Background

Approximately 70% of the people with Parkinson’s disease exhibit involuntary shaking of their limbs when resting [1]. Involuntary shaking of the limbs, also known as tremor, can dominate Parkinson’s disease, and yet responds less well to dopaminergic medications than bradykinesia and rigidity [2, 3]. Deep brain stimulation can provide striking tremor relief however this surgical intervention is invasive and subject to strict selection criteria, which can limit the number of people benefiting to approximately 2% [4, 5]. As a result, there has been growing interest in non-invasive therapies for tremor in Parkinson’s disease. Therapies directly interfacing with the limb rather than cranial stimulation [6, 7] are more tractable and have focused on occluding tremor by stimulation of antagonist muscles or suppressing tremor by stimulation of sensory afferents. However, these approaches can lead to incomplete and unpredictable tremor suppression, muscle fatigue and discomfort, and have not entered in to clinical practice [8,9,10,11,12,Phase-amplitude profiles’ in ‘materials and methods’ and Additional file 1) and then drew 12 points 1000 times from this distribution. This created 1000 surrogate phase-amplitude profiles (1000 by 12) for each participant, accelerometer axis and TOP. Every surrogate phase-amplitude profile (1 by 12) was realigned to the maximum or minimum change in tremor. This was achieved by map** minimum suppression or maximum amplification to 180°. As before, we classified each bin as suppressive when the median change in tremor severity was smaller than zero and amplifying when greater than zero. We then summed the number of instances with suppression or amplification across the 1000 surrogate phase-amplitude profiles. We divided this sum by 1000, normalising it to a value between zero and one reflecting the probability of seeing suppression or amplification at that phase. These probabilities were compared, with a two-sample t-test, to those derived from data recorded during peripheral nerve stimulation and corrected for multiple comparisons using the false discovery rate (FDR) procedure.

Results

Tremor oscillation patterns

We first aimed to identify switches in tremor oscillation patterns (TOPs) such as a switch from a predominant tremor in the x dimension (i.e., pronation-supination) to one in the z dimension (i.e., extension-flexion). In seven out of 10 participants, the peripheral manifestation of tremor varied during the recording session and as a result we observed more than one TOP, indicated by the presence of more than one cluster delineating coefficients contributing to principal components of accelerometer recordings. Implicit in this result is that the dominant cluster (or clusters where the second principal component was also considered) changed over time in these participants exhibiting more than one cluster (Additional file 1). Figure 3 provides an example of how cluster representation in serial 5-s periods changes over time and includes the cluster label, the median tremor signal amplitude and the median rectified EMG envelope in each axis per 5-s period.

Fig. 3
figure 3

An example of how cluster representation in serial 5-s periods changes over time in the signals without stimulation. A Dominant cluster label (orange or green) obtained from the first principal component coefficients is shown for the median accelerometer signal amplitude and B for the median rectified EMG in each channel per 5-s period. C The first principal component coefficients corresponding to the three accelerometer axes. D The labels for the time segments assigned to each of the two clusters. E The corresponding three-dimensional cluster division from the first principal component coefficients

Full size image

Differences between tremor oscillation patterns

We next explored whether there were any physiological differences between clusters (i.e., TOPs) based on features of accelerometer and EMG recordings. Significant differences in tremor peak frequency and amplitude envelope were found for all three accelerometer axes (p \(\le\) 0.0003 for all three axes, as given by the Wilcoxon signed-rank test applied to the absolute value of the difference in tremor amplitude and peak frequency across clusters). EMG peak frequency and amplitude envelope also showed significant differences between clusters (p \(\le\) 0.0003 for all three muscles, as given by the Wilcoxon signed-rank test applied to the absolute value of the difference in EMG amplitude and peak frequency across clusters for the three muscles—abductor pollicis brevis, forearm finger flexors, and forearm finger extensors). It should be noted that the average duration of a cluster during the “without stimulation” condition was 100.5 ± 143.5 s (mean ± SD).

Phase-specific response to peripheral stimulation

Having confirmed that TOPs differ in frequency and amplitude, we next explored how phase-locked stimulation modulated tremor severity. Figure 4 shows an example phase-amplitude profile derived for one participant. Stimulation significantly enhanced or reduced the instantaneous tremor severity depending on the stimulation timing. As highlighted by this example, the most effective stimulation phase, indicated by the phase which induces changes in tremor amplitude beyond natural variability of tremor, was more consistent across different axes of the same cluster (TOP) than across clusters (i.e., cluster 1 suppressive phase of 330° vs. cluster 2 suppressive phase of 120°). At the group level, the correlation between axes in the same cluster was greater than that across clusters (Fig. 5). The difference between the correlations within and between clusters was significant (p-value < 10–7 for a two-sample t-test). Thus although the pattern of modulation differs between clusters from the same hand, within a cluster the pattern of modulation is relatively conserved across axes, providing additional evidence that clusters are meaningful in terms of a common representation.

Fig. 4
figure 4

Example phase-amplitude profiles for one study participant, showing the median change in tremor severity at each phase for the three accelerometer axes and two clusters. Significant median change in tremor severity was identified with respect to the tremor variability during the without stimulation condition following Bonferroni correction for 12 comparisons

Full size image
Fig. 5
figure 5

A Example of the Fisher-corrected correlations for each cluster combination in one study participant. B Mean between and within clusters of the Fisher-corrected correlation across participants

Full size image

At the group level, significant tremor suppression occurred across 12 bins in 12 phase-amplitude profiles for five out of 10 participants, and significant amplification across 16 bins in 12 plots from six participants. In total, 28 bins (1.7%) displayed significant change in tremor severity (Table 2). This number is eight times above the chance level for Bonferroni correction, which was used to determine the significance of different bins in the phase-amplitude profiles. On average, phase-locked median nerve stimulation was able to significantly amplify tremor by 117% ± 243% (mean ± SD) and suppress it by 36% ± 9% (mean ± SD).

Table 2 Summary of number of phase bins, plots and study participants displaying significant tremor suppression or amplification, as well as the number of bins and plots expected at the chance level considering that the Bonferroni correction was applied
Full size table

Angle of stimulation

There was no systematically preferred suppressive or amplifying phase across study participants. Figure 6 shows the number of phase bins across study participants and clusters for which there was significant tremor suppression or significant tremor amplification, at each of the 12 equally spaced stimulation phases (Rayleigh test resulted in p = 0.7204 for suppression and p = 0.2347 for amplification).

Fig. 6
figure 6

Rose plots indicating the number of phase bins for which there was significant tremor suppression or significant tremor amplification at each of the 12 equally spaced stimulation phases. Rayleigh test for departure from circular uniformity resulted in p = 0.7204 for suppression and p = 0.2347 for amplification

Full size image

Next, we considered re-aligned stimulation angles. As to be expected, separately aligning stimulation angles to the most suppressive or amplifying stimulation angle observed in each phase-amplitude profile produced non-uniform distributions at the group level (Fig. 7A and B). However, stimulation and its surrogate data (Fig. 7C) aligned to minima differed significantly, as did stimulation and surrogate data aligned to maxima (Fig. 7D). In the case of suppression, the 150–180° bins were significantly more likely to show amplitude reduction during stimulation than in surrogates. Conversely, the 0–60, 90–120, and 240–330° bins were significantly less likely to be associated with amplitude reduction during stimulation than with surrogates (Fig. 7D; Table 3). The overall pattern was less distinct in the case of amplification, although the probability of amplitude increases and decreases during stimulation was significant in the 60–180, 240–270, and 300–330° bins, respectively. It should be noted that for both suppression and amplification, these grou**s are placed approximately 180° apart.

Fig. 7
figure 7

A Rose plots indicating the probability of significant tremor suppression or tremor amplification at each of the 12 equally spaced stimulation phases where the minimum suppression and maximum amplification angles were realigned to 180°. Rayleigh test resulted in p = 2e−8 for suppression and p = 0.0002 for amplification. B Rose plots indicating the probability of tremor suppression or tremor amplification at each of the 12 equally spaced stimulation phases, regardless of whether tremor modulation was significant, where the minimum suppression and maximum amplification angles in all phase-amplitude profiles were realigned to 180°. Rayleigh test resulted in p = 6e−6 for suppression and p = 0.0334 for amplification. C Rose plots generated from surrogate phase-amplitude profiles indicating the probability of tremor suppression or tremor amplification at each of the 12 equally spaced stimulation phases where the minimum suppression and maximum amplification angles were realigned to 180° regardless of whether tremor modulation were significant. D Rose plots displaying the ratio between the real (B) and surrogate (C) probabilities of suppression or amplification in all phase-amplitude profiles, such that ratios significantly greater than 1 after FDR correction are shown in red, ratios significantly smaller than 1 are shown in green, and ratios that are not significant after FDR correction are shown in grey. Precise p-values given in Table 3

Full size image
Table 3 Significance values corresponding to Fig. 7 where rose plots display the ratio between the real (Fig. 7B) and surrogate (Fig. 7C) probabilities of all phase bins
Full size table

Discussion

We have provided evidence that Parkinsonian rest tremor of the hand often exhibits distinct oscillatory patterns, and that the output of a given tremor oscillator can be modulated in amplitude by peripheral stimulation at specific phases, although these critical phases differ between tremor oscillators.

Multiple tremor oscillators

The existence of independent oscillators driving different peripheral tremor components was inferred from the pattern of tremulous wrist movement in space which could be divided into more than one pattern by principal component and cluster analysis in seven out of ten study participants. The independent nature of these patterns or clusters was supported by cluster separation, significant differences in frequency distribution, significant differences in associated muscle activations, and through differences in the phase-amplitude profiles observed during phase-locked peripheral nerve stimulation. Moreover, the mean correlations across phase-amplitude profiles indicate that the amplitude modulation patterns were more similar across different axes in the same cluster than across the same axis from different clusters. Clusters were dynamic with their likelihood of being dominant altering over time. The latter is in kee** with the inconstancy of coherence between neurons oscillating at tremor frequency, and the inconstancy of the coherence between these neurons and background activity in the STN [47]. Although Parkinsonian rest tremor is considered to represent the effect of independent oscillators in different limbs [27,28,29,30,31], the current study suggests that central tremor oscillators could potentially adopt a much finer structure so that multiple oscillators may contribute to the tremor in a given hand. Electroencephalography and/or local field potentials should be evaluated in order to establish the link between central tremor oscillators and the changes in the pattern of tremulous wrist movement.

Could the presence of more than one cluster during stimulation be due to contamination of the tremulous wrist movements in space by a direct response to stimulation? This is unlikely as we only accepted clusters that were present both with and without peripheral nerve stimulation. In addition, significant differences in frequency and amplitude were found between clusters in the cluster division obtained from the recordings without stimulation. Furthermore, stimulation was performed at just below the motor threshold, so that direct responses were small and inconstant.

Contextual factors shape tremor dynamics

One paradoxical observation is that there was no systematic phase at which peripheral stimulation induced tremor amplification or suppression across study participants. Hence significant effects were only evident after phase-amplitude profiles were realigned to their maxima or minima. This was also the case with stimulation of the ventrolateral thalamus in people with essential tremor [39]. It has previously been shown that median nerve stimulation can induce spiking activity in parts of the thalamus which are also implicated in tremor in Parkinson’s disease [21,22,23,24,25]. Therefore, the precise effect of median nerve stimulation could be influenced by the conduction delays between the spindle afferents and the thalamus. Since stimulation is phase-locked to limb acceleration, the precise relationship between tremor and thalamic tremor cells could also impact stimulation effects [23, 26]. These sources of variation across participants could all contribute to the inconsistencies in stimulation phases that significantly modulated tremor (Fig. 6 and Additional file 1). As demonstrated here, effective stimulation parameters such as the stimulation phase should therefore be determined individually to mitigate this variability across participants. An open question is whether or not systematic phases, those at which stimulation induces tremor amplification or suppression, will emerge if we quantify effects from EMG rather than accelerometer signals. However, this is not trivial as it requires the identification and recording of EMG signals that are relatively selectively involved in one or other cluster.

We should also highlight two important assumptions made in our analysis. The first is that there are no more than two clusters each in the first or second principal components underlying rest tremor of the hand, although this assumption was supported by the distance between the clusters. Second, we assume that the activity of one cluster in each principal component dominates during each 5-s epoch of analysis. Although additional clusters cannot be excluded, their impact is likely to be small. However, we have little evidence to assume that a given cluster consistently dominates throughout each of the arbitrarily defined 5-s epochs of analysis. The presence of one or more additional active clusters within an epoch may again influence the phase at which any amplification or suppression effect predominates, and this confound will not necessarily be addressed by considering EMG rather than accelerometer activity.

Phase-dependent modulation of tremor

At the individual level phase-amplitude profiles contained more bins with significant tremor amplitude amplification or suppression than could be accounted for by chance. Realignment of effects to the phase bin that afforded maximum amplitude reduction or increase in phase-amplitude profiles highlighted two grou**s of phases, associated with significant decreases in the probability of suppression compared to surrogates and placed approximately 180° apart. A comparable effect was evident with regard to the probability of stimulation-induced tremor amplification. These observations raise the possibility that each TOP (or cluster) is underpinned by an oscillator with a frequency twice that of the limb tremor, and that peripheral stimulation is interacting with this harmonic. Such a harmonic could be centrally represented in line with the pattern of tremor modulation reported with phase-locked transcranial alternating current stimulation in people with Parkinsonian rest tremor [6]. Direct recordings of brain activity also point to a coupling of peripheral tremor to central oscillatory activity at twice tremor frequency [48,49,50].

The present results suggest that provided the dominant tremor oscillation is tracked in time, then phase-locked peripheral nerve stimulation may be able to attenuate tremor amplitude. For those study participants with one TOP, determining the stimulation phase to suppress tremor and continuously delivering stimulation phase-locked to this instance would be straightforward. However, the remaining participants in our cohort had two or more tremor components, the dominance of which fluctuated over time. Accordingly, successful stimulation would have to dynamically match the phase to maximally attenuate tremor to the tremor component dominating at that moment in time, a relationship which could perhaps be established through machine learning. But that is not the only issue impeding the development of phase-locked stimulation at the wrist as a non-invasive therapeutic option. The degree of tremor attenuation achieved by phase-locked stimulation when this was maintained at the appropriate phase for 5-s periods is also modest (36% suppression). Sustaining stimulation at the optimal phase for longer may potentially improve the degree of attenuation [6, 39], as might searching for the optimal phase for attenuation with finer phase resolution and determining changes in tremor clusters with finer temporal resolution. Finally, given that coupling of peripheral tremor to central oscillatory activity may be at twice tremor frequency, then trials of stimulation that is phase-locked to this central harmonic are also warranted. This would require the determination of sensitive phases from phase-amplitude profiles derived by stimulating at twice the frequency of TOPs in the periphery.

Limitations of the current study

We have already alluded to the importance of polymyography when investigating any consistency between stimulation phases promoting maximal suppression and amplification of tremor amplitude. Evaluation of changes in central tremor oscillators through electrocorticography and local field potentials will be needed in order to confirm the relationship between peripheral changes in tremor form and central rhythms. Another related limitation of our analyses is that temporal resolution was 5 s which may be too coarse to capture rapid shifting between tremor clusters and is likely to only reveal which TOP dominates within each temporal window. This might also explain the complex form of many phase-amplitude profiles and why they have relatively wide confidence limits as the 5-s analysis windows may be capturing more than one tremor component. Another limitation of our study is that electrical stimulation might have caused sub-motor threshold activation of wrist nerves (i.e., the radial and ulnar nerves) other than the intended target (i.e., the median nerve). Whereas any unforeseen consequences of this activation were minimised by kee** the stimulation below the motor threshold, it would be valuable to characterise the effects of stimulating the median vs. radial or ulnar nerves by intentionally targeting these nerves. In addition, our cohort was relatively small, and we did not investigate the effects of movement or posture on TOPs. It therefore remains to be seen whether these latter conditions change the precise distribution of spinal motor neurons recruited within a cluster, and thereby modify the tremor trajectory in space. Finally, our small cohort does not allow us to explore any relationship between disease progression or phenotype, and the number and organisation of tremor clusters.

Challenges and future directions

Tremor shows great variability within and across individuals. Peripheral stimulation parameters that effectively modulate tremor may therefore vary across people with Parkinson’s disease and resting tremor, but critically may also vary in time as demonstrated in this study. In order to maximise peripheral stimulation efficacy, stimulation parameters should be optimised individually. Similarly, to account for potential changes in tremor form, which could influence efficacy of peripheral stimulation, parameters for this non-invasive therapy may need to be occasionally adjusted. Considering the vast number of parameter combinations (e.g., pulse width, amplitude, frequency and pattern), peripheral stimulation parameters may need to be optimised outside of the laboratory setting using a wearable peripheral stimulator that is capable of remote parameter optimisation. Such an adaptive system could also be used to track an individual’s tremor form in real time using percentage tremor power in different accelerometer axes and adjust stimulation parameters accordingly in order to sustain stimulation efficacy. Automated parameter optimisation schemes such as Bayesian parameter optimisation could be critical in this context in order to achieve parameter optimisation both across individuals and time [51].

Conclusions

We have furnished evidence that Parkinsonian hand tremor may be the product of multiple oscillators leading to discrete patterns of acceleration in three-dimensional space. Oscillators tend to be sensitive to peripheral stimulation, and this leads to discrete patterns of stimulation-phase dependent suppression and amplification. These observations are important in hel** to explain tremor variability, and need to be taken into account if phase-locked stimulation is to be developed as a potential therapeutic intervention to suppress Parkinsonian resting tremor [6, 39]. In particular, the suppressive phase of stimulation may change according to which oscillator dominates at a particular moment in time. The issue of multiple oscillators may be relevant to the development of treatments in other neurological disorders such essential and dystonic tremor, where phase-locked stimulation has been explored as a potential therapeutic technique (15, 16, 39, 40).