston et al. 1997). Cross-correlation of motor unit discharges recorded from left and right homologous muscles reveals the presence of a short duration central peak in the cross-correlogram, indicating shared pre-synaptic input to the left and right homologous motoneurone pools (Mayston et al. 1997). The bilaterality of voluntary and long-latency reflex activity in XKS subjects with abnormally projecting central motor pathways provides a model for examining the neural pathways and mechanisms underlying neurogenic physiological tremor in man. In this study we have examined non-enhanced human physiological tremor and extend the observations of Koster et al. (1998). The data have been published in abstract form (Mayston et al. 1999).
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METHODS |
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All experiments were carried out with the approval of the Joint University College and University College Hospital Committee on the Ethics of Human Research, subjects gave written informed consent and the procedures conformed to the standards set by the Declaration of Helsinki.
Six subjects with XKS and pathological mirror movements were studied (aged 24-64 years, all male). The degree of mirror movements varied in the XKS subjects and ranged from weak to marked (grade 2-3). As described in Mayston et al. (1997), the XKS subjects in this study all showed short-latency abnormal bilateral responses to transcranial magnetic stimulation (TMS). Five of the six subjects showed abnormal crossing of the I1 and E2 components of the CMR with restriction of the short-latency spinal (E1) component of the CMR to the stimulated side (CMRs could not be recorded from K8). Thus XKS subjects show an abnormal distribution of long-latency reflex activity due to abnormal bilateral projection of the corticospinal tracts to homologous left and right upper limb motoneurone pools. Five of the six subjects with XKS (K1, K2, K4, K4a and K8) have been previously described in detail (Quinton et al. 1996; Mayston et al. 1997).
The results from the XKS subjects were compared to those obtained from six healthy control subjects (aged 20-68 years, 5 female). None of the normal subjects had mirror movements. It is known that in normal subjects stimulation with focal TMS given at threshold for a response plus 5% of the maximal stimulator output to the motor cortex results in a contralateral short-latency EMG response in distal muscles; at this stimulus intensity ipsilateral short-latency responses cannot be evoked. The CMR for 1DI was recorded in addition to assessing the laterality of the corticospinal tract using TMS. As expected in the normal subjects the EMG response to TMS was only found in the 1DI contralateral to the stimulated cortex and the CMR was confined to the stimulated side. None of the healthy or XKS subjects showed pathological tremor, and with the exception of the mirror movements motor function in both subject groups appeared to be normal.
EMG and tremor recordings
Pre-gelled surface electrodes (TECA disc/bar electrodes, Medelec, Woking, Surrey, UK) were attached to the skin overlying the left and right index extensor digitorum muscles (EI) with a centre-to-centre distance of 20 mm. The position of the electrodes was adjusted to find the optimal position to record index finger extensor EMG. Simultaneous recordings of tremor were made using accelerometers attached to the distal phalanx of both the left and right index fingers during co-extension of the index fingers (Bruel & Kjaer, type 4393, Denmark, and a vibrometer, type SA-105, Frieburg, Switzerland).
Subjects were seated well supported in an armchair with the forearm, wrist and fingers of each arm supported in a splint and instructed to perform bilateral sustained index finger extension firstly without loading and then with 60 g loading of the dorsal surface of the distal phalanx of the index finger (requiring approximately 10% maximum voluntary contraction to maintain the index finger in a neutral position). The surface EMG was filtered (-3 dB at 20-500 Hz) and amplified. Each data set consisted of simultaneous EMG and acceleration recordings, duration 180 s. The data were stored on magnetic tape (Racal Store 4, Racal, Southampton, UK) for off-line analysis.
Data analysis
Time domain analysis. The times of occurrence of the motor unit spikes were used to perform time-domain analysis. Medium and large spikes were selected for analysis using a level detector (Neurolog NL200, Neurolog, Hemel Hampstead, UK). The resultant trigger pulses were passed into a microcomputer (Dell Pentium, XPS75) via a CED1401 analog-to-digital converter (Cambridge Electronic Design, Cambridge, UK) for processing. Cross-correlograms were constructed between the times of occurrence of motor unit spikes recorded from the left (designated as the reference) and right index extensor (designated as the response) with a bin width of 1 ms and a pre-and post-trigger sweep of 100 ms (Spike2 software, CED). At least 2000 spikes were used from each multi-unit EMG recording. The statistical significance of any peaks detected in the cross-correlation histogram was assessed according to the criteria of Sears & Stagg (1976). The magnitude of any peak was expressed as the index 'k' (the maximum number of counts in the histogram peak divided by the mean level of counts in the histogram; Sears & Stagg, 1976). The half-width of the peak was measured in addition to the duration of any central feature which was determined using cusum (Davey et al. 1986).
Frequency domain analysis. The surface EMG was full-wave rectified and fed to a data collection interface for digitising (CED 1401). The tremor signal was also digitised. The data were sampled at 1000 Hz and the autospectra, coherence, phase and cumulant of the tremor and rectified EMG signals were calculated using software developed by Halliday and Rosenberg (Rosenberg et al. 1989; Halliday et al. 1995). Each segment length was 1024 points in the finite Fourier transforms, giving approximately 175 segments per data set of 180 s duration.
The left and right EMG signal time series were designated 'a' and 'b', respectively. The left and right tremor time series were designated 'x' and 'y', respectively. Calculation of the coherence at any given frequency gives a measure of the association between two processes. It is expressed on a linear scale between 0 and 1.0, where 1.0 indicates total dependence. For the data in the present study the coherence was calculated at 1 Hz intervals between 0 and 70 Hz. For example, coherence between the left and right tremor signal is denoted by |Rxy(
)|2 and the coherence between left and right EMG as |Rab()|2, where is the frequency in hertz. The power for a given process e.g. the left tremor is given by fxx(Â). The phase relationship between two signals, e.g. left and right tremors, is given as 
xy(). The time lag between signals was determined by calculating the slope of the constrained phase plot. In all cases the 95% confidence limit for the coherence was calculated (see Halliday et al. 1995).
The following combinations of rectified EMG and tremor were examined using frequency domain analysis:
(1) Coherence and phase between same-side EMG and tremor.
(2) Coherence and phase across the body for EMG and tremor:
(a) Analog EMG left and right.
(b) Tremor recorded from left and right.
(c) Left EMG and right tremor; right EMG and left tremor.
Measurement of tremor amplitude. The raw tremor signal was rectified and the mean amplitude calculated over a 50 s period using averaging software (Signal Averager, CED).
Statistical analysis
All values are given as means ± S.D. The magnitude and frequency of coherence between same side tremor and rectified EMG were statistically tested for differences between controls and XKS subjects for both unloaded and loaded conditions using one-way ANOVA. Scheffe's post hoc test was applied. Student's unpaired t test was applied to the data to determine if there was a significant difference in the amplitude of tremor between the controls and XKS subjects. Student's paired t test was used to determine if the central cross-correlogram peak parameters detected between left and right EMGs in XKS subjects were significantly different in unloaded and loaded conditions. The chosen level of significance was P < 0.05.
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RESULTS |
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EMG and tremor
Typical examples of the EMG and tremor recorded from a control subject and an XKS subject with mirror movements are shown in Fig. 1. During co-extension of the index fingers against 60 g loading, the left and right extensor indices (EI) EMGs and left and right index finger tremor recordings appear similar in the two subjects. Visual inspection of the raw EMG and tremor signals of all subjects did not reveal any differences between the control and XKS groups. Calculation of mean amplitude of the rectified tremor signal (controls: 1.19 ± 0.47 cm s-2; XKS subjects: 1.42 ± 0.20 cm s-2) showed that there was no significant difference between the two groups (P > 0.05).
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The top panels show left and right extensor indices (EI) EMG recordings for the two subject (scale bar microvolts). The bottom panels show left and right accelerometer signals for the two subjects (scale bar cm s-2).
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Tremor power spectra
During simultaneous left and right index finger extension the power spectra of the tremor signals and their response to inertial loading were similar in controls and the XKS subjects. Figure 2 illustrates typical index finger tremor spectra in the two subject groups. The spectra obtained from the control subject during the unloaded condition contain a dominant peak at approximately 11 Hz with a less distinct peak at approximately 25 Hz (Fig. 2A). The tremor spectra from the XKS subject contain a peak at around 8 Hz and a less distinct peak at approximately 24 Hz (Fig. 2B). Inertial loading (60 g) produces a general decrease in the magnitude of the higher frequency spectral components in both subjects consistent with its known effect on the mechanical-reflex component of tremor (Stiles & Randall, 1967). Loading also resulted in an accentuation and a slight shift downward of the low frequency peak to 9 Hz in the control subject (Fig. 2C) and 7 Hz in the XKS subject (Fig. 2D).
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A and C, control subject tremor spectra during index finger extension against gravity and with 60 g loading. B and D, XKS subject tremor spectra during finger extension against gravity and with 60 g loading. In both subjects inertial loading decreases high frequency spectra and enhances spectral peaks at 7 and 9 Hz. Ordinate: log10 power. Abscissa: frequency, 1 Hz bins.
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For the controls in the unloaded condition, dominant peaks were present in the tremor spectra in a low frequency range (left index: 11.0 ± 1.5 Hz, range 10.0-14.0 Hz; right index: 10.7 ± 1.8 Hz, range 9.0-14.0 Hz; n = 6). There was no significant difference between the left and right fingers for the frequency at which the peak of the tremor frequency occurred (one-way ANOVA, P > 0.05). During inertial loading, the dominant spectral peak did not significantly alter its frequency (left index: 10.5 ± 0.8 Hz, range 10.0-12.0 Hz; right index: 9.8 ± 1.7 Hz, range 8.0-13.0 Hz; one-way ANOVA, P > 0.05). For the control subjects the spectra extended to higher frequencies (see Fig. 2A and C). In some cases a discrete peak was identified at ~22.0 Hz; however, it was more usual to observe a broad range of frequencies. Inertial load produced a decrease in the overall high frequency component of the spectra consistent with the fact that one component of the tremor at this frequency was mechanical.
In the XKS subjects for the unloaded condition, dominant peaks were also observed in a low frequency range. The mean frequency of the peak (left index: 8.0 ± 0.6 Hz, range 7.0-9.0 Hz; right index: 8.2 ± 1.7 Hz, range 7.0-10.0 Hz) was significantly lower than that found for the controls (one-way ANOVA, P < 0.05). Despite this significant difference, it should be noted that these maxima were in the known range for neurogenic physiological tremor (Elble & Randall, 1976, 1978; Findley & Gresty, 1984). Inertial loading did not significantly alter the peak frequency for the low range (left index: 7.7 ± 0.8 Hz, range 7.0-9.0 Hz; right index: 7.8 ± 0.8 Hz, range 7.0-9.0 Hz; n = 6). Like the controls spectra were present over a broad range of higher frequencies, and the power in this range was reduced by inertial loading. In some cases discrete peaks were identified at ~22 Hz (see Fig. 2B and D).
Coherence between same-side EMG and tremor
Coherence and phase were calculated between EI rectified EMG and index finger tremor on the same side. In both subject groups significant coherence was found across a broad range of frequencies (predominantly 6-40 Hz). The coherence maxima were located in a low and a high frequency range in both the control and the XKS subjects. An example of coherence and constrained phase (i.e. for ease of visual representation the phase is plotted between ± 
radians) data from the unloaded condition for a control subject and an XKS subject are shown in Fig. 3A and B. In both subjects there is significant coherence between 6 and 40 Hz, with some coherence in excess of 40 Hz in the XKS subject. There are coherence maxima in the ranges 6-12 and 15-40 Hz in both subjects. Inertial loading (Fig. 3C and D) accentuates the low frequency coherence peaks but significant EMG-tremor coherence up to 35 Hz remains in both subjects. The frequencies and magnitudes of the coherence maxima are summarised in Table 1.
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A and C, control subject coherence and phase during finger extension against gravity and with 60 g loading. B and D, XKS subject coherence and phase during finger extension against gravity and with 60 g loading. The dotted line for this and other figures indicate the 95% confidence limit for the coherence. In all conditions there is significant coherence between 6 and 40 Hz. The constrained phase plots (note wrap around at +
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One-way ANOVA revealed a significant difference between controls and XKS subjects in the frequency at which maximal coherence was detected from the left hand in the unloaded condition (controls unloaded left hand: 11.2 ± 1.5 Hz; XKS unloaded left hand: 7.8 ± 0.8 Hz; P < 0.05, n = 6). It should be noted that both these frequencies of EMG-tremor coherence were within the known 7-12 Hz range of neurogenic tremor. Comparison of the remainder of the coherence parameters using ANOVA (see Table 1) did not reveal any other significant differences between controls and XKS subjects.
The constrained phase plots shown as insets indicate that the tremor signal lags behind the EMG signal reflecting delays in electro-mechanical coupling. It is important to note that for the low frequency (6-12 Hz) range of EMG-tremor coherence, the slope of the phase was found to go through zero and thus it is appropriate to model the system as one containing a pure delay. In the examples illustrated the EMG-tremor lags calculated from the phase in the control subject were 15.9 ms for the low frequency range and 18.5 ms for the unloaded and loaded conditions, respectively. The respective lags for the low frequency range in the XKS subject were 23.9 ms for the unloaded and 26.4 ms for the loaded conditions. There was no significant difference between the values calculated for the left and right sides, and therefore the data for left and right were pooled. The mean lag for the unloaded controls in the low range was: 26.6 ± 7.7 ms; the mean for the loaded controls in the corresponding frequency range was: 35.7 ± 8.8 (n = 12). The mean phase lag for the low frequency range for the XKS subjects unloaded was 26.5 ± 3.9 ms; loaded: 35.9 ± 9.6 ms (n = 12). There were no significant differences in the EMG-tremor lags between controls and XKS subjects in either unloaded or loaded conditions. The phase slope for the higher 15-40 Hz frequency range was less steep. However, the slope of the phase over the high frequency range of coherence did not go through zero and thus for these frequencies the system cannot be modelled on the assumption of a pure delay (Halliday et al. 1998).
Coherence across the body
(a) Left and right EMG
Time domain analysis. A short duration central peak in the cross-correlogram indicates the presence of shared pre-synaptic input to the motoneurone pools innervating the muscle pair under study. Figure 4A shows a cross-correlogram constructed between times of occurrence of the selected EMG spikes recorded from left and right EI of a control subject during co-extension of the loaded index fingers. The cross-correlogram is flat indicating that the motoneurone pools supplying this homologous muscle pair do not receive shared synaptic input and are controlled independently. This was the finding for all control subjects for both the unloaded and loaded conditions. In contrast, all the cross-correlograms of the subjects with XKS and mirror movements contained a short duration peak centred around time zero, indicating the presence of abnormal shared common pre-synaptic input to the motoneurone pools innervating left and right EI muscles. An example is shown in Fig. 4B. For this subject during the unloaded condition, there is a short duration peak of 14 ms (half-width 6 ms) and size k = 2.0 centred around time zero in the cross-correlogram. Contraction against an inertial load had little effect on the magnitude or duration of the central peak (Fig. 4C). In the XKS subjects during the unloaded condition, the mean size (k) of the peak was 2.0 ± 0.6, mean duration 21.2 ± 11.7 ms, and mean half-width 11.0 ± 3.7 ms, (n = 6). Central cross-correlogram peak parameters were not significantly affected by inertial loading (mean peak size, k = 2.0 ± 0.5, duration 20.8 ± 7.9 ms and half-width 12.5 ± 6.3; Student's paired t test, P > 0.05, n = 6).
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A, cross-correlogram constructed between times of occurrence of left and right EI EMG motor-unit spikes in a control subject. B and C, the cross-correlograms constructed between left and right EI EMG motor-unit spikes in an XKS subject during unloaded and loaded conditions contain a central peak. D, no significant coherence between left and right EI rectified analog EMGs in the control subject; same data as A. E and F, significant coherence between left and right EI rectified analog EMGs in the XKS subject during unloaded and loaded conditions; same data sets as B and C, respectively. G, no significant coherence between left and right index finger tremor recordings; same data set as A and D. H and I, significant coherence between left and right index finger tremor recordings during unloaded and loaded conditions; same data sets as B and E, and C and F, respectively. The phase shown as insets in D-I behaves randomly when there is no coherence (D and G). For the XKS subjects the phase is approximately flat across the frequencies of significant coherence indicating synchronisation of the signals. Ordinate A-C, counts; abscissa A-C, time, 1 ms bin width. Ordinate, D-I, coherence 0-0.8; abscissa, D-I, frequency, 1 Hz bins. Insets: phase ±
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Frequency domain analysis. No coherence was detected between left and right EI EMG recorded from the controls during simultaneous left and right index finger extension (Fig. 4D). In contrast, for the XKS subjects coherence was observed between left and right EI EMGs across a broad range of frequencies (6-40 Hz) with maxima for the unloaded condition of ~8 and ~22 Hz; the corresponding values for the loaded condition were ~8 and ~23 Hz. (Fig. 4E and F). The frequency and size of coherence peaks for left and right EMG for the unloaded and loaded conditions are summarised in Table 1. In the examples shown in Figs. 4E and F, the phase over the frequencies for which there is significant coherence shows a small positive slope. This indicates that with respect to the reference signal (left EMG), the timing of the response EMG signal (right EMG) was in advance on average by 3 ms (lag -3 ms). Such small timing differences can be accounted for by minor differences in central and peripheral conduction time (see Farmer et al. 1990 for discussion). Taking the XKS group as a whole, the phase between left and right EMG was zero indicating that the shared EMG frequencies were synchronous in keeping with the central location of the peak obtained from time domain analysis.
(b) Left and right tremor
Frequency domain analysis. As in the example in Fig. 4G, in all of the control subjects there was no coherence between simultaneously recorded left and right index finger tremor despite the presence in both tremor recordings of marked spectral peaks at similar frequencies (see Fig. 2). Thus in normal subjects the left and right tremor signals, like their EMGs, are independent with no consistent phase relationship. In contrast a typical XKS subject shows significant coherence between left and right tremor in the range 4-40 Hz with maxima at ~8 and ~23 Hz in both the unloaded (Fig. 4H) and loaded conditions (Fig. 4I). Calculation of the phase between left and right tremor (insets in Fig. 4H and I) indicated zero delay between the left and right tremor signals in unloaded and loaded conditions. Taking the XKS group as a whole, the left-right phase associated with the abnormally coherent tremor frequencies was zero. The results of left-right tremor coherence for all the control and XKS subjects are given in Table 1.
(c) Right EMG and left tremor; left EMG and right tremor
Frequency domain analysis. Figure 5A shows that in a control subject there is no significant coherence between right EMG and left tremor. This was found for all control subjects and was unaffected by inertial loading. In contrast, for an XKS subject, there is significant coherence between right EI EMG and left index finger tremor in the range 6-30 Hz with maxima at ~8 and ~25 Hz (Fig. 5B). There was a striking similarity between coherence detected between left and right EMGs, left and right tremor, right EMG and left tremor and left EMG and right tremor. This result indicates that the EMG signal recorded from one side is linked to the tremor recorded from the opposite side. Moreover, the coherence range and maxima are similar to those found for ipsilateral EMG-tremor recordings in XKS and control subjects (see Table 1). These similarities are further emphasised by the phase (see inset in Fig. 5B) which indicates that the left tremor lags the right EMG by approximately 34.6 ms for frequency range 6-12 Hz, a similar value to those detected for ipsilateral EMG-tremor recordings in controls and XKS subjects (compare Figs 2 and 5). Contrast this phase lag to the zero phase relationship that is obtained for crossed EMG-EMG coherence and crossed tremor-tremor coherence. The mean lag between EMG and tremor in the 6-12 Hz range for the unloaded finger was 26.9 ± 14.6 and 28.7 ± 7.6 ms for left EMG to right tremor and right EMG to left tremor, respectively. The corresponding values for the loaded condition were 34.1 ± 6.8 and 38.9 ± 3.2 ms for left EMG-right tremor and right EMG to left tremor (n = 6). The frequency and size of the coherence peaks for right EMG and left tremor and left EMG and right tremor are summarised in Table 1.
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A, the control subject does not show significant coherence; the phase is random. B, significant coherence is present between 6 and 30 Hz; the negative phase slope indicates that at low frequencies of significant coherence the EMG precedes the tremor. The phase is random for frequencies in excess of 30 Hz. Abscissa: coherence [ |Rbx(
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Figure 6 summarises diagrammatically the relationships as revealed by coherence analysis between all possible EMG-tremor combinations in both subject groups.
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Diagram showing the significant EMG-EMG, tremor-tremor and EMG-tremor interactions in the control (dashed lines) and XKS subjects (continuous lines).
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DISCUSSION |
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The main finding of this study is that, in contrast to normal subjects, subjects with XKS and pathological mirror movements with an abnormal bilateral corticospinal projection show coherence between left and right finger tremor signals in the range 6-40 Hz with maxima at ~8 and ~22 Hz. We have further demonstrated that in these subjects there is abnormal coherence between left and right EI EMGs with maxima at similar frequencies to those detected between the left and right tremor signals. The range of coherent frequencies encompasses that of classical human neurogenic physiological tremor (7-12 Hz). In addition, the data provide further evidence to support the view that the frequency range of human neurogenic tremor extends up to 40 Hz (see McAuley et al. 1997; Halliday et al. 1999). The data thus provide strong evidence to support the hypothesis that the low and high frequency neurogenic components of normal human physiological tremor result from oscillatory activity in supraspinal neural pathways.
Koster et al. (1998) studied enhanced physiological tremor in control subjects and three subjects with mirror movements. In these experiments intravenous salbutamol was administered in order to produce visible tremor, hyperhydrosis and tachycardia. Koster et al. (1998) demonstrated significant cross-spectral components between the EMGs of left and right wrist extensor muscles in the frequency range 6-12 Hz. The equivalent calculation for left and right tremor was not reported. Thus comparison between the present data and those of Koster et al. (1998) is difficult. Both studies show abnormal coherence of the 6-12 Hz EMG components in mirror movement subjects. Our results were obtained during normal finger extension, those of Koster et al. (1998) during wrist extension with greater loading (1000 g). During enhanced physiological tremor there is obvious modulation of the raw EMG signal at the tremor frequency (Stiles, 1976, 1980; Hagbarth & Young, 1979; Lakie et al. 1986). Enhanced physiological tremor results in broad duration motor-unit synchronisation and coherence of rectified EMG and tremor only at the visible tremor frequency (Logigian et al. 1988). In non-enhanced physiological tremor the duration of motor-unit synchronisation is much less (Logigian et al. 1988) and the frequency range of coherence between motor units within a muscle and between motor units and tremor is broad although still contains obvious maxima (Halliday et al. 1999). The activity transmitted in pathways responsible for EMG synchronisation in the time and frequency domain may change during the transition from non-enhanced to enhanced physiological tremor. It may be argued from the mirror movement data presented here and by Koster et al. (1998) that abnormally projecting bilateral central nervous system pathways underlie abnormally shared enhanced and non-enhanced physiological tremor.
Tremor and ipsilateral coherence
In the present study, the raw tremor spectra were similar in the controls and the XKS subjects and for both subject groups the tremor spectra behaved similarly during bilateral inertial loading. In both groups the peak spectral components were generally within the 7-12 Hz range of physiological tremor (for one control subject the peak was at 14.0 Hz). However, in comparison to the controls, the XKS group was at the low end of this range and there was a statistical difference between the two groups. This raises the question as to whether the low frequency peak in the tremor spectrum in the Kallmann's group may be the sign of a pathological tremor peculiar to XKS subjects, which may have a different mechanism from physiological tremor. This seems unlikely to us. While it is true that the mean frequency of the peaks in the power spectra of the controls and XKS subjects in the low frequency range were significantly different in this study with the exception of one control subject, the values (range: controls 8-14 Hz; XKS subjects 7-10 Hz) were within the normal range (7-12 Hz) of neurogenic physiological tremor (Elble & Randall, 1976, 1978; Findley & Gresty, 1984). In addition, widths of the spectral peaks were such that there was considerable overlap of the range of frequencies making up the tremor peak between the two groups in the present study (see Fig. 2), and the mean amplitude of the rectified tremor signal did not significantly differ between the controls and XKS subjects.
Frequency domain analysis of EMG and tremor recorded on the same side of the body revealed evidence of coherence and phase that was similar in both the control and XKS subjects. Inertial loading did not greatly influence the range or the maxima of the frequencies of the ipsilateral EMG-tremor coherence in either the control subjects or those with XKS. Furthermore, the range and frequency maxima of the ipsilateral EMG-tremor coherence in the controls and the XKS subjects were similar to those described by Halliday et al. (1999) using a similar experimental protocol. The delay between EMG and tremor, calculated from the slope of the phase between EMG and acceleration signals in the range 7-12 Hz was similar to that described previously for normal subjects during position holding and during slow finger movements (Halliday et al. 1995; Wessberg & Vallbo, 1996; Wessberg & Kakuda, 1999; Arihara & Sakamoto, 1999). Overall the similarities between the tremor spectra (see discussion above) and the ipsilateral EMG-tremor coherence in the controls and XKS subjects support the view that, with the exception of the abnormal sharing of tremor in the XKS subjects, the nature of the physiological tremor did not differ substantially between the two groups.
Coherent left and right tremor and EMG in XKS subjects
In keeping with data from earlier studies (Marsden et al. 1969; Koster et al. 1998), left and right finger tremor recordings from the healthy subjects did not show significant coherence. In contrast, left and right tremor recordings from subjects with XKS and mirror movements showed coherence in the frequency range 6-40 Hz with maxima at ~8 and ~22 Hz. Calculation of the phase indicated that in contrast to the ipsilateral EMG-tremor, the coherent frequencies of left and right tremor were synchronous. In XKS subjects the range of shared frequencies and their maxima were similar to those detected between the subjects' left and right EMGs, between left EMG and right finger tremor and between right EMG and left finger tremor. The range and maxima of the coherence between left and right were not affected by inertial loading.
Previous studies have shown that the shared voluntary motor command in mirror movement subjects is transmitted by activity in corticospinal axons which project both contra- and ipsilaterally giving rise to abnormal synchronisation of motor-unit firing between homologous left and right muscles (Farmer et al. 1990; Farmer et al. 1991; Carr et al. 1993; Mayston et al. 1997). We have now demonstrated abnormal coherence between left and right EMG. The present study demonstrates that one mechanism for abnormal sharing of neurogenic physiological tremor in XKS involves in-phase central oscillations. Indeed, had there not been abnormal shared physiological tremor then one would have to conclude that in-phase oscillations of the corticospinal input to motoneurones is not an underlying mechanism for tremor production.
The abnormal left-right EMG coherence in XKS subjects is similar to that seen for single motor unit pairs recorded from within the first dorsal interosseous muscle during steady contraction in normal subjects (Farmer et al. 1993). The presence of coherence between left and right EMGs in XKS subjects supports the concept that the corticospinal tract is involved in common modulation of motor unit discharges (Farmer et al. 1993; Mills & Schubert, 1995; Conway et al. 1995). We suggest that zero phase lag coherence between groups of motor units is one mechanism by which the neurogenic components of physiological tremor become manifest in normal subjects. The neurogenic components of physiological finger tremor overlap with the mechanical reflex components and therefore distinguishing the two and their relative contributions to the tremor record is difficult. In the XKS subjects the mean magnitude of coherence between left and right tremor frequencies in unloaded and loaded conditions was 0.5 and 0.7, respectively, for the low frequency range (~8 Hz) and 0.2 for the high range (~23 Hz). This would suggest that in the high and low frequency bands between 20 and 70% of the tremor signals are shared; the abnormal neuroanatomy of these subjects determines that these shared tremor components can only be neurogenic. Therefore, we conclude that oscillations in the central motor pathways provide a significant contribution to the tremor signal in the range 6-40 Hz, particularly at the frequency maxima of ~8 and ~22 Hz. From estimations of the coherence between EMG and tremor in healthy subjects, Halliday et al. (1999) estimated that on average 20% and at most 70% of the linear components of the two finger tremor signals could be accounted for by coherent extensor indicis EMG activity.
Central nervous pathways and physiological tremor
Unilateral transcranial magnetic stimulation results in bilateral short-latency responses in hand and forearm muscles of subjects with XKS and mirror movements. These subjects do not show abnormal bilaterality of spinal latency reflexes but do show abnormal bilateral distribution of long-loop transcortical reflexes. It should be noted that in the XKS subjects the crossed coherence between EMG and tremor, i.e. left EMG-right tremor and right EMG-left tremor was similar to that detected between ipsilateral EMG and tremor. These similarities and the absence of crossing of spinal latency excitatory reflexes in XKS suggest that oscillations in spinal reflex pathways do not produce significant common modulation of motor unit firing and therefore do not contribute to non-enhanced neurogenic tremor (Lippold, 1970; Joyce & Rack, 1974). Because of the known crossing of long-latency stretch reflex and CMRs in mirror movement subjects (Farmer et al. 1990; Matthews et al. 1990; Capaday et al. 1991; Carr et al. 1993; Mayston et al. 1997) it is possible that oscillations in transcortical reflex pathways are responsible for the left-right EMG and tremor coherence. However, because of the additional delays inherent in long-loop reflexes it can be argued that the upper limit of the frequency of oscillations that can be sustained by this mechanism alone is low, probably less than 4 Hz (see Kakuda et al. 1999 for discussion).
Supraspinal oscillations arising in inferior olivary neurons have been proposed for the generation of 8-12 Hz tremor (Lamarre, 1979; Llinas & Yarom, 1986). However, there is little direct evidence in man for such a mechanism. As found by Koster et al. (1998) for enhanced physiological tremor, the present results demonstrate abnormal left-right coherence maxima at ~8 Hz in the XKS subjects. The data thus provide strong support for the hypothesis that 8-12 Hz physiological tremor is centrally mediated. Whilst we cannot exclude sharing of 8-12 Hz tremor via abnormal bilateral non-corticospinal e.g. reticular or rubrospinal pathways, the mirror movements in XKS subjects show a strong predilection for distal hand muscle motoneurone pools which are known to receive strong direct corticospinal input.
Studies of single motor unit activity from EI and physiological tremor from the finger reveal coherence between motor unit discharges and tremor at ~8-12 Hz (Elble & Randall, 1976). Recently, these findings have been confirmed and the range of motor unit-tremor coherence extended to ~40 Hz with maxima at ~9 and ~20 Hz (Conway et al. 1995; Halliday et al. 1995, 1999). Similar results have been found during larger force contractions against an elastic load in which EMG-tremor coherence maxima are present at ~10, ~20 and ~40 Hz (McAuley et al. 1997).
During movement and sustained muscle contraction the motor cortex local field potential in sub-human primates shows periods during which there are 15-35 Hz oscillations (Murthy & Fetz, 1992; Sanes & Donoghue, 1993; Donoghue et al. 1998; see Farmer 1998 for review). In primates this oscillatory activity is coherent at ~20 Hz with EMG recorded during the hold period of a ramp and hold task (Baker et al. 1997). In man, during isometric contraction and finger extension against gravity, the MEG (magnetoencephalogram) and EEG recorded from over primary motor cortex are coherent with contralateral EMG in the frequency range 15-40 Hz (Conway et al. 1995; Salenius et al. 1997; Halliday et al. 1998; Brown et al. 1998). It is interesting to note that early attempts to correlate EEG with tremor failed to demonstrate any correspondence between the 10 Hz alpha rhythm and physiological tremor (Lippold, 1970). However EEG-EMG coherence can be detected in the range 3-13 Hz yet the effects are smaller and less consistent than for the higher (15-40 Hz) frequency range (Mima et al. 2000). It should be noted that coherence between tremor and EEG/MEG has as yet not been directly examined. We acknowledge that reconciling the differences in left-right coherence strength between the low and high frequency ranges with data from previous EEG/MEG-EMG coherence experiments is difficult. The fact that the peak in the EEG/MEG-EMG coherence at the 8-12 Hz frequency band is either absent or small, does not mean that an 8-12 Hz component is not present in the signal transmitted via the corticospinal pathway. Rather, such a signal may only contribute weakly to the EEG/MEG signal recorded from the scalp, possibly due to the very wide cerebral distribution of the origin of alpha band frequencies, many of which do not relate to central motor control.
Despite the differences in coherence magnitude the findings of MEG/EEG-EMG coherence studies are consistent with data for the present study in which bilaterally projecting corticospinal pathways transmit physiological tremor across a range of frequencies between 6 and 40 Hz. The finding of abnormal left-right coherence in subjects with XKS and mirror movements strongly supports the hypothesis that a significant proportion of neurogenic physiological tremor across a wide range of frequencies in normal subjects is produced by oscillatory activity in corticospinal inputs to spinal motoneurones.
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Acknowledgements
We wish to thank the Astor Equipment Fund (UCH Trust, London) and the Human Movement and Balance Unit (Institute of Neurology, Queen Square, London) for the accelerometers. We thank Dr David Halliday and Professor Jay Rosenberg for the time and frequency domain analysis package. The Wellcome Trust supported M.J.M.
Corresponding author
M. J. Mayston: Department of Physiology, University College London, Gower Street, London WC1E 6BT, UK.
Email: m.mayston@ucl.ac.uk
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