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MS 0275 Received 27 October 1999; accepted after revision 8 December 1999.
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ABSTRACT |
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INTRODUCTION |
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In 1983, Goodman & Kelso showed that voluntary movements were made in phase with the spontaneous tremor at the instant of movement initiation. Consequently, movements could be made slightly more economically by taking advantage of the momentum generated by the tremor. Travis (1929) had earlier shown an apparent relationship between tremor and movement. He used a high-speed cine-camera and concluded that some of the well-known trial-by-trial variation in reaction time depended on 'the temporal relationship between the stimulus and the muscular rhythm'. Tiffin & Westhafer (1940) came to a similar conclusion.
The work briefly described above relates to physiological tremor, but similar claims for the relationship of voluntary movement to tremor cycle have been made for pathological tremors. Elble et al. (1994) showed that in essential tremor, there was a phasic linkage between the tremor and the movement, but this occurred in such a way that the movement was effectively opposed by the spontaneous tremor. Wierzbicka et al. (1993), using an isometric technique, noted that there was a phasic link between voluntary rapid force generation onset and tremor cycle in the case of Parkinsonian tremor.
These observations have led to a view that there may be a mechanistic relationship between tremor and movement as a consequence of entrainment of spinal neurons influencing the timing of volitional muscle activation. The functional significance of the linkage may, however, be less, or at least more variable, than has been suggested. Physiological tremor is not significantly coherent in different limbs (Marsden et al. 1969), although the task of maintaining a posture is common to both hands. In some preliminary experiments using back-averaging from the moment of movement initiation no consistent phase relationship between the movement and physiological tremor was found (Lakie et al. 1991). There was also no relationship when an artificial rhythmic tremor was generated by mechanical or electrical means (Lakie & Villagra, 1993, 1994).
A difficulty with these preliminary observations is that it is possible that the physiological tremor did not contain a prominent neurally generated component. Although nearly all subjects have a peak in their wrist tremor power spectrum at a frequency between 8 and 12 Hz, this may arise as a consequence of the mechanically resonant properties of the wrist, and the motor unit input may represent little more than incoherent 'noise' which drives the system. Motor unit entrainment, although present in the 8-12 Hz component of tremor, is weak in most people (Elble, 1986). 'Enhanced' physiological tremor, first described by Hagbarth & Young (1979), can be produced by mild fatigue or repeated rapid movements. In enhanced tremor the increased size of oscillation of the joint is accompanied by synchronous activity in the postural muscles. This may be due to reflex 'driving' of the tremor as it is also associated with synchronous activity in the afferent fibres. Alternatively, it may arise centrally as a consequence of increased rhythmicity in motor output. Lakie et al. (1986) showed that enhanced tremor with entrained EMG was readily produced when the wrist was required to maintain its position against gravity for long periods, and intermittently subjected to rapid movements.
In the present experiments we used enhanced tremor to produce a large rhythmic tremor of the hand in which there was a clear relationship between the mechanical and EMG rhythms. We then examined the relationship between the events of the tremor cycle and the initiation of a rapid flexion movement of the wrist. The movements were made in response to a visual stimulus which was presented at chosen points on the subject's tremor cycle. By this means it was possible to see clearly the effect of presenting the stimulus at different points in the tremor cycle and to examine in detail the relationship between the phasing of the tremor cycle and the voluntary movement at the moment of its initiation.
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METHODS |
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Subjects
There were eleven subjects, five male and six female (age range, 21-65 years; mean, 39·45 years). All were free from any illness and were not taking any medication. The subjects gave their informed consent and approval was obtained from the local ethical committee. All subjects participated in the reaction time part of the experiment and eight took part in the experiments employing the averaging of acceleration and EMG.
Apparatus
The subject was comfortably seated in an adapted chair. The flexed upper limb was supported at waist level by a shaped forearm cradle to a point just proximal to the pronated wrist, thus allowing free movement of that joint in the vertical plane. A miniature single axial accelerometer (ICS 3021, EuroSensor UK) cemented onto a light (15 g) polycarbonate splint was attached to the dorsum of the right hand by a Velcro strap and to the digits by micropore tape. This splint permitted unrestricted movement at the wrist joint, but prevented movement of the joints of the fingers, so that if the wrist joint was flexed, the hand and fingers moved as a whole. When the hand was horizontal the DC tilt component was minimised by subtracting an offset voltage. A fixed-gain AC amplifier (time constant, 
1·0 s) raised the signal to an appropriate level for recording, and ensured that slight differences in the resting inclination of the wrist did not cause saturation. The overall sensitivity was 14·0 cm s-2 V-1.
The apparatus comprised a specially constructed visual reaction timer. The subject's tremor signal was fed to a comparator. The comparator was a zero-crossing detector of selectable polarity. The experimenter could choose whether the output pulse of the comparator was produced by the acceleration waveform going from positive to negative, or from negative to positive. Thus, the output pulse was always produced when the subject's hand was experiencing zero acceleration (i.e. moving at constant velocity, and in dynamic equilibrium). As the motion of the hand approximated quite well to a sinusoid, this ensured that the output pulse was produced at nearly the centre point of the tremor oscillation, with the hand moving at its greatest velocity in either flexion (downwards) or extension (upwards). A third setting allowed the output pulse to be produced at random instants.
The apparatus was armed by the experimenter and an output pulse was produced either at the subject's next zero-crossing in the chosen direction, or at random. The output pulse was used to initiate a single bright flash from a strobe light positioned in front of the subject, start a clock (which was set to zero when the apparatus was armed), and trigger a signal averager (CED 1401 and Sigavg program, CED, Cambridge, UK).
The signal averager recorded the acceleration of the wrist and the rectified surface EMG of the flexor carpi radialis and extensor digitorum communis muscles. Surface EMG was recorded by miniature skin-mounted silver disc electrodes incorporating an integrated amplifier with a gain of 1000. The data sampling rate was 1000 Hz, and the recording epoch was 2·0 s, with 1·0 s before the trigger. The EMG signals were bandpass filtered with cut-off frequencies of 2 and 300 Hz, and the tremor signal was low-pass filtered with a cut-off frequency of 40 Hz. Twenty-five sweeps were averaged in each condition. For each subject, inspection of the averager output showed the mean response strategy for each of the triggering conditions.
Additional relevant data came from the reaction timer circuit. The clock (100 MHz counter/timer, R. S. Ltd, UK) was started as described above, and it was stopped by a second comparator circuit which was set to an arbitrary threshold greater than the largest spontaneous tremor size that we encountered. This threshold corresponded to 60 cm s-2 of acceleration in the downward (flexion) direction, and the reaction time was measured with a resolution of 0·1 ms.
Experimental technique
The subjects were told that their reaction time was being measured. They were not informed that the timing of the stimulus was often contingent on their tremor cycle, nor did any of the subjects become aware of this. The subjects were instructed to move the hand rapidly downwards ('flex the wrist as quickly as possible') when they saw a single flash of light (80 J (15 µs)-1) from a xenon flash tube (Shimpo 301 Ltd, Japan) placed at eye level 1·5 m in front of them. The subjects were given an audible warning that they could expect a flash within the next 1-3 s. The apparatus was noiseless in operation, and the subject could not see the experimenters. A large number of practice trials (usually 25) were given. This allowed the subjects to become familiar with the apparatus, and the large number of rapid movements in quick succession produced in each subject a considerable increase in tremor size (enhanced tremor). Many of the subjects commented on this; their postural tremor became visible to the investigators and themselves. Stimuli were then delivered in three groups of 25 with the flash occurring under the three different conditions. Any reaction time of > 0·5 s was rejected and excluded from the average. As the required movement was downwards in each case, we refer to the stimulus as 'up' (occurring when the wrist was moving upwards), 'down' (when the wrist was moving downwards) and 'random' (when it occurred independent of the tremor cycle). The order of presentation of the three groups was randomised.
Data analysis
The reaction times obtained from the digital clock were subjected to statistical analysis. This gave values for the mean (± S.D.) and median reaction times for each subject in the three conditions (up, down and random). The averager record was subjected to two forms of analysis, as described below.
Correlation of the enhanced tremor and EMG. The wrist was supported against gravity by maintained activity in the extensor muscle. A cross-correlation analysis (1000 points, 0·5 s offset) was performed between the acceleration signal and the rectified extensor EMG for the 1·0 s of the record that preceded the stimulus. Tremor wavelength (and thus frequency) was calculated by performing an autocorrelation of the acceleration signal for the same period.
Time to EMG initiation. The movement was produced by activation of the flexor musculature. The timing of this was measured by a cursor. This process encounters the problem of sensitivity to spurious noise preceding the point of activation. This problem was overcome by establishing the root mean square (r.m.s.) level of the flexor signal for the 1·0 s period before the stimulus and taking a value of 4 times this as the threshold at which voluntary EMG activity commences. As the postural activity was ocurring in the extensor group of muscles it might seem more natural to have studied extension movements. However, when this was attempted it proved impossible to detect unambiguously the onset of the movement-related EMG and thus the timing of the response.
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RESULTS |
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Reaction times
The reaction time is defined as the time elapsed between the flash and the acceleration of the hand reaching a threshold level (60 cm s-2) in the flexion direction. The reaction times (median values) for all eleven subjects are shown in Fig. 1. The median values for the subjects ranged from 108 to 208 ms. From this figure it is clear that there is no obvious systematic advantage in terms of a more rapid response in presenting the stimulus in the up, down or random condition. The mean reaction times for all the subjects under each condition were 153·8 ms, up; 150·8 ms, down; and 143·5 ms, random. There was only a minor difference between the values, and this was not significant (ANOVA, F ratio 0·37, P > 0·5). The time taken to produce a mechanical response was independent of the spontaneous tremor phase at the instant the stimulus was presented. It was also possible that there might be a more consistent response when the stimulus presentation was in a certain tremor phase. To investigate this, the coefficient of variation (c.v. = S.D./mean reaction time) was calculated for each subject in each of the three conditions (Fig. 2). For all the subjects, the coefficient of variation was not significantly greater or less under any condition of stimulus presentation (10·05 %, up; 9·81 %, down; and 11·93 %, random; ANOVA, F ratio 0·31, P > 0·5).
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No condition produced a consistently faster response. All values are the median of 25 trials. | ||
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Variance is different between subjects and between conditions, but no stimulus condition produced a generally more consistent response. | ||
The enhanced tremor involves neural modulation - cross-correlation of tremor waveform and extensor EMG
Inspection of the averaged traces in eight subjects suggested that there was a strong correlation between the tremor waveform and the rectified extensor EMG. Accordingly, cross-correlation analysis was used to compare the two channels for the period of 1·0 s that preceded the stimulation. A typical result is shown in Fig. 3. The maximal positive value (0·75) of the correlation function is at 51 ms. That is, the acceleration signal lags the rectified EMG by 51 ms. This value is consistent with the delay produced by excitation- contraction coupling in the muscles and caused by the mechanical inertia of the hand and muscles. This correlation was evident in all the subjects. There was also a small correlation evident between the flexor EMG and the acceleration in some subjects. This muscle did not have a postural role in this task and the size of the cross-correlation function was small. The mean value for the extensor muscle was 0·70, and for the flexor 0·11. In the subjects where a flexor EMG correlation was detectable it was approximately 180 deg out of phase with the extensor EMG.
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The maximal value of the cross-covariance function is 0·75, which suggests that the two waveforms are highly correlated. The acceleration lags the EMG by 51 ms, and the subsequent peak is at 176 ms giving a period of 125 ms which corresponds to a frequency of ~8 Hz. In this subject the tremor frequency determined by FFT analysis and by autocorrelation of the tremor waveform was 7·1 Hz. | ||
In Fig. 3, subsidiary peaks are evident approximately 140 ms before and 125 ms after the principal one. This is the period of the tremor oscillation. In this subject a value for tremor frequency of 7·1 Hz was determined by performing an autocorrelation on the tremor waveform, or by directly performing a fast Fourier transform (FFT) on the tremor waveform. The tremor frequencies obtained by autocorrelation are included in Table 1.
Table 1. Tremor frequencies and flexor EMG latencies for the eight subjects who participated in the averager experiments
| Subject | Frequency (Hz) |
EMG latency (ms) | ||
| Up | Down | Random | ||
| 1 | 8·66 | 83 | 78 | 79 |
| 2 | 8·62 | 104 | 103 | 83 |
| 3 | 9·7 | 137 | 131 | 121 |
| 4 | 6·75 | 77 | 69 | 75 |
| 5 | 11·6 | 130 | 121 | 114 |
| 6 | 7·14 | 129 | 118 | 118 |
| 7 | 6·41 | 88 | 84 | 86 |
| 8 | 7·81 | 103 | 144 | 102 |
| Mean | 8·3 | 106·37 | 106 | 97·25 |
Relationship of movement initiation to tremor phase
Inspection of the averaged acceleration allowed the relationship of the voluntary movement to the tremor waveform to be elucidated. Figure 4 shows the effect for one subject, of presenting the stimulus in the up or down situation. Two features are immediately obvious. First, the timing and profile of flexor EMG activity are very similar for the two conditions. The agonist muscle was activated with a latency (defined by the criterion described in the Methods section) of 137 ms in the upward trigger condition, and 131 ms in the downward trigger condition after the flash of light. This is consistent with the above observation that the reaction time is independent of the phase of the tremor at the time of stimulus presentation. The timing of the flexor EMG onset for all the subjects under the three conditions is shown in Table 1. The values are not different from each other (ANOVA, F ratio 0·87, P > 0·5). Secondly, extensor EMG is clearly modulated at the frequency of the tremor. In Fig. 4 it can be seen to persist beyond the instant at which the stimulus was delivered, and it is still evident at the point where the flexor EMG activation starts. Thus, the movement seems abruptly to interrupt the spontaneous electrical and mechanical rhythm.
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All traces associated with the up condition are shown dotted. For clarity the up EMG records have been offset by +0·5 mV. Phasic activity can be clearly seen in the extensor EMG up to and beyond the stimulus point (time zero) and up to the time of movement initiation. The timing of the flexor burst and the movement that it generates are similar in the two conditions. The movement is associated with a triphasic EMG pattern (Hallett et al. 1975). The antagonist burst can be seen interposed between the two agonist peaks. | ||
Figure 5 shows a corresponding result from a different subject. The random trigger condition is included, and for clarity, only the flexor EMG is shown and the time base is expanded. The latency of the flexor EMG in this record is 130 ms, up condition; 121 ms, down condition; and 114 ms, random condition. It is impossible to say with certainty where the tremor ends and the movement begins, but inspection of this figure would suggest a value of approximately 140 ms. This would imply for this subject an electromechanical delay of approximately 30 ms for the flexor muscles. This value is comparable to that obtained by cross-correlation analysis for the extensor muscles. In Fig. 5 the movement commences in a way that is very clearly out of phase with the spontaneous tremor in the up stimulus condition. Thus, it shows in a very simple way that the movement is not linked to any particular tremor phase. When the stimulus is presented in the down condition (in phase with the intended movement) the tremor continues for one entire cycle and merges relatively imperceptibly with the movement. When the stimulus is presented at random, the tremor averages to a practically straight line as would be anticipated from randomly sampling a periodically oscillating signal.
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Up, dotted line; down, thick line; and random, thin line. For clarity, the up EMG record has been offset by +0·3 mV, and the down EMG record by +0·6 mV. The mechanical and electrical events are similar in the three conditions. The abrupt interaction of the tremor waveform with the voluntary movement is striking in the up condition. | ||
Relationship of tremor frequency to reaction time
If reaction time were dependent on the events of the tremor cycle, it would be advantageous to have a rapid tremor rhythm. In Fig. 6, the tremor frequency of each subject is plotted against the time to initiation of flexor EMG (under random triggering conditions). EMG values were employed rather than the time to movement initiation as this removes any confounding influence of the muscle contraction time. There is considerable scatter in the presented data, and the correlation (which is in the wrong sense) is not significant. More rapid reaction times were not associated with the highest tremor frequencies.
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There is considerable scatter. The regression line gradient is in the 'wrong' direction but is not significantly different from zero (P > 0·05). | ||
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DISCUSSION |
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In these experiments the subjects produced a voluntary rapid wrist flexion movement in response to a flash of light. The mechanical delays recorded fit in well with other observations for subjects of a comparable age range using more conventional button-pressing responses (Welford, 1980).
The tremor was clearly rhythmic and was associated with rhythmically varying EMG activity in the postural muscle (extensor digitorum communis). This is in agreement with other studies of enhanced tremor (Logigian et al. 1988). There was often some minor movement-related activity in the flexor muscles and the cross-correlation analysis revealed that this was also phase locked to the mechanical cycle, and in antiphase with the extensor activity. The rhythmicity of these oscillations can be seen in Figs 4 and 5. Triggering from the tremor waveform zero-crossings effectively generates the autocorrelation of the tremor before and after the trigger point. Often eight or more cycles could be clearly discerned. The enhanced tremor was large (more than 15 times the size of the physiological tremor in 2 subjects), and its frequency (mean value 8·3 Hz, Table 1) was towards the low end of the normal range (now usually considered to be 7-11 Hz; Findley & Gresty, 1984). The existence of a strong correlation and the value of the lag between the extensor EMG and the acceleration demonstrate that the rhythmic EMG activity is responsible for the tremor waveform. The source of this oscillation is beyond the scope of this paper, but it is presumably either of central origin or the result of a mechanical-reflex synchronisation. The generally low frequency of the enhanced tremor may be consistent with a change in the mechanical-reflex component of enhanced tremor (Stiles, 1976).
There are four main pieces of evidence which suggest that the voluntary movement takes place at an instant that is not determined in any obvious way by the phase of the enhanced tremor. Firstly, the reaction time and variability were independent of the tremor phase at the instant of stimulus presentation. It should be clear from inspection of Figs 4 and 5 that it is mechanically advantageous to have the stimulus presented in the down phase. This is because the reaction time is approximately one tremor cycle long and the voluntary movement is then approximately in phase with the next tremor cycle. Despite this, there was no significant advantage in terms of reaction time or consistency of response in having the stimulus presented in this phase, and neither up nor down was better than a random presentation. The variability of reaction time was not caused by the movement control mechanism having to wait for a propitious moment in the tremor cycle. Secondly, the use of averaging allows the tremor acceleration of the hand to be studied immediately before the time of movement initiation. This permits the relationship of the movement to the tremor phase at the moment of making the movement to be studied. Movement interacts in an entirely different way with the mechanical tremor rhythm when the stimulus is presented in the up and the down situations. In the up case in Fig. 5 the movement is clearly out of phase with the tremor. Because of the inertia of the moving parts the discontinuity is never particularly sharp and a deceptive appearance of an in phase movement can be created. Villagra (1994) has shown that methods which rely on visual identification of phase, as in many of the early experiments, are unreliable, as the observer tends to see a phase relationship where one does not exist. Thirdly, the rhythmical modulation of the extensor EMG could be seen to continue after the point of stimulus presentation. In both trigger conditions it could be seen to persist beyond the point of flexor EMG initiation. The movement is abruptly imposed on the spontaneous extensor EMG rhythm, which only dies away as the movement commences. The moment of flexor activation cannot be related to the rhythmical activity in the extensor EMG as this is 180 deg different in phase at the moment of stimulus presentation in the up and down conditions. There was also usually some slight tremor-based modulation of the flexor EMG; as this also occurred at a constant phase in the tremor cycle the voluntary movement was not in phase with it either. Finally, Fig. 6 shows that there was no significant advantage in terms of reaction time in possessing a fast tremor frequency. A simple prediction for the initiation of movement, if it was contingent on some central or peripheral event which varied cyclically, would be that the average time taken to respond would be less if the frequency of cycling were higher.
It has been suggested that the 8-12 Hz component of physiological tremor may represent the output of a central oscillator (the olivo-cerebellar clocking mechanism; Llinàs, 1991). This clock may be responsible for the rather weak rhythmicity at 8-12 Hz which has been detected in voluntary movement (Vallbo & Wessberg, 1993) and the coherence between the EMG waveforms of different muscular groups (Farmer, 1998, 1999; McAuley et al. 1999). In the present experiments with enhanced tremor, it is likely that a motor neuronal modulation will occur which is much deeper and more rhythmic than that produced by the 8-12 Hz rhythm under physiological conditions. Nonetheless, even this enhanced modulation is easily over-ridden by descending central commands. It is likely, but not inevitable, that the weaker physiological modulation could also be over-ruled when rapid reactive movements are made. However, with physiological tremor the situation may be different when self-paced, slower or more delicate movements are made. Also, finger movements may differ from movements of the whole hand. Finally, we did not examine the effect of inertial or spring loading on tremor frequency. Therefore, it is unclear whether the tremor in our subjects was enhanced mechanical reflex, 8-12 Hz or both. The results of our study might have been different had we examined delicate ballistic movements by people with prominent 8-12 Hz tremor.
The present results conflict with earlier reports which have suggested that there might be a simple functional linkage between the phasing of an involuntary movement (tremor) and a voluntary rapid movement. Most previous work (e.g. Goodman & Kelso, 1983) has depended on observer-based analysis of recorded traces and is open to several criticisms. The likelihood of phasic relationships being reported where none exist has already been mentioned. Also, several of the earlier reports have used the attainment of a displacement threshold as a criterion for movement initiation. This is unsatisfactory as the hand or finger does not oscillate about a fixed position; accordingly the distance traversed to attain a displacement threshold is continually changing and this can seriously undermine the results.
There might be slight energetic advantages if tremor and movement were linked, but there would be the much more fundamental disadvantage that in order to make a movement in phase with the tremor it would be necessary to wait for an integer multiple of the tremor period before making a response. This would often result in a considerable increase in the time taken to respond which could hardly be a biological advantage. There is considerable benefit in having the ability to make voluntary movements which are not contingent on a 'clocking cycle' of oscillation as slow as 100 ms.
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REFERENCES |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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| Elble, R. J. (1986). Physiologic and essential tremor. Neurology 36, 225-231 | [Abstract] |
| Elble, R. J., Higgins, C. & Hughes, L. (1994). Essential tremor entrains rapid voluntary movements. Experimental Neurology 126, 138-143 | [Medline] |
| Farmer, S. F. (1998). Rhythmicity, synchronization and binding in human and primate motor systems. The Journal of Physiology 509, 3-14 | [Abstract/Full Text] |
| Farmer, S. F. (1999). Perspectives. Pulsatile central nervous control of human movement. The Journal of Physiology 517, 3. | |
| Goodman, D. & Kelso, J. A. S. (1983). Exploring the functional significance of physiological tremor: a biospectroscopic approach. Experimental Brain Research 49, 419-431 | [Medline] |
| Findley, L. J. & Gresty, M. A. (1984). In Contemporary Neurology, ed. Harrison, M. J. G., pp. 168-182. Butterworths, London. | |
| Hagbarth, K.-E. & Young, R. R. (1979). Participation of the stretch reflex in human physiological tremor. Brain 102, 509-526 | [Medline] |
| Hallett, M., Shahani, B. T. & Young, R. R. (1975). EMG analysis of stereotyped voluntary movements in man. Journal of Neurology, Neurosurgery and Psychiatry 38, 1154-1162 | [Abstract] |
| Lakie, M. & Villagra, F. (1993). Voluntary movements are not phase locked to small rhythmic passive movements in man. The Journal of Physiology 473, 210P. | |
| Lakie, M. & Villagra, F. (1994). The lack of a phase relationship between electrically induced tremor and voluntary movement in man. The Journal of Physiology 475.P, 30P. | |
| Lakie, M., Walsh, E. G. & Wright, G. W. (1986). Passive mechanical properties of the wrist and mechanical tremor. Journal of Neurology, Neurosurgery and Psychiatry 49, 660-676. | |
| Lakie, M., Wiseman, R. M., Arblaster, L. A. & Villagra, F. (1991). The lack of a relationship between physiological tremor and voluntary wrist movements in man. The Journal of Physiology 435, 55P. | |
| Llinàs, R. R. (1991). The noncontinuous nature of movement execution. In Motor Control: Concepts and Issues, ed. Humphrey, D. R. & Freund, H. J. John Wiley & Sons, UK. | |
| Logigian, E. L., Wierzbicka, M. M., Bruyninckx, F., Wiegner, A. W., Shahani, B. T. & Young, R. R. (1988). Motor unit synchronisation in physiologic, enhanced physiologic and voluntary tremor in man. Annals of Neurology 23, 242-250 | [Medline] |
| McAuley, J. H., Farmer, S. F., Rothwell, J. C. & Marsden, C. D. (1999). Common 3 and 10 Hz oscillations modulate human eye and finger movements while they simultaneously track a visual target. The Journal of Physiology 515, 905-917 | [Abstract/Full Text] |
| Marsden, C. D., Meadows, J. C., Lange, J. W. & Watson, R. S. (1969). The relation between physiological tremor of the two hands in healthy subjects Electroencephalography and Clinical Neurophysiology 27, 179-185 | [Medline] |
| Stiles, R. N. (1976). Frequency and displacement amplitude relations for normal hand tremor. Journal of Applied Physiology 40, 44-54 | [Medline] |
| Tiffin, J. & Westhafer, F. L. (1940). The relation between reaction time and temporal location of the stimulus on the tremor cycle. Journal of Experimental Psychology 27, 318-324. | |
| Travis, L. E. (1929). The relation of voluntary movement to tremors. Journal of Experimental Psychology 12, 515-524. | |
| Vallbo, A. B. & Wessberg, J. (1993). Organization of motor output in slow finger movements in man. The Journal of Physiology 469, 673-691 | [Abstract] |
| Villagra, F. (1994). The relationships linking tremor size and skilled performance with limb temperature, and voluntary movement with tremor phase. PhD thesis, University of Birmingham. | |
| Welford, A. T. (1980). Reaction Times. Academic Press, London. | |
| Wierzbicka, M. M., Staude, G., Wolf, W. & Dengler, R. (1993). Relationship between tremor and the onset of rapid voluntary contraction in Parkinson's disease. Journal of Neurology, Neurosurgery and Psychiatry 56, 782-787 | [Abstract] |
We would like to thank the subjects who participated in the experiments.
Corresponding author
M. Lakie: Applied Physiology Research Group, School of Sport and Exercise Sciences, University of Birmingham, Birmingham B15 2TT, UK.
Email: m.d.lakie{at}bham.ac.uk
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