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1Department of Biomedical Engineering, Duke University, Durham, North Carolina; and 2Center for Neurological Restoration and 3Neurological Surgery, Cleveland Clinic Foundation, Cleveland, Ohio
Submitted 15 May 2007; accepted in final form 15 July 2007
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ABSTRACT |
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INTRODUCTION |
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; Gross and Lozano 2000; Schuurman et al. 2000). DBS is also being investigated for treatment of epilepsy (Goodman 2004; Hodaie et al. 2002) and psychiatric disorders (Gross 2004), including obsessive-compulsive disorder (Nuttin et al. 2003) and depression (Carpenter 2006; Mayberg et al. 2005). Despite the clinical success of DBS, the underlying physiological mechanisms of action are unclear (Breit et al. 2004; Garcia et al. 2005; Grill and McIntyre 2001; McIntyre et al. 2004b). This lack of knowledge may limit the application of DBS for treating novel diseases; it also complicates the identification of optimal anatomical targets and the selection of appropriate stimulation parameters. The purposes of this investigation were to quantify the effects of paired-pulse DBS on tremor in subjects with essential tremor and to provide insight into the mechanisms responsible for these effects by analysis with a computational model.
The effects of frequency of DBS within the ventral intermediate nucleus of the thalamus (Vim) on tremor in essential tremor subjects are well documented. Reductions in tremor are typically observed only when the frequency of stimulation is >90 Hz; conversely, low-frequency DBS (<50 Hz) often worsens symptoms (Benabid et al. 1991; Kuncel et al. 2006; Ushe et al. 2004, 2006). However, no one has addressed whether high frequency alone is a sufficient condition for successful treatment of tremor with Vim DBS. We hypothesized that in addition to the average stimulation rate, pulse-to-pulse changes in the stimulation frequency are also important in determining the effectiveness of DBS. We tested this hypothesis within the confines of two questions.
First, how does the temporal spacing of pulses across stimulus trains with the same average rate influence the effectiveness of Vim DBS at reducing tremor? DBS typically uses regular high-frequency stimulation with constant interpulse intervals, but we measured the effects of high-frequency paired-pulse stimulation (nonconstant interpulse intervals) on tremor. We chose to examine subjects with essential tremor and Vim DBS because of the well-established and short latency of therapeutic tremor reduction (Benabid et al. 1991; Lyons and Pahwa 2004; Ushe et al. 2004).
Second, what are the stimulus-dependent changes in neuronal firing that may underlie the observed changes in tremor during Vim DBS? To address this question, we used a computer-based biophysical model of thalamocortical relay neurons to simulate the response of Vim thalamic neurons to paired-pulse stimulation. We quantified the responses of these model neurons to the same stimulus trains tested in essential tremor subjects. We then assessed the effects of paired-pulse stimulation on synchronous model neuronal bursts, irregular firing, and neuronal entrainment to the stimulus. The model provided insights into the potential neuronal responses that may underlie the observed tremor effects. Tremor results highlight the importance of pulse-to-pulse changes in stimulation frequency as opposed to just its mean rate, and modeling results suggest that the mechanisms by which tremor reduction occurs during DBS include the regularization of neuronal activity.
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METHODS |
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Five essential tremor subjects participated in the study after giving their written informed consent. Subject B was examined during stimulation of both the right and left Vim thalamus; therefore a total of six thalami were examined. The study protocol was approved by the Cleveland Clinic Foundation Institutional Review Board. Before their participation in the study, participants were diagnosed with essential tremor and were scheduled for DBS electrode implant surgery. Tremor medications were not withheld during the course of the study. The relevant demographic characteristics and stimulation settings for each subject are shown in Table 1.
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Stimulus magnitude was selected by increasing the amplitude of unpaired 130-Hz DBS until tremor reduction was observed in the subject or until the subject reported significant side effects (paresthesias, which subsided on discontinuation of stimulation). Subject reported side effects tended to decrease over the course of stimulation experiments, making it possible to perform the protocol at more than one stimulus amplitude for most subjects (n = 4). The amount of time available for experiments varied and was curtailed in some cases by subject fatigue and operating room scheduling considerations. Other than brief periods of paresthesias just noted, there were no adverse events and no incidents of infection. Contact 0 was tested first, and then more dorsal contacts were used if tremor suppression was unsatisfactory with contact 0.
A triaxial accelerometer (Model CXL04LP3; Crossbow Technology, San Jose, CA) was taped to the back of the hand contralateral to the stimulator. The subject was instructed to hold an empty plastic cup "almost but not quite touching the lips" as if drinking, with the shoulder slightly abducted and the elbow unsupported (Fig. 1D), and the accelerometer signal was sampled at 1 kHz during the final 20 s of stimulation.
To obtain a single quantitative descriptor of tremor for each trial, we combined the three accelerometry signals (ax, ay, and az) into one signal (acceleration = 
) and performed spectral analysis on the acceleration signal. We calculated the power spectral density, which quantifies the amount of power at each frequency, using the psd function (power spectral density; Welch's averaged periodogram, Hanning window, FFT length = 4,000) in MATLAB (The MathWorks, Natick, MA). We then defined tremor power as the integral of the power spectral density between 1 and 8 Hz (Fig. 1E). This frequency range eliminated the effects of gravity on the accelerometer (present only at 0 Hz) and included the primary tremor frequency of all subjects. This frequency range included the first harmonic of the primary tremor frequency in some subjects, but the spectral density of tremor power at harmonic frequencies was one to two orders of magnitude less than the tremor power at the primary frequencies. The tremor power measurements were log-normally distributed (Supplementary Note B).1 Therefore we used the natural logarithm of the integrated power for all tremor analyses. Data from two experiments on subject B were excluded, including those performed in the left thalamus. For a complete justification for the omission of these data, see Supplementary Note B. In brief, some data were recorded during stimulation with amplitudes that lay near the boundary between the subject's response to low versus high amplitudes, and the tremor responses were strictly bimodal. The tremor responded in a manner consistent with being stimulated randomly at low and high amplitudes, and the overarching amplitude effect precluded more sensitive analysis of changing the temporal spacing of paired-pulse trains. Thus the data presented here represent five thalami in five different subjects.
Computational model
We used computer-based models of thalamocortical relay neurons to simulate the response of Vim thalamus neurons to paired-pulse stimulation. The model of the thalamocortical relay neuron (McIntyre et al. 2004a) included representations of the dendritic tree, soma, and a double-cable axon (60 nodes of Ranvier) with geometries based on a three-dimensional reconstruction of a filled thalamocortical cell from rat (Destexhe et al. 1998), and the axon diameter was selected as representative of those in ventrolateral thalamus (Kultas-Ilinsky et al. 2003). The model neurons were implemented in NEURON (Hines and Carnevale 1997) and the transmembrane potential in response to the extracellular stimulation was obtained by backward Euler implicit integration with a time step of 0.01 ms.
We simulated 100 identical noncommunicating neurons randomly positioned within a sphere of 3-mm radius. The stimulating point source electrode was positioned at the center of the sphere (Fig. 2A). The center of the cell body of each model neuron was positioned within the sphere by generating uniformly distributed random polar coordinates. The axons extended in the same direction well beyond the sphere and the output of each model cell was recorded near the distal end of the axon. The extracellular voltages V, produced by extracellular stimulation with a point source electrode, were calculated at each position using V(r) = I
/4
r, where I is the current amplitude, r is the radial distance from the electrode, and = 500 
· cm is the resistivity of the infinite isotropic homogeneous extracellular medium.
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; Kobayashi et al. 2003; Lee et al. 2003; Magnin et al. 2000) (Figs. 1E and 2B). The bursts were driven by an internal current injection in the soma with an amplitude of 1.05 nA and a pulse duration of 30 ms. Quantitative analysis of model output
Several different measures were used to quantify the effects of paired-pulse DBS on the pattern of activity in the model thalamic neurons.
CV.
The coefficient of variation (CV) for each model neuron spike train was calculated as the SD of the interspike interval (ISI) distribution divided by the mean of the ISI distribution. High CVs were indicative of increased bursting in neurons compared with random firing. CV = 0 was not calculated for spike trains with fewer than two spikes over the entire duration of the simulation (
five-model neurons had fewer than three spikes per trial for any IPIdiff).
BURST INDEX.
Because we knew the temporal location of the intrinsic burst episodes, we defined a burst index that was different from the most commonly used burst index (Legendy and Salcman 1985)
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CV2.
A potential drawback of the CV is that a cell bursting at regular and predictable intervals has a very large CV because several short ISIs are followed by a very long ISI. Thus the CV may overestimate the irregularity of bursting neurons. By compensating for similar consecutive ISIs within bursts, CV2 measures neuronal firing regularity corrected for bursting (Holt et al. 1996). The CV2 for each model neuron spike train was the average CV for every consecutive ISI pair in the train (Fig. 2C), and was calculated as
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CVPAIR. Another potential drawback of the CV lies in the paired nature of the stimulus trains. CVpair provided a way to remove the dependence of CV on the paired nature of the stimulus trains. We defined the CVpair for each model neuron spike train as the CV for a spike train based on a new distribution of interspike intervals ISIpair, where ISIpair,i = [(isii + isii+1)/2] (Fig. 2D). If a particular neuron were phase-locked to the stimulus train, then the mean ISI of any consecutive pair of spikes [(isii + isii+1)/2] for that neuron would be 7.7 ms, regardless of the intrapair and interpair interval of the stimulus train. Thus the CVpair for all stimulus trains was zero, whereas the CV and CV2 of the stimulus trains decreased linearly with interpulse interval. Thus CVpair provided a way to assess the regularity of neuronal firing after eliminating irregularity arising from the paired spacing of the stimulus pulses. CVpair = 0 for spike trains with fewer than three spikes over the entire duration of the simulation.
Statistical analysis
Results are reported as means ± SE and statistical significance was defined at 
= 0.05. Statistical differences were determined using ANOVA, followed by Tukey's HSD (honestly significantly different) test for tremor measurements or post hoc Bonferroni multiple-comparisons tests for computational model results. Multiple comparisons were made using the multcompare function (multiple comparison test, Bonferroni correction) in MATLAB. Linear regression models were implemented in JMP version 6.0 for Mac OS X (SAS Institute, Cary, NC). The random-effect term for the mixed-effects regression model was subject[stimulus magnitude]. We used the ksdensity function (compute density estimate, Gaussian kernel, bandwidth = 0.05 ms) in MATLAB to estimate probability densities. For paired-pulse stimulation at amplitudes large enough for 100% activation, burst indices, CV and CVpair appeared to be normally distributed (QQ normality plot). However, for stimulation at 40 and 70% activation levels, burst indices, CV, CV2, and CVpair were multimodally distributed, as determined by inspection of histograms. Accordingly, significance tests of burst indices, CV, CV2, and CVpair were performed on just the 100% activation levels. CV2 distributions were multimodal at 100% activation, and the Kruskal-Wallis test was used for CV2 data. The population mean cumulative calculations of these firing statistics (burst index, CV, CV2, CVpair) stabilized by the end of the 400-ms simulations.
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RESULTS |
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We measured postural tremor responses to paired-pulse stimulation in five thalami of five subjects with essential tremor (Fig. 1, A–E). Consistent with previous studies, we observed significant tremor reduction in response to regular (unpaired) 130-Hz DBS compared with stimulation "OFF" (P < 0.05, Tukey's HSD) (Fig. 3A). However, 65-Hz DBS did not reduce tremor significantly compared with stimulation "OFF" (P < 0.5, Tukey's HSD). Tremor was also reduced for unpaired 130 Hz compared with regular (unpaired) 65-Hz DBS, but the difference was not significant (P < 0.07, Tukey's HSD).
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Each circle in Fig. 3C represents the mean log tremor power across all thalami during paired-pulse DBS. The open square and open circle represent, respectively, the log tremor responses to unpaired 65- and 130-Hz DBS. The solid line in Fig. 3C represents a fixed-effects regression model for the mean tremor power. We regressed log tremor power on IPIdiff for all trials in which the mean stimulation rate was 130 Hz (including unpaired 130-Hz DBS trials). We excluded tremor measurements with unpaired 65-Hz DBS and trials with stimulation "OFF" to make comparisons of tremor power at the same average stimulation rate. The difference between the intrapair and interpair intervals had a significant effect on tremor (P < 0.015, two-sided test on significance of IPIdiff regression coefficient), and tremor increased significantly as a function of IPIdiff [slope = 0.07 mV2/ms, 95% confidence interval (CI): 0.016–0.12 mV2/ms, model R2 = 0.01].
Changes in tremor also occurred across subjects and with changes in stimulus magnitude, and larger stimulus magnitudes evoked greater tremor suppression than did smaller stimulus magnitudes. In an exemplar subject (Fig. 3D), when the stimulus magnitude was increased from 0.3 to 1.0 mA, tremor power was reduced by several orders of magnitude. This result satisfies intuition because low-intensity stimuli are expected to have little effect on tremor.
To isolate changes in tremor arising from IPIdiff from changes resulting from subject and stimulus magnitude, we conducted a linear mixed-model regression of log tremor power as a function of IPIdiff. The random factor in the mixed-effects model was stimulus magnitude nested within subject, and this factor allowed the intercept of the mixed-effects model to vary across subjects and across stimulus magnitudes within each subject. As an example, the solid line in Fig. 3B represents the linear mixed-effects model for subject D at 1.4 mA. The descriptive power of the mixed-effects model was much higher than the fixed-effects model (R2 = 0.71). After accounting for variations in tremor due to stimulus magnitude and subject differences, it was even more apparent that the difference between intrapair and interpair intervals had a significant effect on tremor (P < 0.0001, two-sided test on significance of IPIdiff regression coefficient). Tremor increased significantly as a function of IPIdiff (slope = 0.07 mV2/ms, 95% CI: 0.04–0.10 mV2/ms, model R2 = 0.71). This result demonstrated that DBS with an average rate of 130 Hz was more effective at reducing tremor when pulses were evenly spaced than when there were large differences between intrapair and interpair intervals.
Model neuron responses to paired-pulse stimulation
We used computer-based models of thalamocortical relay neurons to estimate the response of Vim thalamic neurons to paired-pulse DBS (Fig. 2A). The model neuron responses for several values of IPIdiff are shown in Fig. 4A, where each row within each raster plot represents the firing times for one of the 100 model neurons. Raster plots for additional values of IPIdiff are shown in Supplementary Note A. The raster plots are centered on an intrinsic burst episode that lasts for about 50 ms (darker band of activity in the center of the rasters). This band disappeared (i.e., bursts were disrupted) when the frequency of unpaired stimulation increased from 65 to 130 Hz, but reappeared during paired-pulse stimulation with large IPIdiff. Thus model neurons appeared to exhibit fewer bursts when they were stimulated by unpaired 130-Hz pulses than when they were stimulated by paired pulses with large IPIdiff or by unpaired 65-Hz pulses (Fig. 4A).
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The mean CV of the fully activated population of model neurons was lower for unpaired 130-Hz stimulation than for paired-pulse stimulation with large IPIdiff (Fig. 4C). For multiple IPIdiff >7 ms, the mean CV for the population of modeled neurons was significantly higher than the mean CV for unpaired 130-Hz stimulation (ANOVA, P < 0.0001; multiple comparisons two-sided test with Bonferroni-corrected critical P < 0.00037 for = 0.05). Both unpaired and paired high-frequency stimulation induced more regular firing patterns, but firing of model neurons was significantly more regular for stimulation with unpaired-pulse trains than with paired-pulse trains with large differences between intrapair and interpair intervals. The CV is a nonspecific measure of neuronal firing variability and does not quantify specific changes in model neuron firing patterns. Therefore we subsequently performed more detailed analyses to characterize the changes in neuronal firing patterns.
Paired-pulse DBS affects model neuron burst activity
We defined a burst index to quantify the effects of DBS on burst activity: model cells in which intrinsic bursts were completely replaced by stimulus-locked spiking activity had a burst index of 0.5, whereas cells that did not respond to DBS and continued to generate intrinsic bursts had a burst index of 1.0.
Similar to the distribution CVs, the distribution of burst indices across the population of model neurons stimulated with low-intensity currents was bimodal with one mode at 1.0, representing those cells that were not activated by the stimulus, and a lower mode between 0.5 and 0.8, representing those cells that were activated by the stimulus (Fig. 5A). As with the CV, the distribution of burst indices for the population of model neurons tended toward a normal distribution when stimulus currents were large enough (Fig. 5A), and we proceeded with statistical analyses of the model cell responses at 100% activation.
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= 0.05) (Fig. 5B). The apparent reduction in bursts for trains with low IPIdiff in the raster plots (Fig. 4A) was not just a by-product of model cells firing more rapidly during regular 130-Hz stimulus trains—the pattern of model neuronal firing was quantitatively different. Paired-pulse DBS affects the ability of model neurons to entrain to stimulus
We reordered the model neuron responses shown in Fig. 4A according to the CV of neuronal ISIs. The reordered plots are shown in Fig. 6A, where the bottommost row of each raster plot represents the spike train for the model neuron with the lowest CV for the given IPIdiff. The sorted raster plots for all values of IPIdiff are shown in Supplementary Note A.
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) or globus pallidus (Bar-Gad et al. 2004). The model neurons in the fully activated population were more likely to respond with phase-locked firing when they were stimulated by high-frequency pulses that were more evenly spaced than when they were stimulated by paired-pulse trains with large differences between intrapair and interpair intervals. For IPIdiff >7 ms, there were no model neurons that responded with phase-locked firing. On the other hand, for IPIdiff <7 ms, between 9 and 27 of 100 model neurons responded with phase-locked firing (Fig. 6B). For all IPIdiff, there were several (7–19) model neurons that demonstrated rapid firing entrainment and the number of model neurons that showed this behavior was uncorrelated with IPIdiff (Fig. 6B). The remainder of the model neurons fired in mixed modes where bursts and spontaneous spikes were intermingled with stimulus-evoked spikes (Fig. 6A), and there was no discernible commonality in spatial position among model neurons that exhibited either type of entrainment to the stimulus. These results revealed that model neurons were more likely to exhibit regular phase-locked firing during stimulation with unpaired-pulse trains than for paired-pulse trains with large differences between intrapair and interpair intervals.
Paired-pulse DBS affects the regularity of model neuronal firing
To estimate the effects of paired-pulse DBS on the regularity of model neuronal firing, we calculated two measures of the variability of neuronal output: CV2 and CVpair. These two measures of regularity were not influenced by the presence of bursts or the paired nature of the stimulus trains, respectively.
The CV may have overestimated the irregularity of bursting model neurons, but CV2 corrected for bursting by compensating for similar consecutive ISIs that were contained within bursts (Fig. 2C). The locations of the modes in the distributions of CV2 were qualitatively unchanged when additional cells were activated (Fig. 7A), but the number of model cells in each mode was dependent on stimulation intensity. The CV2 of model cells that were not activated by the stimulus was 0.35, but when the threshold current for activation of a particular cell was exceeded, that cell would respond so that its CV2 changed from 0.35 to some value within the other CV2 mode(s) (Fig. 7A). The median CV2 of the fully activated population of model neurons was lower for unpaired 130-Hz stimulation than for paired-pulse stimulation with large IPIdiff (Fig. 7B). For IPIdiff >1 ms, the median CV2 for the model neuron population was significantly higher than the median CV2 for unpaired 130-Hz stimulation (Kruskal-Wallis, P < 0.0001; multiple comparisons two-sided test with Bonferroni-corrected critical P < 0.00037 for = 0.05). Stimulus trains with large differences between the intrapair and interpair pulse intervals caused model neurons that were phase locked to the stimulus trains to have much higher values of CV2 than unpaired 65-Hz trains. This is because the CV2 of the stimulus trains also increased as a function of IPIdiff. For IPIdiff >13 ms, model neurons were refractory to the second pulse in each pair, and had values of CV2 that were near the values for unpaired 65-Hz stimulation. Thus after compensating for similar consecutive ISIs that were contained within bursts, firing of model neurons was significantly more regular for stimulation with unpaired-pulse trains than with paired-pulse trains with large differences between intrapair and interpair intervals.
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= 0.05). High-frequency stimulation with unpaired-pulse trains regularized model neuronal output more than paired-pulse trains with large differences between intrapair and interpair intervals. |
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DISCUSSION |
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Tremor was dependent on the pattern of DBS, and a high average frequency alone was not a sufficient condition for maximal tremor reduction. Consistent with previous studies, tremor was reduced compared with stimulation "OFF" during regular 130-Hz DBS but not during regular 65-Hz DBS (Benabid et al. 1991; Boraud et al. 1996; Grill et al. 2004; Kuncel et al. 2006; Lyons and Pahwa 2004; Ushe et al. 2004, 2006). Similar frequency tuning has been observed for other symptoms in other disease states, including Parkinson's disease (Fogelson et al. 2005; Timmermann et al. 2004) and epilepsy (Mirski and Fisher 1994). However, stimulus trains with the same average rate but nonregular interpulse intervals were less effective at reducing tremor. Previous studies evaluated the effects of changing the temporal pattern of DBS in healthy monkeys (Ma and Wichmann 2004) and in persons with Parkinson's disease (Montgomery 2005). DBS of the subthalamic nucleus (STN) in healthy monkeys with a pattern derived from the STN firing pattern in parkinsonian monkeys disrupted motor performance, whereas stimulation with regular interpulse intervals at the same average rate did not disrupt motor performance (Ma and Wichmann 2004). In subjects with Parkinson's disease, movement times were shorter (i.e., DBS was more effective) during continuous STN DBS than when DBS was cycled "ON" and "OFF" for either 0.1 or 0.5 s, although all patterns had the same average rate (Montgomery 2005). Although these results were derived under different experimental conditions, they are consistent with our conclusion that the pattern of stimulation alters the efficacy of DBS.
We identified several changes in the firing properties of model thalamocortical neurons that paralleled the changes in tremor measured in human subjects. Compared with regular (unpaired) 130-Hz stimulation, paired-pulse trains with large IPIdiff 1) increased the proclivity of model neurons to fire synchronous bursts, 2) increased the irregularity of model neuronal firing, and 3) decreased the probability that model neurons were entrained to the stimulus. These modeling results lead us to hypothesize that by decreasing synchronous bursts, regularizing neuronal firing, and entraining neurons to the stimulus, effective high-frequency DBS overrides pathological oscillatory activity in the stimulated nucleus and replaces it with more regularized firing. These findings also suggest that effective high-frequency DBS opposes the effects of essential tremor by overriding oscillatory bursts and irregular activity in the thalamus. There is an increase in bursting, irregular activity, and in the overall rate of activity in the Vim thalamus of subjects with essential tremor compared with subjects without essential tremor (Molnar et al. 2005a). We previously found that changes in model neuron response variability as a function of frequency matched remarkably well the changes in tremor as a function of frequency (Grill et al. 2004), and suggested that the function of high-frequency DBS is to override pathological activity. Our current findings are consistent with this hypothesis: DBS with high-frequency regular (unpaired) pulse trains increases the ability of DBS to entrain and regularize the output of model thalamic neurons compared with DBS with paired-pulse trains at the same average rate. Because DBS in the Vim may stimulate both Vim and Vop thalamic neurons, areas receiving excitatory cerebellar inputs and inhibitory pallidal inputs may both be excited. The roles of these inputs in the etiology of essential tremor are not well defined, and our results do not clarify the role of either type of input in the generation or suppression of tremor.
There are several potential explanations as to why the paired-pulse trains with large differences in intrapair and interpair pulse intervals were less effective at reducing tremor than regular (unpaired) DBS at the same average rate. One hypothesis is that the nonregular nature of the paired-pulse trains with large IPIdiff prevented the stimulus trains from overriding pathological activity in the stimulated nucleus. The ability of extracellular stimuli to mask intrinsic neuronal activity by entrainment is strongly dependent on the rate of stimulation, relative to the underlying rates of intrinsic activity (Grill et al. 2004). High-frequency DBS in the Vim of essential tremor subjects increased the amplitudes of motor-evoked potentials generated from transcranial magnetic stimulation—suggesting that Vim DBS increased the activity of thalamic outputs (Molnar et al. 2005b). Conversely, this effect was not seen when low-frequency DBS was applied in the same subjects (Molnar et al. 2005b). The long interpulse intervals present in the trains with large IPIdiff may have thus been too long to mask the intrinsic activity and, even in the presence of stimulation, the intrinsic pathological activity persisted. A second hypothesis is that the lack of effectiveness of the paired-pulse trains resulted from the long interpulse intervals (
14 ms) enabling and even promoting rebound bursts in thalamus. Recent computational (Babadi 2005) and experimental (Person and Perkel 2005) results indicate that nonregular stimulus trains trains, per se, do not lead to thalamic bursting and disruption of thalamic fidelity, but rather pauses between spikes in trains of thalamic input that exceeded 25 ms (<50 Hz) lead to burst responses in thalamus. The present findings are consistent with these previous data and suggest further that instantaneous pauses in DBS on the order of 15 ms are sufficient to decrease the effectiveness of DBS stimulus trains even when the trains have a high average rate.
Experimental limitations
Experiments were conducted 1 to 3 days after DBS lead implantation, and tremor is usually reduced during this period as a result of focal brain edema causing a "microthalamotomy" effect. However, the microthalamotomy effect was not a significant setback to our study. All subjects still exhibited tremor, and that tremor was responsive to DBS. Although the amount of baseline tremor was variable across subjects, our mixed-effects models revealed significant effects of changing the interpair and intrapair intervals in the presence of subject as a random effect. Further, we analyzed tremor measurements comparatively and all measurements within each subject included contributions from the same microthalamotomy effect. Notably, these experiments could not have been performed using the conventional implantable pulse generator, which can generate pulse trains of only fixed frequency, and our only opportunity to conduct these experiments was the period between implantation of the electrode and pulse generator.
The short duration of DBS before assessment of tremor and the short interval between trials was a limitation of our study. Although the trials may be too short to enable full development of the effects of stimulation, similarly short trial lengths have been used in studies of parameter settings (Kuncel et al. 2006; Moro et al. 2002; O'Suilleabhain et al. 2003; Rizzone et al. 2001) and are used routinely for intraoperative testing and postoperative tuning. Tremor reduction after onset of DBS generally occurs "within a few seconds" (Beuter and Titcombe 2003; Holsheimer et al. 2000). In addition, longer trials would be more likely to cause subject fatigue. The negative impacts of the short trial length were minimized by randomizing the ordering of trials and by making relative comparisons of tremor.
We used stimulus pulses different from those generated by the implanted pulse generators (Medtronic). Standard DBS pulses are asymmetric with long-duration, low-amplitude recharge phases, which would preclude testing interpulse intervals 
1–2 ms without disrupting the recharge phase. However, it is not likely that our primary results were affected by these changes in the shape of the pulse waveform. This is supported by the fact that increases in tremor as a function of IPIdiff were observed with both cathodic and anodic lead-phase pulse trains (Table 1).
Computational model considerations
We used computational models of thalamocortical relay neurons to estimate the responses of real neurons to paired-pulse DBS, but did not record activity from any neurons in vivo. Pathological activity in Vim thalamic neurons in persons with tremor was represented in our computational model as synchronous bursting at 4 Hz. Synchronous bursting in the thalamus has been associated with both essential tremor and Parkinson's disease (Hua and Lenz 2005; Lenz et al. 1994). Recent studies identified tremor cells in thalamic neurons of essential tremor subjects, but reported that the incidence of tremor cells is lower in essential tremor than in Parkinson's disease (Brodkey et al. 2004; Kobayashi et al. 2003; Lee et al. 2003). However, these studies were performed with the subject at rest and essential tremor symptoms are manifested primarily as postural tremor. When Vim neurons were examined during postural tremor, about 64% of the neurons manifested tremor-related activity (Hua and Lenz 2005). The mean intraburst interval of our model neurons was 4 ms (250 Hz) and the mean interburst interval was 218 ms (4.6 Hz)—values close to those identified in essential tremor subjects (Hua and Lenz 2005), as well as in subjects with Parkinson's disease (Magnin et al. 2000). Although the synchronization of all 100 model neurons represented an extreme case and simplified our calculation of the burst index, the CV, CV2, and CVpair of neuronal firing would not change if the neurons were desynchronized.
Our computational model did not include synapses or connections between the neurons in the population. Even though this is an oversimplification of the network morphology of the Vim thalamus, it is nonetheless remarkable that even in this simple model, the changes in firing patterns with IPIdiff closely paralleled changes in tremor with IPIdiff. Further, there is still substantial debate regarding which networks, channels, and transmitters are implicated in burst generation in tremor neurons. Therefore inducing bursting by means of a simple current injection may be just as valid as a more complicated, yet still speculative, methods of burst generation. It is also noteworthy that the variability of the model neuron responses was caused exclusively by differences in the spatial position of the neurons with respect to the point source electrode. Thus differences in the positions of neurons with respect to the electrode may play as large a role in determining neural responses to DBS in the stimulated nucleus as more complicated network dynamics and interconnections within the stimulated nucleus. This speculation is supported by the dichotomy of somatic and axonal spiking in response to DBS (McIntyre et al. 2004a).
In conclusion, the ability of DBS to control tremor, as well as to entrain and regularize the firing of model neurons, was dependent not only on the average rate of stimulation, but also on pulse-to-pulse changes in the rate of stimulation. Therefore both the rate and patterns of DBS play an important role in DBS function in essential tremor, and high frequency is not a sufficient condition for effective DBS. Similar experiments should be performed in other diseases and targets to characterize better how changes in DBS pulse spacing affect DBS outcomes.
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DISCLOSURE |
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FOOTNOTES |
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1 The online version of this article contains supplemental data. 
Address for reprint requests and other correspondence: W. Grill, Duke University, Department of Biomedical Engineering, Hudson Hall, Room 136, Box 90281, Durham, NC 27708-0281 (E-mail: warren.grill{at}duke.edu)
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ABSTRACT
INTRODUCTION
Mean CV is significantly higher than the mean CV for unpaired 130-Hz DBS (ANOVA, P < 0.0001; multiple comparisons 2-sided test with Bonferroni-corrected critical P < 0.00037 for 
Median CV2 is significantly higher than the median CV2 for both unpaired 65- and 130-Hz DBS. C: estimated CVpair distributions for 3 stimulus trains at 40, 70, and 100% activation current amplitudes. Location of the modes for activated neurons changed minimally as a function of activation level. Legend in A applies to C as well. D: mean CVpair (±SE) as a function of IPIdiff for 100% activation. *Mean CVpair is significantly lower than the mean CVpair for unpaired 65-Hz DBS.