Stimulus features underlying reduced tremor suppression with temporally patterned deep brain stimulation

Abstract

Deep brain stimulation (DBS) provides dramatic tremor relief when delivered at high-stimulation frequencies (more than ∼100 Hz), but its mechanisms of action are not well-understood. Previous studies indicate that high-frequency stimulation is less effective when the stimulation train is temporally irregular. The purpose of this study was to determine the specific characteristics of temporally irregular stimulus trains that reduce their effectiveness: long pauses, bursts, or irregularity per se. We isolated these characteristics in stimulus trains and conducted intraoperative measurements of postural tremor in eight volunteers. Tremor varied significantly across stimulus conditions (P < 0.015), and stimulus trains with pauses were significantly less effective than stimulus trains without (P < 0.002). There were no significant differences in tremor between trains with or without bursts or between trains that were irregular or periodic. Thus the decreased effectiveness of temporally irregular DBS trains is due to long pauses in the stimulus trains, not the degree of temporal irregularity alone. We also conducted computer simulations of neuronal responses to the experimental stimulus trains using a biophysical model of the thalamic network. Trains that suppressed tremor in volunteers also suppressed fluctuations in thalamic transmembrane potential at the frequency associated with cerebellar burst-driver inputs. Clinical and computational findings indicate that DBS suppresses tremor by masking burst-driver inputs to the thalamus and that pauses in stimulation prevent such masking. Although stimulation of other anatomic targets may provide tremor suppression, we propose that the most relevant neuronal targets for effective tremor suppression are the afferent cerebellar fibers that terminate in the thalamus.

Fig. 1.

Intraoperative measurements of tremor in response to different temporal patterns of thalamic deep brain stimulation (DBS). A: trial timeline that was followed to measure tremor suppression under experimental conditions. B: triaxial raw accelerometer signals (A_X, A_Y, and A_Z) recorded during 2 tremor trials in subject F. The raw traces illustrate the acceleration magnitude in each of the 3 dimensions during 20-s trials with DBS off (i) and during 185-Hz Regular DBS (ii). Scale bars in (ii) apply to both traces. C: power spectral density for the acceleration trial signals shown in B with DBS off (i) and during 185-Hz Regular DBS (ii).

Fig. 2.

Stimulus trains designed to test whether pauses, bursts, or irregularity per se are the causes of the ineffectiveness of temporally irregular DBS. A–C: high-entropy log-uniform distributions with various frequency limits. Sample stimulus trains are shown in insets above corresponding distributions. A: Uniform stimulus distribution designed with a minimum at 90 Hz and a geometric mean of 185 Hz. B: Unipeak stimulus distribution with wider frequency limits than the Uniform stimulus. C: Bimodal stimulus distribution, where the frequency limits were adjusted such that interpulse intervals (IPIs) were either greater or less than the therapeutic frequency range. D: Absence trains had a geometric mean frequency of 185 Hz and pauses of 50.7 ms that came at a rate of 4.4 Hz. E: Presence trains had a geometric mean frequency of 185 Hz and brief bursts of stimulus pulses that lasted 52.57 ms and came at a rate of 4.4 Hz.

Fig. 3.

Computational model of the response of thalamic neurons to DBS. A: schematic representation of 3-dimensional (3-D) cable model of a thalamocortical (TC) neuron and 4 terminating axons providing input to the TC neuron. Elements with bold lines were biophysically modeled and subjected to the extracellular potentials generated by stimulation, whereas elements with light lines were modeled as virtual axon branches that mimicked activity in the biophysical axons with a time delay consistent with action potential propagation down an axon branch. B: prism representation of the ventral intermediate (Vim) thalamus (Benabid et al. 1998; Mobin et al. 1999) and sample 3-D locations of 50 cell bodies within the nucleus. C: coronal view of Vim thalamus with DBS electrode drawn to scale. The orientations of the TC neuron and input axons are also shown; however, the neural elements are not drawn to scale. D: sagittal view of Vim thalamus taken 15 mm lateral to the anterior commissure-posterior commissure (AC-PC) line, with DBS electrode drawn to scale. The orientations of the TC neuron and input axons are also shown, but these elements are not drawn to scale. The reticular nucleus (RN) and thalamic interneuron (TIN) axons cannot be seen because they extend directly in the lateral and medial directions, respectively. Legend in D also applies to C. CTX, cortex; CER, cerebellum; NMDA, N-methyl-d-aspartate; AMPA, dl-α-amino-3-hydroxy-5-methylisoxazole-4-propionic acid.

Fig. 4.

Tremor during different temporal patterns of thalamic DBS. A: mean ± SE log-transformed tremor power across 7 experimental conditions in all 8 subjects. Significant changes in tremor were observed across stimulus condition (repeated-measures ANOVA). *As compared with tremor during stimulation off, tremor was suppressed significantly during Regular 185-Hz DBS, Uniform DBS, Unipeak DBS, and Presence DBS. Tremor tended toward suppression during Bimodal and Absence DBS compared with DBS off but not significantly. †Tremor was suppressed more effectively with Regular DBS than with Bimodal DBS. B: data pooled across stimulus-train characteristics: no pauses vs. pauses (i); no bursts vs. bursts (ii); and periodic vs. irregular (iii). Lines connect tremor measurements within subjects. *Stimulus trains with pauses were significantly less effective than stimulus trains without pauses (P < 0.002, paired t-test). There were no significant differences in tremor between trains with bursts and those without bursts (P = 0.24) or between trains that were irregular and those that were periodic (P = 0.35, paired t-test).

Fig. 5.

Model neuron responses to different temporal patterns of DBS. Responses for a single-model TC neuron during stimulation off (A), Regular (B), Uniform (C), Unipeak (D), Bimodal (E), Absence (F), and Presence (G) DBS are shown. Somatic and axonal transmembrane potentials (V_m) are illustrated along with rasters showing the times of action potentials in CER, CTX, RN, and TIN terminals. The times of harmaline-generated inputs to CER (Harm), Poisson inputs to CTX (Poiss), and DBS stimulus pulses are also indicated. Traces illustrate the responses during 1 s of stimulation. The time scale bar in A applies to all traces in the figure, whereas the amplitude scale bar refers to only the soma and axon traces in each panel. Somatic spikes and/or bursts occurred only during periods of time when there were pauses in both the stimulus train and the CER input to the thalamus. These events were only evident during stimulation with Unipeak, Bimodal, and Absence trains as well as in the stimulation off condition.

Fig. 6.

Responses of 10 model neurons to different temporal patterns of DBS. The times of action potentials for 10 of 50 TC neurons are shown as rasters during stimulation off (A) as well as during Regular (B), Uniform (C), Unipeak (D), Bimodal (E), Absence (F), and Presence (G) DBS. Rasters illustrate the times of action potentials in the distal axon of each TC neuron during 1 s of stimulation. The top 3 rows in each panel are the responses of regular spiking TC neurons, the next 2 rows are the response of random-spiking TC neurons, and the bottom 5 are bursting TC neurons. The time scale bar in A applies to all panels. These data are intended to provide an overview of the responses of the model neurons during the different stimulus conditions.

Fig. 7.

Average spike-train entropies of model neurons in response to different temporal patterns of DBS. A: average entropy of ISI distributions for model neuron responses across stimulation conditions. B: average entropy of log-transformed ISI distributions for model neuron responses across stimulation conditions. The entropy for the log-transformed ISI distributions was used to provide a direct comparison with the stimulus-train log-transformed IPI entropy. If the neurons responded faithfully to every stimulus pulse, the entropy would be the same for the log ISIs and log IPIs. Data are shown as means ± SE. Markers not containing the same letters are significantly different from each other [P < 0.05, post hoc comparisons with Fisher protected least significant difference (PLSD)]. Insets in A and B illustrate the correlation between the spike-train entropies for a given condition as a function of the mean log-transformed tremor power for the same condition across 8 subjects. C: median entropy of model log-transformed ISI distributions vs. the average entropy of the stimulus-train log-transformed IPI distributions. Dashed line represents a 1:1 correlation. Points for all conditions except Absence DBS fell very close to the 1:1 line.

Fig. 8.

Fraction of somatic V_m power in the burst-driver band. A: power in somatic V_m in the burst-driver band (5.8 ± 1 Hz) across stimulation conditions. Data are shown as means ± SE. Markers not containing the same letters are significantly different from one another (P < 0.05, post hoc comparisons with Fisher PLSD). The 2 insets illustrate the fraction of somatic V_m in the burst-driver band as a function of mean tremor across 8 subjects. The left inset includes all experimental conditions, and the right inset includes only the conditions with stimulation on. B: power in the burst-driver band of the cross-correlation between the smoothed axonal spike rates during a given condition and stimulation off. Data are shown as means ± SE. Markers not containing the same letters are significantly different from one another (P < 0.05, post hoc comparisons with Fisher PLSD). The inset illustrates the correlation between the axonal spike rate cross-correlations and the mean tremor in 8 subjects across conditions with stimulation on. C: difference between the somatic V_m power in the burst-driver band for each neuron during stimulation with a given characteristic [Power (with): pauses, bursts, or irregularity] and the power in the burst-driver band for each neuron during stimulation without a given characteristic [Power (without): no pause, no bursts, periodic], respectively. *P < 0.0001, Fisher PLSD.

Fig. 9.

Stimulation of cerebellar terminals exclusively is effective at eliminating somatic V_m burst-driver power. Somatic V_m burst-driver power during stimulation off and regular 185-Hz DBS (closed bars) along with somatic V_m burst-driver power during stimulation off and intracellular stimulation of cerebellar terminals only (CER only; open bars) are shown. Because of differences in the total somatic V_m power between 0 and 5,000 Hz during intracellular cerebellar and extracellular DBS, we compared the absolute value of power in the burst-driver band rather than the proportion of power. Data are shown as the means ± SE across the population of 50 TC neurons.

Fig. 10.

Response of M (a unitless time course of adenosine and/or acetylcholine in the synaptic cleft) to stimulation. A: time course of M in response to a single-stimulus pulse (arrowhead) follows an α-function. B: time course of M in response to a 10-s epoch of DBS at 10 and 185 Hz. In these cases, the α-function responses to individual stimulus pulses summate temporally and stabilize at different steady-state amplitudes (au = arbitrary units, unitless).

Fig. 11.

Comparison of responses of model and in vitro TC neurons. A: responses to 60-ms depolarizing pulses were similar to those recorded in in vitro thalamic slices under various levels of direct current (DC) polarization. (i): Reponses from thalamic neurons recorded from guinea pig slices in a hyperpolarized cell (left), a cell at rest potential (middle), and a depolarized cell (right; Jahnsen and Llinas 1984). (ii): Reponses of model thalamic neuron to a depolarizing pulse of 0.55 nA for 60 ms at hyperpolarized (left), rest (middle), and depolarized (right) potentials. B: model rebound responses to 45-ms hyperpolarizing pulses was similar to those of the same thalamic slice neurons. (i): Responses of in vitro neurons (Jahnsen and Llinas 1984). (ii): Responses of the model TC neuron. C: model responded to DC hyperpolarization with rhythmic bursting. (i): Responses of in vitro neurons (McCormick and Pape 1990). (ii): Responses of the model TC neuron.

Fig. 12.

Comparison of thalamic model activity with data recorded in human Vim. A: V_m recordings from model regular- (i), random- (ii), and burst-spiking (iii) neurons. B, (i): action potential raster recorded from Vim of human with essential tremor (ET; Hua and Lenz 2005). (ii): Action potential raster recorded from model burst-spiking neuron. C: firing rates in the Vim and ventral caudal (Vc) thalamus in subjects with ET (Ohara et al. 2007) along with the firing rates of the model Vim neurons (means ± SE = 23.4 ± 1.8 Hz). The human Vc data are shown to demonstrate that the internuclear difference is much larger than the difference between the model and human Vim. Model firing-rate estimates were averaged across all 50 neurons during the time period from 2 to 12 s with stimulation off.

Fig. 13.

Comparison of firing patterns in model and human thalamic neurons. A: mean normalized autopower computed for tremor-related neurons in human thalamus during postural tremor exhibits a strong peak at ∼5 Hz (Hua and Lenz 2005). B: mean normalized autopower computed for the population of 50 model neurons shows a similar peak at ∼5 Hz. Normalized autopower was averaged across all 50 neurons during the time period from 2 to 12 s with stimulation off. C: preburst ISIs in the Vim and Vc thalamus in subjects with ET (Ohara et al. 2007) along with the preburst ISIs of the model Vim neurons. The human Vc data are shown to demonstrate that the internuclear difference is much larger than the difference between the model and human Vim. Model preburst ISI estimates were made by combining all averaged across the 25 bursting neurons during the same time period (means ± SE = 173 ± 2 ms). D: poststimulus inhibition seen after 0.5 s of stimulation at 200 Hz observed in human thalamus (top; Dostrovsky and Lozano 2002) and in the model Vim neuron (bottom). Time scale bar applies to both traces. V_m (20 mV) scale bar applies only to the bottom trace, as the top trace is an extracellular recording. Thick gray bar represents stimulation on in both the human and model.

Fig. 14.

Effects of stimulus amplitude and frequency on V_m fluctuations at burst-driver frequency. A: average spike-train entropy across stimulus amplitudes during stimulation with Regular 185-Hz DBS. B: average spike-train entropy across stimulus frequencies during stimulation with Regular DBS at 7.5 V. C: somatic V_m power in burst-driver band (5.8 ± 1 Hz) across stimulus amplitudes during stimulation with Regular 185-Hz DBS. D: somatic V_m power in burst-driver band (5.8 ± 1 Hz) across stimulus frequencies during stimulation with Regular DBS at 7.5 V. Data are shown as means ± SE.