Concurrent Parkinson tremors

Transcription

1 Keywords: 9974 Journal of Physiology (2000), 529.1, pp Concurrent Parkinson tremors G. P. Moore, L. Ding* and H. M. Bronte-Stewart Department of Neurological Sciences, Stanford University Medical Center, Stanford, CA and *Department of Neuroscience, University of Pennsylvania, Philadelphia, PA 19104, USA (Received 12 August 1999; accepted after revision 7 August 2000) 1. Concurrent resting and postural tremors of patients with idiopathic Parkinson s disease were monitored using transducers responding to angular velocity of rotation. Spectra and correlation functions were calculated for each pair of records. 2. When concurrent tremor spectra share indistinguishable fundamental frequencies, have statistically significant peaks in their coherence spectra at those fundamental frequencies, and show significant peaks in their cross-correlation functions near zero delay, they are classified as linearly dependent. When such tremor records are superimposed, their phaselocked behaviour is evident. 3. Pairs of correlated concurrent tremors, of varying duration, have been observed in both hands, both feet and in either hand and the contralateral or ipsilateral foot. Correlated tremors may be concurrent with other tremors that are independent. We hypothesize that correlated Parkinson tremors arise from one or more common (and possibly unilateral) central sources. Concurrent tremors are frequently observed in patients with Parkinson s disease, but it is difficult to determine by visual inspection alone whether they are independent. Individual tremors often have similar frequencies, amplitudes and patterns, creating an impression of synchronized behaviour even when none is present. Conversely, when tremors are indeed correlated, their spectral composition may be so different as to obscure their relationship, which, in any event, may be present only for relatively short time periods. The question of independence between concurrent tremors has been addressed, directly or indirectly, in previous studies whose conclusions are somewhat inconsistent or ambiguous (Hunker & Abbs, 1990; O Suilleabhain & Matsumoto, 1998; Timmer et al. 1998; Hurtado et al. 1999; Raethjen et al. 2000). We demonstrate here that the question is not simple or straightforward, and attempt to provide a general methodology for studying the relations between concurrent tremors. We present evidence that some concurrent Parkinson tremors show behaviour difficult to reconcile with a hypothesis of independence. These include epochs of indistinguishable dominant frequencies, and cross-correlation functions and coherence spectra that are statistically significant. When records of these tremors are superimposed, their phaselocking is unmistakable. These lines of evidence lead to the conclusion that transient periods of co-ordination between concurrent tremors or their sources are a general, but not invariant, feature of Parkinson s disease. This implies that concurrent tremors are driven at times by a common (and possibly unilateral) source. METHODS The study was performed according to the Declaration of Helsinki and the procedures were approved by the local ethics committee. Our subjects, patients diagnosed with advanced idiopathic Parkinson s Disease, were tested, with written informed consent, while undergoing screening for neurosurgery. Their anti-tremor medication was discontinued 24 h prior to testing. During recording, the patients were seated comfortably with arms and feet supported. Spontaneous resting and postural tremors were recorded by transducers secured to their hands or feet. These novel sensors, based on a gyroscopic principle, are part of a motion monitoring system (Motus Bioengineering Corporation, Benicia, CA, USA) and, unlike conventional accelerometers, are sensitive to angular velocity of rotation and indifferent to their orientation with respect to gravity. In some records shown here, the sensors were placed on the dorsum of the hand and oriented so that they responded principally to pronation supination rotations of the wrist. If the hand tremors had additional components along other axes, such as radial or ulnar flexion, wrist flexion or extension, or movements of the fingers, they were not registered by the sensor. As long as the upper arm remained stationary, the sensor responded only to rotations of the wrist. In other trials the transducer was secured to the foot and oriented so that the principle motion monitored was either flexion extension or internal external rotation of the foot about the ankle. Each sensor weighs about 60 g, has a low noise level (2 3 deg s r.m.s.), and a flat response to 30 Hz. Ten seconds of data were digitized in each trial at a rate of 100 samples s per sensor.

2 274 G. P. Moore, L. Ding and H. M. Bronte-Stewart J. Physiol Tremors often have similar frequencies even when unquestionably independent, as, for example, tremors from a single individual on different occasions (Hunker & Abbs, 1990) or from two different individuals. When concurrent tremors have similar frequencies they may, when observed clinically, appear to be correlated when they are not, and since tremors undergo moment-to-moment amplitude and frequency fluctuations (O Suilleabhain & Matsumoto, 1998), their relationship may seem uncertain even if they are correlated. For this reason, we have attempted, in the examples shown here based on tremor data of relatively simple harmonic composition, to avoid confusing true and apparent independence, true and apparent correlation. It is not a simple matter to establish whether two tremors are independent. Direct visual inspection of the records may be misleading, as our examples show, if the two tremors have different harmonic content. Tremors are also non-stationary, i.e. their statistical properties may change rapidly over time, and spectra and correlation functions calculated over such periods may obscure a dynamic relation present at some times but not others. Tremors may also be non-linearly dependent but, by the usual linear tests, appear to be independent. Occasionally, for example, one tremor may exhibit a single large peak at a frequency that is a harmonic of the fundamental frequency of the other tremor and yet show little activity at the fundamental frequency itself: the tremors would be statistically uncorrelated (linearly independent) but not truly independent. A number of techniques should be used to test for linear independence between tremors. First, it should be determined whether the spectra of the two tremors have significant peaks at indistinguishable frequencies. When they do not, it may still be desirable to calculate the coherence spectrum (see below) to determine if there are frequencies at which the tremors appear to be significantly related in a linear sense even though the power level of one tremor at that frequency is much less than that of the other. When tremors share significant peaks in their spectra, one next determines whether those peaks appear concurrently in any subsection of the record or whether they arise at different times. If the peaks are never concurrent, the tremors may be assumed to be linearly independent. If there are concurrently shared spectral peaks, the cross-correlation function and the coherence spectrum should be calculated over the section of the record where the shared peaks occur. When the power spectra do not share significant peaks, the cross-correlation function and coherence spectrum have magnitudes approaching zero, the key signs of linear independence. When the spectral composition of the tremors indicates that a single fundamental frequency dominates both tremors, as is the case in most of the examples shown here, then the cross-correlation function, and its analogue in the frequency domain, the coherence spectrum, have magnitudes approaching 1 0. In such cases we superimpose the two tremor records to confirm by visual inspection that the tremors are phase-locked, i.e. synchronized with a time delay. It is important to note that any uncorrelated activity within the tremors, and of course any other concurrently recorded motor activity independent of the tremors, will reduce the magnitude of the coherence and cross-correlation functions. The same would apply to contributions of the gravitational field when conventional accelerometers are employed, or to EMG signals when they are used to monitor tremor activity. Auto- and cross-spectra were calculated using standard fast Fourier transform (FFT) algorithms (Bendat & Piersol, 1993). The 1000 data points were extended with zeros to make 1024 points. Prior to calculating tremor spectra, sinusoidal functions, centred at frequencies where little tremor activity was present, were sometimes added to the digitized tremor data. These do not affect spectral estimates at other frequencies and demonstrate how sinusoids of known frequency and amplitude are treated by the analysis procedures. Spectra were not averaged. Linear power scales were used in all figures. The frequency resolution of the spectral calculations (separation between spectral points), is equal to 1ÏT (Hz), where T is the record length in seconds, and is given in the legends. To obtain the coherence function, we averaged the auto-spectral estimates of the tremors, Gxx(f) and Gyy(f), and the cross-spectral estimates, Gxy(f), from consecutive non-overlapping subsections of the entire record, averaging the real and imaginary components separately. Here, x(t) and y(t) are the two tremor time series, and f is the frequency variable (in Hz) of the spectral estimates, G. Using these, the coherence spectrum was then estimated by: ãâ(f) = Gxy( f) ÂÏGxx( f)gyy( f) (Bendat & Piersol, 1993). Subdividing the record increased the separation between the estimated spectral points, reducing the frequency resolution of the spectrum. To minimize the presence of leakage to side-lobes in the spectrum, each subsection of the record was first transformed using a cosine (Hanning) window and padded with zeros to make 1024 points before applying an FFT procedure. The resulting spectral plots are linear interpolations between the calculated spectral points. The coherence function has a value between 0 (linear independence) and 1 (perfect linear dependence), and estimates the degree to which a given frequency component in the tremors maintains a constant phase relation across the record. The coherence is independent of the magnitude of the spectral components in the record. Thus the coherence at a given frequency may be high even if one or both tremors have little power at that frequency. The issue of what constitutes a significant peak in the coherence function is of great importance. The usual statistical tests are formulated for the case in which one wants to detect a sinusoid common to two signals, but hidden in noise. Our tremor records are often sinusoids many times larger than any component that could be regarded as either functional or instrumental noise. The problem is not in detecting the sinusoids but determining if they are linearly related (i.e. have identical frequencies and a fixed phase relation), or whether they are independent and simply have nearby frequencies. It is useful, therefore, to conduct tests using simulated data to determine the effectiveness of coherence measures in determining whether tremors with nearby, but not identical, frequencies are distinguished using short records. It may in some instances be an intractable problem, since the very nature of coherence analysis reduces, rather than sharpens, the precision in determining frequency and phase. We therefore show here only cases in which the coherence at the main spectral frequencies is well above or below the nominal 99 % confidence limits given in Rosenberg et al. (1989). Coherence calculations have been employed before in studying the relation between tremor, EMG and single neurone signals (Lenz et al. 1988; Halliday et al. 1995; Zirh et al. 1997; Timmer et al. 1998; Hurtado et al. 1999; Raethjen et al. 2000). The cross-correlation function at lag k (here equal to 10k ms) was computed as follows: 1 N k Cxy(k)= Óx(j)y(j + k), N k j=1 where x(j) and y(j) are the original time series data with their means subtracted; N is the number of data points used in the calculation. Autocorrelation functions were computed by substituting either x(j) or y(j) for the other variable in this equation.

3 J. Physiol Concurrent Parkinson tremors 275 Confidence limits for the cross-correlation function may be found in Halliday et al. (1995), but again, our records do not satisfy the usual assumptions for those tests in which the goal is to detect a sinusoid common to two signals but hidden in noise. Parkinson tremors are often so periodic, and their frequencies so similar, that cross-correlations often appear to have significant structure, and the problem is only compounded by short records. Conversely, some of the tremor records reported here contain significant power at harmonics of the fundamental frequency. Odd harmonics in particular reduce the amplitudes in the cross-correlation, obscuring the magnitude and the estimated significance of the underlying dependence between the tremors. We consider the results reported here, based on relatively uncomplicated time series data, to be unambiguously significant or non-significant. We leave for the future how the question of independence might be studied in more ambiguous and complex cases. RESULTS The tremor records shown in Fig. 1A were recorded during 10 s of concurrent movements of a Parkinson patient exhibiting resting tremor in all four extremities. The three tremors shown here (the fourth was not recorded) have a similar appearance with respect to their basic frequency and the presence of amplitude modulation. The hand tremor scale is reduced by a factor of 5 for comparison because of its larger amplitude. Whether there is any relationship between the tremors is not evident from casual inspection of the records or by observing the patient. Both tremors from the left side show smaller deflections, and these correspond to the harmonics in their spectra. In Fig. 1B,wecomparetwopairsofthetremorsinthe frequency domain. On the left we compare the foot tremors. On the right are shown the spectra of the two left-side tremors, i.e. the left hand and foot tremors. The foot spectrum (thick line) is identical to that shown on the left. We omit the third pair (right foot left hand) because the data were very similar, qualitatively and quantitatively, to the hand foot pair shown. It can be seen that the foot tremors have similar spectra, with considerable overlap in their main peaks near 5 Hz. Only the left foot tremor shows a peak at the first-harmonic frequency near 10 Hz. (The peak near 19 Hz is introduced for scaling purposes and not derived from the original data.) The hand foot spectra (the hand data attenuated by a factor of 5 for comparison) have far less overlap at their fundamental frequencies. Their peaks at the first harmonic are also separated. These relations are further clarified by examining the coherence spectra in Fig. 1C. For the foot tremors, shown on the left, there is a broad peak located in the region of the fundamental frequencies, and it is well above the 99 % significance line, indicating a strong linear relationship between the two foot tremor spectra. This indicates that the frequency and phase relations of the two tremors are significantly correlated over this 10 s record. The coherence spectrum computed from the foot hand tremors is of a magnitude well below the 99 % significance line, confirming that, on average, the two tremors exhibit different frequencies and therefore shifting phase relations over the same period. In Fig. 1D, we examine the data from a third perspective using the cross-correlation function calculated from the same pairs of records. On the left, the sinusoidal shape of the correlation function reflects the similarity (or identity) and the stability of the basic frequencies. The position of the central peak at 30 ms indicates that the two tremors are slightly delayed in the timing of their maximum or minimum angular velocity. The correlation function on the right shows that over this 10 s period the hand foot tremors, on average, are essentially uncorrelated. Thus, in this example, we have strong evidence suggesting linear independence between the hand foot tremors, and a strong suggestion of non-independence of the foot tremors. We note that there may be a stronger relationship between the hand foot tremors at some brief and isolated portions of the record, but in practical terms we do not pursue such a situation further. Conversely, though we have strong evidence here of a dependent relationship between the foot tremors, we can also look further to see if that dependence is maintained throughout the 10 s, or perhaps confined to an identifiable subsection of the record. If it is present only in a subsection of the record, then we expect the correlation to be even greater in that subsection. If the correlation is maintained throughout the record, all additional uncorrelated activity weakens their apparent correlation. This point is made clearer in Fig. 2. In Fig. 2A, the foot tremor records are superimposed but with the right foot record delayed (shifted to the right) by +30 ms. The similarity of the two in both amplitude and waveform over the period 2 7 s is unmistakable. Within the whole period of observation the tremors appear to make transitions from essentially independent processes (0 2 s; 7 8 s) to essentially identical processes (2 7 s; 8 10 s) without any evidence of discontinuity. The calculations in Fig. 2B D are based on the subsection of the record from 2 to 7 s. The spectra shown in Fig. 2B are, except for the presence of the harmonic peak in one tremor, nearly identical. We provide alternative interpretations of the spectra below (see Discussion). The peak of the coherence spectrum has risen to 0 93, indicating a nearly linear relationship, and the cross-correlation function has peaks approaching ±0 9, also indicating almost perfect correlation. In the previous example, all three tremor records appeared similar, but their complexity and amplitude modulation made difficult any judgements about their independence on the basis of visual inspection alone. Another instance where independence is difficult to judge is shown in Fig. 3A. Here concurrent resting tremors of both feet have waveforms so different that they appear unrelated. In Fig. 3B, their spectra, calculated over the subsection from 0 to 3 s, are superimposed, from which it can be seen that they differ primarily with respect to their very different harmonic

4 276 G. P. Moore, L. Ding and H. M. Bronte-Stewart J. Physiol Figure 1 A, resting ankle rotation tremors of both feet recorded concurrently with a resting pronation supination tremor of the left hand. Female Parkinson s disease patient, 69 years old, off medication. Left foot, bottom (thick line); left hand, middle; right foot, top. Affected side: right. Vertical scale: ±20 deg s for the foot tremors, ±100 deg s for the hand. External rotation velocity of the feet, and hand supination velocity, positive. Sampling rate for each channel: 100 s. B, spectra calculated over the 10 s record. Left side: spectra from the left (thick line) and right feet. Equal amplitude scaling. Right side: spectra of the left foot (thick line) and left hand (thin line) tremors. The relative scaling of the hand tremor is reduced by a factor of 5. Prior to calculating the spectra, 19 Hz sine waves with peak-to-peak amplitudes equivalent to 20 (foot) and 100 (hand) deg s were added digitally to the data records. Separation of spectral points, 0 1 Hz. C, coherence spectra calculated from the entire 10 s record using 15 non-overlapping, 64-point subsections of the record. Left side: coherence spectrum of the foot tremors. Values above the horizontal line are significant at the 99 % level (see Methods). The peak coherence, near 6 5 Hz, is approximately 0 6. Right side: coherence spectrum for the left foot left hand tremors. Scale markers: Spectral resolution, approximately 1 5 Hz. D, cross-correlation functions calculated from the entire 10 s record. Reference tremor: left foot. Left side: correlation between the tremor data from the left and right feet. The maximum at 30 ms has a value of Right side: correlation between the left foot and left hand. Note the absence of any significant correlation. Vertical scale: ±1 0.

5 J. Physiol Concurrent Parkinson tremors 277 weights. Their sharply tuned fundamental frequencies, near 5 Hz, appear identical. The left foot tremor actually has more than half of its energy at the higher harmonic frequencies, reflecting the waveform difference seen in the raw data. The right foot tremor also has energy at the same i.e. indistinguishable harmonic frequencies. A broad peak near 5 Hz in the coherence spectrum (not shown) had a value close to 1 0, indicating a nearly exact linear relationship between the tremors at that frequency. Auto- and cross-correlation functions calculated from the first 4s of data are shown in Fig. 3C. These reflect the stability of the shared fundamental frequency near 5 Hz and the presence of its higher harmonics. Since a fundamental and its harmonics have a non-linear relationship, the presence of both here actually reduces the magnitude of the primary (linear) correlation. The cross-correlation function shows that the fundamental and harmonic frequencies are shared by the two tremors and that the tremors reach their peak velocities at slightly different times i.e. are phaselocked. This is confirmed by direct observation of the superimposed tremors in Fig. 3D. Because the tremors are cyclic, neither should be assumed to lead the other in any causal sense. A similar example is shown in Fig. 4A. These concurrent postural tremors of the hands appear quite different on visual inspection. An examination of their relationship in Figure 2 A, superposition of the foot tremors shown in Fig. 1. The record for the right foot (thin line) has been delayed (shifted right) by 30 ms, a value suggested by the position of the central peak in the crosscorrelogram of Fig. 2D. External rotationvelocity of the feet positive. Vertical scale:±20 deg s. B, spectra of the foot tremors from the period 2 7 s. Left foot, thick line. Spectral resolution, 0 2 Hz. The peak near 19 Hz is derived from sinusoids added to the digital record as in Fig. 1B. C, coherence spectrum for the foot tremors, calculated from seven 64-point subsections of the data from 2 7 s using a Hanning window. Separation of spectral points, approximately 1 5 Hz. The peak coherence value is estimated to be 0 93 near 5 7 Hz. Values above the horizontal line are significant at the 99 % confidence level. Vertical scale: D, cross-correlation function for the foot tremors calculated from 2 7 s. The positive central peak of the cross-correlation at 30 ms is approximately Vertical scale: ±1 0.

6 278 G. P. Moore, L. Ding and H. M. Bronte-Stewart J. Physiol the spectral domain reveals the close coupling between them. In Fig. 4B, the tremor spectra, calculated from the data over the sub-record from 5 0 to 9 5 s, are superimposed (though with unequal scaling). They appear to share indistinguishable peak frequencies near 6 and 9 Hz. Indeed, the right hand tremor (thick line) has appreciable power only at those two frequencies. If only this tremor were observed it would be presumed that these were two independent frequencies. However, the peak near 3 Hz in the tremor spectrum from the right hand reveals the presence of an unusually lowfrequency fundamental, and indicates that the other peaks in both spectra are harmonics of that fundamental (which is missing along with the third harmonic near 12 Hz, in the tremor of the left hand). So, despite the apparent complexity of the tremors, both are seen to share a single common fundamental. Their different harmonic weights contribute to the complexity of their cross-correlation function (Fig. 4C) reducing the overall magnitude of some peaks. The form of the correlation function is largely determined by the relative magnitudes and phases of the two dominant shared spectral frequencies, and can be simulated using simple weighted sums of sinusoids. Sections of the two tremor records are superimposed in Fig. 4D. The left hand record (thin line) has been shifted to the right (delayed) by 20 ms, a timing offset suggested by the cross-correlation function (Fig. 4C). It can be seen that the two tremors are phase-locked and, in this delayed sense, synchronized. Figure 3 A, angular velocity of concurrent resting tremors from both feet of a 60-year-old female Parkinson s disease patient off medication. The sensors were oriented to record flexion extension rotations about the ankle. Right foot, thick line (bottom trace); left foot, thin line (top). Extension velocities positive. Vertical scales: ±50 deg s. B, spectra calculated over the subsection of the record from 0 to3susing a Hanning window. Linear vertical scale. Right foot, thick line; left foot, thin line. Sine waves, 19 Hz, equivalent to 50 deg s peak-to-peak, were added to the digital data before calculating spectra. Separation of spectral points, 0 3 Hz. The lowest frequency peak is estimated to be at 5 4 Hz. The coherence at this peak, calculated using 8 segments of 32 points each over the epoch 0 3 s, is estimated to be Separation of spectral points for the coherence calculation, 3 Hz. C, auto- and crosscorrelation functions with delays ranging from 0 5 to +0 5 s. Calculated from the first4sofdata.top trace: autocorrelation function for the right foot. Middle trace: autocorrelation for the left foot. Bottom trace: cross-correlation function; reference channel, left foot. Note the central peak in the crosscorrelation at +30 ms.thevalueatthatpeakis approximately Vertical scale: ±1 0. D, superposition of the tremor records, 0 3 s. Vertical scale: ±50 deg s.

7 J. Physiol Concurrent Parkinson tremors 279 DISCUSSION The examples shown here demonstrate that for brief periods of time there can be a marked degree of correlation between concurrent resting and postural tremors in Parkinson patients. This is more commonly but not exclusively observed bilaterally between corresponding extremities, but we have seen the phenomenon at some time in each possible pair of the four extremities. Figure 1 demonstrates bilateral phase-locked tremors, but also shows a third tremor with a different fundamental frequency, from which we conclude that even in patients demonstrating a propensity for correlation and synchronization, other independent tremors may also exist concurrently. Since episodes of correlation may be brief and the tremors appear dissimilar, they may be difficult to detect. Even more refined analytical tools, such as spectral and correlation functions, may, if the timespan over which they are computed is too broad, miss periods of highly dependent bilateral tremors. This may account for the difference between our results, derived from 10 s (or briefer) records, and those of Raethjen et al. (2000), based on 30 s records, who reported finding inter-limb tremor correlations in only one of 22 patients with Parkinson s disease (using EMG signals as markers of tremor activity). O Suilleabhain & Matsumoto (1998) using different methods report somewhat higher percentages of what may have been synchronized tremors. In the examples of Figs 3 and 4, little amplitude or frequency modulation of the tremors takes place: the amplitude distribution is stable and the spectral peaks are relatively invariant. During bilateral synchrony a single frequency dominates both tremors. The simplest interpretation of the data is that the basic frequency of these concurrent, synchronized tremors is determined by a single source. Initially, that source may be unilateral, but eventually it dominates, entrains or drives tremors bilaterally. It is not a simple matter to determine which side dominates bilateral synchronized tremors, nor how, anatomically or functionally, that influence would be manifested. It is possible, of course, that bilateral correlations could arise at a spinal level through some combination of reflex pathways. Figure 4 A, angular velocity of concurrent postural tremors from both hands of a 64-year-old female Parkinson s disease patient off medication. Both tremors were complex and multi-axial; the transducers were oriented to record pronation supination of the hands. Right hand, thick line (bottom); left hand, thin line (top). Pronation velocities positive. Vertical scales: ±90 deg s. The final 5sofdataareshown.B, spectra calculated from the data above. Thick line, right hand. Thin line, left hand. Linear vertical scale; scaling factor for left hand spectrum is twice that for the right. Sine waves, 18 Hz, equivalent to 90 deg s peak-to-peak (right hand) and 45 deg s (left hand) were added to the data before calculating spectra. Separation of spectral points, 0 2 Hz. The coherence spectrum (not shown), calculated from eight 32_point sub-sections of the record from 6 75 to 9 25 s, had a peak value of 0 97 at a frequency near 10 Hz. Separation of spectral points for the coherence calculation, 3 Hz. C, crosscorrelationfunctioncalculatedfromthesame5sofdata. Reference tremor: right hand. Note the central peak at 20 ms. The largest peak has a value of 0 9. Vertical scale: ± 1 0. D, superposition of the tremor records from 6 75 to 9 25 s. The left hand record (thin line) has been shifted to the right (delayed) by 20 ms. Vertical scale: ±90 deg s. Pronation velocities positive.

8 280 G. P. Moore, L. Ding and H. M. Bronte-Stewart J. Physiol In Fig. 2B, by contrast, three spectral lines are present near 5 Hz. It is important, however, to distinguish between the spectra themselves and the several models of the underlying process which might lead to those spectra. From a formal point of view the tremors in Fig. 2 could arise from the linear superposition of sinusoids at the frequencies and amplitudes displayed in the spectra. This is the formal meaning of the spectrum: the original data can be reconstructed from the phase and amplitude information in the spectrum. Both tremors in Fig. 2, however, also exhibit amplitude modulations, suggesting that their spectra could be explained by an alternative non-linear model of the tremor-generating process: namely, amplitude modulation of a single sinusoidal generator (Gresty & Buckwell, 1990). The fact that the three peaks in the spectrum near 5 Hz are closely and rather evenly spaced, a characteristic spectral feature of sinusoids subjected to sinusoidal amplitude modulation, is suggestive. In principle, there is no way, based on these data, to decide which of these, or other, models is superior. Both models could account for the original tremor data and their spectra. If the amplitudemodulation hypothesis is correct, then both tremors share not only a single common frequency source, but also are subject to similar, though not necessarily identical, modulation processes. There are reports of central neurones recorded concurrently with tremor (or tremor-associated EMG signals) from the motor thalamus (Lenz et al. 1988; Zirh et al. 1998) and the internal segment of the globus pallidus (Hutchison et al. 1997; Hurtado et al. 1999) in Parkinson s patients undergoing neurosurgery. Samples of tremors from 1_methyl-4-phenyl- 1,2,3,6-tetrahydropyridine (MPTP)-treated green monkeys and unit activity recorded in the subthalamic nucleus (Bergman et al. 1994) have also been published. One would expect, of course, that neurones involved in tremor genesis would share a fundamental frequency with the tremors, but it is perhaps pertinent that some central neurones firing in bursts at a basic fundamental frequency also have significant activity at the harmonics of that frequency (Lenz et al. 1988; Bergman et al. 1994, 1998a,b; Nini et al. 1995; Zirh et al. 1998). The expected behaviour of a central neurone associated with the tremors shown in Fig. 2, with their multi-peaked spectra, would depend on the model of the generating process. For the two hypotheses already mentioned linear superposition of sinusoidal oscillators versus amplitude modulation of a single oscillator the relation of the spike train to the tremor would be entirely different. If the superposition model were correct, one would expect to see neurones firing in bursts at each of the three observed, presumably fundamental, frequencies. It is possible, though unlikely, that a single neurone (or group) could do this. Perhaps, instead, several ensembles would contribute to the process, each coherent with one of the fundamental frequencies. But if the amplitude-modulation hypothesis were correct, and the processes determining frequency and amplitude were anatomically and functionally separated, one would still expect a group of neurones to be coherent with the central (fundamental) peak. But no central tremorgenerating group would show activity at the side-band frequencies located on either side of the fundamental, which arise from the modulation process itself. Amplitudemodulating neurones or processes would exhibit cyclic activity at lower frequencies (less than 1 Hz in this example) that define the timescale of amplitude modulation. Those low frequencies would not be reflected as significant peaks in the tremor spectra. Low-frequency oscillatory activity observed in neurones associated with modulation would therefore not appear to have any relation to the tremor spectrum, and might be judged unrelated or irrelevant. The tremors shown in Figs 3 and 4 are presumed to arise from a single source; the tremors in Fig. 2 could also arise from a single frequency source. But it is possible that individual tremors can arise from more than one frequency generator, the evidence for which would be multiple significant peaks in the spectra. (Since spectra calculated from records taken over an extended period of time confound non-stationary behaviour, e. g. changing tremor frequencies, with the presence of multiple independent generators, caution is required.) Some of these generators might be coupled, others not. In this case, though the tremors are not entirely independent, the tremor records would certainly appear different, and their spectra might be of sufficient complexity to make identification of a shared source difficult. The coherence spectrum might be useful, though the presence of additional independent sources of power near the shared frequencies would also make this problematic. Central tremor-generating neurones would be coherent with those frequencies in the tremor associated with their activity but not with frequencies derived from other independent sources. Whether this occurs remains to be seen, but single neurone recordings obtained with concurrent tremor records during surgical procedures may help to clarify how many independent generators are active at a givenmomentforeachtremor. We can postulate the existence of ensembles of neurones whose interactions determine the fundamental frequency of a tremor, and possibly its harmonic content as well. Additional processes, which need not be periodic, would serve to determine its amplitude from moment to moment. Our data suggest that, at some points in time, signals from the generator of one tremor determine, strongly influence, or entrain the generator of a concurrent tremor. Interactions between generators may even be reciprocal. We cannot say at how many levels or sites these interactions occur, nor identify the conditions in which the synchronizing interaction is established or broken. More study will be required to determine the prevalence and duration of these periods of tremor correlation (and the periods that separate them), and the extent to which unpaired or ipsilateral extremities are

9 J. Physiol Concurrent Parkinson tremors 281 involved (O Suilleabhain & Matsumoto, 1998; Raethjen et al. 2000). Still more work will be required to determine the pathways and processes that underlie them. The point is not whether synchronization is common, but what it implies if it exists at all. Timmer, J., Lauk, M., Pfleger, W. & Deuschl, G. (1998). Crossspectral analysis of physiological tremor and muscle activity. II. Application to synchronized electromyogram. Biological Cybernetics 78, Zirh, T. A., Lenz, F. A., Reich, S. G. & Dougherty, P. M. (1998). Patterns of bursting occurring in thalamic cells during parkinsonian tremor. Neuroscience 83, Bendat, J. S. & Piersol, A. G. (1993). Engineering Applications of Correlation and Spectral Analysis. 2nd edn. John Wiley & Sons, New York. Bergman, H., Feingold, A., Nini, A., Raz, A., Slovin, H., Abeles, M. & Vaadia, E. (1998a). Physiological aspects of information processing in the basal ganglia of normal and parkinsonian primates. Trends in Neurosciences 21, Bergman, H., Raz, A., Feingold, A., Nini, A., Nelken, I., Hansel, D., Ben-Pazi, H. & Reches, A. (1998b). Physiology of MPTP tremor. Movement Disorders 13, suppl. 3, Bergman, H., Wichman, T., Karmon, B. & DeLong, M. R. (1994). The primate subthalamic nucleus. II. Neuronal activity in the MPTP model of parkinsonism. Journal of Neurophysiology 72, Gresty, M. & Buckwell, D. (1990). Spectral analysis of tremor: understanding the results. Journal of Neurology, Neurosurgery, and Psychiatry 53, Halliday, D. M., Rosenberg, J. R., Amjad, A. M., Breeze, P., Conway, B. A. & Farmer, S. F. (1995). A framework for the analysis of mixed time seriesïpoint process data theory and application to the study of physiological tremor, single motor unit discharges and electromyograms. Progress in Biophysics and Molecular Biology 64, Hunker, C. J. & Abbs, J. H. (1990). Uniform frequency of parkinsonian resting tremors in the lips, jaw, tongue, and index finger. Movement Disorders 5, Hurtado, J. M., Gray, C. M., Tamas, L. B. & Sigvardt, K. A. (1999). Dynamics of tremor-related oscillations in the human globus pallidus: A single case study. Proceedings of the National Academy of Sciences of the USA 96, Hutchison, W. D., Lozano, A. M., Tasker, R. R., Lang, A. E. & Dostrovsky, J. O. (1997). Identification and characterization of neurons with tremor-frequency activity in human globus pallidus. Experimental Brain Research 113, Lenz, F. A., Tasker, R. R., Kwan, H. C., Schnider, S., Kwong, R., Murayama, Y., Dostrovsky, J. O. & Murphy, J. T. (1988). Single unit analysis of the human ventral thalamic nuclear group: correlation of thalamic tremor cells with the 3 6 Hz component of parkinsonian tremor. Journal of Neuroscience 8, Nini, A., Feingold, A., Slovin, H. & Bergman, H. (1995). Neurons in the globus pallidus do not show correlated activity in the normal monkey, but phase-locked oscillations appear in the MPTP model of Parkinsonism. Journal of Neurophysiology 74, O Suilleabhain, P. E. & Matsumoto, J. Y. (1998). Time-frequency analysis of tremors. Brain 121, Raethjen, J., Lindemann, M., Schmaljohann, H., Wenzelburger, R., Pfister, G. & Deuschl, G. (2000). Multiple oscillators are causing parkinsonian and essential tremor. Movement Disorders 15, Rosenberg, J. R., Amjad, A. M., Breeze, P., Brillinger, D. R. & Halliday, D. M. (1989). The Fourier approach to the identification of functional coupling between neuronal spike trains. Progress in Biophysics and Molecular Biology 53, Acknowledgements This work was supported by the Kaiser Foundation Health Plan. We thank Patty Smith and Mary Molander for their technical assistance, and David Hary for helpful discussions. Corresponding author G. P. Moore: Department of Neurology and Neurological Sciences, Room A343, Stanford University Medical Center, 300 Pasteur Drive, Stanford, CA , USA. gmoore@usc.edu