In models of electrical stimulation of the nervous system, the electric potential is typically calculated using the quasi-static approximation. The quasi-static approximation allows Maxwell's equations to be simplified by ignoring capacitive, inductive and wave propagation contributions to the potential. While this simplification has been validated for bioelectric sources, its application to rapid stimulation pulses, which contain more high-frequency power, may not be appropriate. We compared the potentials calculated using the quasi-static approximation with those calculated from the exact solution to the inhomogeneous Helmholtz equation. The mean absolute errors between the two potential calculations were limited to 5-13% for pulse widths commonly used for neural stimulation (25 micros-1 ms). We also quantified the excitation properties of extracellular point source stimulation of a myelinated nerve fiber model using potentials calculated from each method. Deviations between the strength-duration curves for potentials calculated using the quasi-static (sigma = 0.105 S m(-1)) and Helmholtz approaches ranged from 3 to 16%, with the minimal error occurring for 100 micros pulses. Differences in the threshold-distance curves for the two calculations ranged from 0 to 9%, for the same value of quasi-static conductivity. A sensitivity analysis of the material parameters revealed that the potential was much more strongly dependent on the conductivity than on the permittivity. These results indicate that for commonly used stimulus pulse parameters, the exact solution for the potential can be approximated by quasi-static simplifications only for appropriate values of conductivity.

Deep brain stimulation (DBS) of the basal ganglia can alleviate the motor symptoms of Parkinson's disease although the therapeutic mechanisms are unclear. We hypothesize that DBS relieves symptoms by minimizing pathologically disordered neuronal activity in the basal ganglia. In human participants with parkinsonism and clinically effective deep brain leads, regular (i.e., periodic) high-frequency stimulation was replaced with irregular (i.e., aperiodic) stimulation at the same mean frequency (130 Hz). Bradykinesia, a symptomatic slowness of movement, was quantified via an objective finger tapping protocol in the absence and presence of regular and irregular DBS. Regular DBS relieved bradykinesia more effectively than irregular DBS. A computational model of the relevant neural structures revealed that output from the globus pallidus internus was more disordered and thalamic neurons made more transmission errors in the parkinsonian condition compared with the healthy condition. Clinically therapeutic, regular DBS reduced firing pattern disorder in the computational basal ganglia and minimized model thalamic transmission errors, consistent with symptom alleviation by clinical DBS. However, nontherapeutic, irregular DBS neither reduced disorder in the computational basal ganglia nor lowered model thalamic transmission errors. Thus we show that clinically useful DBS alleviates motor symptoms by regularizing basal ganglia activity and thereby improving thalamic relay fidelity. This work demonstrates that high-frequency stimulation alone is insufficient to alleviate motor symptoms: DBS must be highly regular. Descriptive models of pathophysiology that ignore the fine temporal resolution of neuronal spiking in favor of average neural activity cannot explain the mechanisms of DBS-induced symptom alleviation.

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.

Summary: Deep brain stimulation (DBS) is an established treatment for symptoms in movement disorders and is under investigation for symptom management in persons with psychiatric disorders and epilepsy. Nevertheless, there remains disagreement regarding the physiological mechanisms responsible for the actions of DBS, and this lack of understanding impedes both the design of DBS systems for treating novel diseases and the effective tuning of current DBS systems. Currently available data indicate that effective DBS overrides pathological bursts, low frequency oscillations, synchronization, and disrupted firing patterns present in movement disorders, and replaces them with more regularized firing. Although it is likely that the specific mechanism(s) by which DBS exerts its effects varies between diseases and target nuclei, the overriding of pathological activity appears to be ubiquitous. This review provides an overview of changes in motor symptoms with changes in DBS frequency and highlights parallels between the changes in motor symptoms and the changes in cellular activity that appear to underlie the motor symptoms.

The frequency of stimulation is one of the primary factors determining the effectiveness of deep brain stimulation (DBS) in relieving tremor. DBS efficacy, however, may depend not only on the average frequency of stimulation, but also on the temporal pattern of stimulation. We conducted intraoperative measurements of the effect of temporally irregular DBS (nonconstant interpulse intervals) on tremor. As the coefficient of variation of irregular high frequency DBS trains increased, they became less effective at reducing tremor (mixed effects regression model, P<0.04).These data provide evidence that the effects of DBS are dependent not only on the average frequency of DBS, but also on the regularity of the temporal spacing of DBS pulses.

Birdno MJ, Cooper SE, Rezai AR, Grill WM. Pulse-to-pulse changes in the frequency of deep brain stimulation affect tremor and modeled neuronal activity. J Neurophysiol 98: [1675][1676][1677][1678][1679][1680][1681][1682][1683][1684] 2007. First published July 18, 2007; doi:10.1152/jn.00547.2007. The effectiveness of deep brain stimulation (DBS) in relieving the symptoms of movement disorders is dependent on the average frequency of stimulation. However, no one has yet examined whether the effectiveness of DBS in relieving tremor is dependent on the pulse-to-pulse (instantaneous) frequency of DBS. We examined the effects of pairedpulse thalamic DBS on tremor in subjects with essential tremor and on the firing of model neurons in a biophysically based computational model of DBS. 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 pulse intervals. Similar correlations were observed in the firing patterns of model neurons: increasing the difference between the intrapair and interpair intervals rendered model neurons more likely to fire synchronous bursts, more likely to fire irregularly, and less likely to entrain to the stimulus. The tremor responses provide evidence that the pulse-to-pulse frequency of DBS, not just its average rate, plays an important role in DBS function. Modeling results also suggest that effective DBS overrides oscillatory pathological activity and replaces it with more regularized neuronal firing patterns. I N T R O D U C T I O NChronic high-frequency stimulation of the brain, or deep brain stimulation (DBS), is an effective treatment for motor symptoms in Parkinson's disease, dystonia, and essential tremor (Benabid et al. 1991;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 Ͼ90 Hz; conversely, low-frequency DBS (Ͻ50 Hz) often worsens symptoms (Benabid et al. 1991;Kuncel et ...

Objective The effectiveness of deep brain stimulation (DBS) depends on both the frequency and the temporal pattern of stimulation. We quantified responses to cycling DBS with constant frequency to determine if there was a critical on and/or off time for alleviating tremor. Methods We measured postural tremor in 10 subjects with thalamic DBS and quantified neuronal entropy in a network model of Vim thalamic DBS. We tested 12 combinations of cycling on/off times that maintained the same average frequenc7y of 125 Hz, four constant frequency settings, and baseline. Results Tremor and neural firing pattern entropy decreased as the percent on time increased from 50% to 100%. Cycling with stimulation on for at least 60% of the time was as effective as regular stimulation. All cycling settings reduced the firing pattern entropy of model neurons from the no stimulation condition by regularizing pathological firing patterns, either through synaptically-mediated inhibition or axon excitation. Conclusions These results indicate that pauses present in cycling stimulation decreased its effectiveness in suppressing tremor, and that changes in the amount of tremor suppression were strongly correlated with changes in the firing pattern entropy of model neurons. Significance Cycling stimulation may reduce power consumption during clinical DBS, and thereby increase the battery life of the implanted pulse generator.

Thalamic deep brain stimulation (DBS) is an effective treatment for tremor, but the mechanisms of action remain unclear. Previous studies of human thalamic neurons to noted transient rebound bursting activity followed by prolonged inhibition after cessation of high frequency extracellular stimulation, and the present study sought to identify the mechanisms underlying this response. Recordings from 13 thalamic neurons exhibiting low threshold spike (LTS) bursting to brief periods of extracellular stimulation were made during surgeries to implant DBS leads in 6 subjects with Parkinson's disease. The response immediately after cessation of stimulation included a short epoch of burst activity, followed by a prolonged period of silence before a return to LTS bursting. A computational model of a population of thalamocortical relay neurons and presynaptic axons terminating on the neurons was used to identify cellular mechanisms of the observed responses. The model included the actions of neuromodulators through inhibition of a non-pertussis toxin sensitive K+ current (IKL), activation of a pertussis toxin sensitive K+ current (IKG), and a shift in the activation curve of the hyperpolarization-activated cation current (Ih). The model replicated well the measured responses, and the prolonged inhibition was associated most strongly with changes in IKG while modulation of IKL or Ih had minimal effects on post-stimulus inhibition suggesting that neuromodulators released in response to high frequency stimulation are responsible for mediating the post-stimulation bursting and subsequent long duration silence of thalamic neurons. The modeling also indicated that the axons of the model neurons responded robustly to suprathreshold stimulation despite the inhibitory effects on the soma. The findings suggest that during DBS the axons of thalamocortical neurons are activated while the cell bodies are inhibited thus blocking the transmission of pathological signals through the network and replacing them with high frequency regular firing.