Submyelin potassium accumulation may functionally block subsets of local axons during deep brain stimulation: a modeling study

Activation and depression of neural and hemodynamic responses induced by the intracortical microstimulation and visual stimulation in the mouse visual cortex

Objective. Intracortical microstimulation (ICMS) can be an effective method for restoring sensory perception in contemporary brain-machine interfaces. However, the mechanisms underlying better control of neuronal responses remain poorly understood, as well as the relationship between neuronal activity and other concomitant phenomena occurring around the stimulation site.Approach. Different microstimulation frequencies were investigatedin vivoon Thy1-GCaMP6s mice using widefield and two-photon imaging to evaluate the evoked excitatory neural responses across multiple spatial scales as well as the induced hemodynamic responses. Specifically, we quantified stimulation-induced neuronal activation and depression in the mouse visual cortex and measured hemodynamic oxyhemoglobin and deoxyhemoglobin signals using mesoscopic-scale widefield imaging.Main results. Our calcium imaging findings revealed a preference for lower-frequency stimulation in driving stronger neuronal activation. A depressive response following the neural activation preferred a slightly higher frequency stimulation compared to the activation. Hemodynamic signals exhibited a comparable spatial spread to neural calcium signals. Oxyhemoglobin concentration around the stimulation site remained elevated during the post-activation (depression) period. Somatic and neuropil calcium responses measured by two-photon microscopy showed similar dependence on stimulation parameters, although the magnitudes measured in soma was greater than in neuropil. Furthermore, higher-frequency stimulation induced a more pronounced activation in soma compared to neuropil, while depression was predominantly induced in soma irrespective of stimulation frequencies.Significance. These results suggest that the mechanism underlying depression differs from activation, requiring ample oxygen supply, and affecting neurons. Our findings provide a novel understanding of evoked excitatory neuronal activity induced by ICMS and offer insights into neuro-devices that utilize both activation and depression phenomena to achieve desired neural responses.

Dynamics of neuronal firing modulated by high-frequency electrical pulse stimulations at axons in rat hippocampus

Objective. The development of electrical pulse stimulations in brain, including deep brain stimulation, is promising for treating various brain diseases. However, the mechanisms of brain stimulations are not yet fully understood. Previous studies have shown that the commonly used high-frequency stimulation (HFS) can increase the firing of neurons and modulate the pattern of neuronal firing. Because the generation of neuronal firing in brain is a nonlinear process, investigating the characteristics of nonlinear dynamics induced by HFS could be helpful to reveal more mechanisms of brain stimulations. The aim of present study is to investigate the fractal properties in the neuronal firing generated by HFS.Approach. HFS pulse sequences with a constant frequency 100 Hz were applied in the afferent fiber tracts of rat hippocampal CA1 region. Unit spikes of both the pyramidal cells and the interneurons in the downstream area of stimulations were recorded. Two fractal indexes-the Fano factor and Hurst exponent were calculated to evaluate the changes of long-range temporal correlations (LRTCs), a typical characteristic of fractal process, in spike sequences of neuronal firing.Mainresults. Neuronal firing at both baseline and during HFS exhibited LRTCs over multiple time scales. In addition, the LRTCs significantly increased during HFS, which was confirmed by simulation data of both randomly shuffled sequences and surrogate sequences.Conclusion. The purely periodic stimulation of HFS pulses, a non-fractal process without LRTCs, can increase rather than decrease the LRTCs in neuronal firing.Significance. The finding provides new nonlinear mechanisms of brain stimulation and suggests that LRTCs could be a new biomarker to evaluate the nonlinear effects of HFS.

Estimation of the transmission delays in the basal ganglia of the macaque monkey and subsequent predictions about oscillatory activity under dopamine depletion

The timescales of the dynamics of a system depend on the combination of the timescales of its components and of its transmission delays between components. Here, we combine experimental stimulation data from 10 studies in macaque monkeys that reveal the timing of excitatory and inhibitory events in the basal ganglia circuit, to estimate its set of transmission delays. In doing so, we reveal possible inconsistencies in the existing data, calling for replications, and we propose two possible sets of transmission delays. We then integrate these delays in a model of the primate basal ganglia that does not rely on direct and indirect pathways' segregation and show that extrastriatal dopaminergic depletion in the external part of the globus pallidus and in the subthalamic nucleus is sufficient to generate β-band oscillations (in the high part, 20-35 Hz, of the band). More specifically, we show that D2 and D5 dopamine receptors in these nuclei play opposing roles in the emergence of these oscillations, thereby explaining how completely deactivating D5 receptors in the subthalamic nucleus can, paradoxically, cancel oscillations.

Activation and depression of neural and hemodynamic responses induced by the intracortical microstimulation and visual stimulation in the mouse visual cortex

Objective . Intracortical microstimulation can be an effective method for restoring sensory perception in contemporary brain-machine interfaces. However, the mechanisms underlying better control of neuronal responses remain poorly understood, as well as the relationship between neuronal activity and other concomitant phenomena occurring around the stimulation site. Approach . Different microstimulation frequencies were investigated in vivo on Thy1-GCaMP6s mice using widefield and two-photon imaging to evaluate the evoked excitatory neural responses across multiple spatial scales as well as the induced hemodynamic responses. Specifically, we quantified stimulation-induced neuronal activation and depression in the mouse visual cortex and measured hemodynamic oxyhemoglobin and deoxyhemoglobin signals using mesoscopic-scale widefield imaging. Main results . Our calcium imaging findings revealed a preference for lower-frequency stimulation in driving stronger neuronal activation. A depressive response following the neural activation preferred a slightly higher frequency stimulation compared to the activation. Hemodynamic signals exhibited a comparable spatial spread to neural calcium signals. Oxyhemoglobin concentration around the stimulation site remained elevated during the post-activation (depression) period. Somatic and neuropil calcium responses measured by two-photon microscopy showed similar dependence on stimulation parameters, although the magnitudes measured in soma was greater than in neuropil. Furthermore, higher-frequency stimulation induced a more pronounced activation in soma compared to neuropil, while depression was predominantly induced in soma irrespective of stimulation frequencies. Significance . These results suggest that the mechanism underlying depression differs from activation, requiring ample oxygen supply, and affecting neurons. Our findings provide a novel understanding of evoked excitatory neuronal activity induced by intracortical microstimulation and offer insights into neuro-devices that utilize both activation and depression phenomena to achieve desired neural responses.

Interactions between cathodic- and anodic-pulses during high-frequency stimulations with the monophasic-pulses alternating in polarity at axons-experiment and simulation studies

Background. Electrical neuromodulation therapies commonly utilize high-frequency stimulations (HFS) of biphasic-pulses to treat neurological disorders. The biphasic pulse consists of a leading cathodic-phase to activate neurons and a lagging anodic-phase to balance electrical charges. Because both monophasic cathodic- and anodic-pulses can depolarize neuronal membranes, splitting biphasic-pulses into alternate cathodic- and anodic-pulses could be a feasible strategy to improve stimulation efficiency.Objective. We speculated that neurons in the volume initially activated by both polarity pulses could change to be activated only by anodic-pulses during sustained HFS of alternate monophasic-pulses. To verify the hypothesis, we investigated the interactions of the monophasic pulses during HFS and revealed possible underlying mechanisms.Approach. Different types of pulse stimulations were applied at the alvear fibers (i.e. the axons of CA1 pyramidal neurons) to antidromically activate the neuronal cell bodies in the hippocampal CA1 region of anesthetized ratsin-vivo. Sequences of antidromic HFS (A-HFS) were applied with alternate monophasic-pulses or biphasic-pulses. The pulse frequency in the A-HFS sequences was 50 or 100 Hz. The A-HFS duration was 120 s. The amplitude of antidromically-evoked population spike was measured to evaluate the neuronal firing induced by each pulse. A computational model of axon was used to explore the possible mechanisms of neuronal modulations. The changes of model variables during sustained A-HFS were analyzed.Main results. In rat experiments, with a same pulse intensity, the activation volume of a cathodic-pulse was greater than that of an anodic-pulse. In paired-pulse tests, a preceding cathodic-pulse was able to prevent a following anodic-pulse from activating neurons due to refractory period. This indicated that the activation volume of a cathodic-pulse covered that of an anodic-pulse. However, during sustained A-HFS of alternate monophasic-pulses, the anodic-pulses were able to prevail over the cathodic-pulses in activating neurons in the overlapped activation volume. Model simulation results show the mechanisms of the activation failures of cathodic-pulses. They include the excessive membrane depolarization caused by an accumulation of potassium ions, the obstacle of hyperpolarization in the conduction pathway and the interactions from anodic-pulses.Significance. The study firstly showed the domination of anodic-pulses over cathodic-pulses in their competitions to activate neurons during sustained HFS. The finding provides new clues for designing HFS paradigms to improve the efficiency of neuromodulation therapies.

The Therapeutic Frequency Profile of Subthalamic Nucleus Deep Brain Stimulation in Rats Is Shaped by Antidromic Spike Failure

The therapeutic mechanisms of subthalamic nucleus (STN) deep brain stimulation (DBS) may depend on antidromic activation of cortex via the hyperdirect pathway. However, hyperdirect pathway neurons cannot reliably follow high-stimulation frequencies, and the spike failure rate appears to correlate with symptom relief as a function of stimulation frequency. We hypothesized that antidromic spike failure contributes to the cortical desynchronization caused by DBS. We measured in vivo evoked cortical activity in female Sprague Dawley rats and developed a computational model of cortical activation from STN DBS. We modeled stochastic antidromic spike failure to determine how spike failure affected the desynchronization of pathophysiological oscillatory activity in cortex. We found that high-frequency STN DBS desynchronized pathologic oscillations via the masking of intrinsic spiking through a combination of spike collision, refractoriness, and synaptic depletion. Antidromic spike failure shaped the parabolic relationship between DBS frequency and cortical desynchronization, with maximum desynchronization at ∼130 Hz. These findings reveal that antidromic spike failure plays a critical role in mediating the dependency of symptom relief on stimulation frequency.SIGNIFICANCE STATEMENT Deep brain stimulation (DBS) is a highly effective neuromodulation therapy, yet it remains uncertain why conventionally used stimulation frequencies (e.g., ∼130 Hz) are optimal. In this study, we demonstrate a potential explanation for the stimulation frequency dependency of DBS through a combination of in vivo experimental measurements and computational modeling. We show that high-frequency stimulation can desynchronize pathologic firing patterns in populations of neurons by inducing an informational lesion. However, sporadic spike failure at these high frequencies limits the efficacy of the informational lesion, yielding a parabolic profile with optimal effects at ∼130 Hz. This work provides a potential explanation for the therapeutic mechanism of DBS, and highlights the importance of considering spike failure in mechanistic models of DBS.

Mechanisms Underlying Poststimulation Block Induced by High-Frequency Biphasic Stimulation

OBJECTIVE

To reveal the possible mechanisms underlying poststimulation block induced by high-frequency biphasic stimulation (HFBS).

MATERIALS AND METHODS

A new axonal conduction model is developed for unmyelinated axons. This new model is different from the classical axonal conduction model by including both ion concentrations and membrane ion pumps to allow analysis of axonal responses to long-duration stimulation. Using the new model, the post-HFBS block phenomenon reported in animal studies is simulated and analyzed for a wide range of stimulation frequencies (100 Hz-10 kHz).

RESULTS

HFBS can significantly change the Na+ and K+ concentrations inside and outside the axon to produce a post-HFBS block of either short-duration (<500 msec) or long-duration (>3 sec) depending on the duration of HFBS. The short-duration block is due to the fast recovery of the Na+ and K+ concentrations outside the axon in periaxonal space by diffusion of ions into and from the large extracellular space, while the long-duration block is due to the slow restoration of the normal Na+ concentration inside the axon by membrane ion pumps. The 100 Hz HFBS requires the minimal electrical energy to achieve the post-HFBS block, while the 10 kHz stimulation is the least effective frequency requiring high intensity and long duration to achieve the block.

CONCLUSION

This study reveals two possible ionic mechanisms underlying post-HFBS block of axonal conduction. Understanding these mechanisms is important for improving clinical applications of HFBS block and for developing new nerve block methods employing HFBS.

Effects on heart rate from direct current block of the stimulated rat vagus nerve

Objective.Although electrical vagus nerve stimulation has been shown to augment parasympathetic control of the heart, the effects of electrical conduction block have been less rigorously characterized. Previous experiments have demonstrated that direct current (DC) nerve block can be applied safely and effectively in the autonomic system, but additional information about the system dynamics need to be characterized to successfully deploy DC nerve block to clinical practice.Approach.The dynamics of the heart rate (HR) from DC nerve block of the vagus nerve were measured by stimulating the vagus nerve to lower the HR, and then applying DC block to restore normal rate. DC block achieved rapid, complete block, as well as partial block at lower amplitudes.Main Results. Complete block was also achieved using lower amplitudes, but with a slower induction time. The time for DC to induce complete block was significantly predicted by the amplitude; specifically, the amplitude expressed as a percentage of the current required for a rapid, 60 s induction time. Recovery times after the cessation of DC block could occur both instantly, and after a significant delay. Both blocking duration and injected charge were significant in predicting the delay in recovery to normal conduction.Significance. While these data show that broad features such as induction and recovery can be described well by the DC parameters, more precise features of the HR, such as the exact path of the induction and recoveries, are still undefined. These findings show promise for control of the cardiac autonomic nervous system, with potential to expand to the sympathetic inputs as well.

Adding a single pulse into high-frequency pulse stimulations can substantially alter the following episode of neuronal firing in rat hippocampus

Background. High-frequency stimulation (HFS) sequences of electrical pulses are commonly utilized in many types of neuromodulation therapies. The temporal pattern of pulse sequences characterized by varying inter-pulse intervals (IPI) has emerged as an adjustable dimension to generate diverse effects of stimulations to meet the needs for developing the therapies.Objective:To explore the hypothesis that a simple manipulation of IPI by inserting a pulse in HFS with a constant IPI can substantially change the neuronal responses.Approach. Antidromic HFS (A-HFS) and orthodromic HFS (O-HFS) sequences were respectively applied at the alveus (the efferent axons) and the Schaffer collaterals (the afferent axons) of hippocampal CA1 region in anesthetized ratsin-vivo. The HFS sequences lasted 120 s with a pulse frequency of 100 Hz and an IPI of 10 ms. In the late steady period (60-120 s) of the HFS, additional pulses were inserted into the original pulse sequences to investigate the alterations of neuronal responses to the changes in IPI. The amplitudes and latencies of antidromic/orthodromic population spikes (APS/OPS) evoked by pulses were measured to evaluate the alterations of the evoked firing of CA1 pyramidal neurons caused by the pulse insertions.Main Results. During the steady period of A-HFS at efferent axons, the evoked APSs were suppressed due to intermittent axonal block. Under this situation, inserting a pulse to shorten an IPI was able to redistribute the following neuronal firing thereby generating an episode of oscillation in the evoked APS sequence including APSs with significantly increased and decreased amplitudes. Also, during the steady period of O-HFS without obvious OPS, a pulse insertion was able to generate a large OPS, indicating a synchronized firing of a large population of post-synaptic neurons induced by a putative redistribution of activations at the afferent axons under O-HFS.Significance. This study firstly showed that under the situation of HFS-induced axonal block, changing an IPI by a single-pulse insertion can substantially redistribute the evoked neuronal responses to increase synchronized firing of neuronal populations during both antidromic and O-HFS with a constant IPI originally. The finding provides a potential way to enhance the HFS action on neuronal networks without losing some other functions of HFS such as generating axonal block.

HFAC Dose Repetition and Accumulation Leads to Progressively Longer Block Carryover Effect in Rat Sciatic Nerve

This paper describes high-frequency nerve block experiments carried out on rat sciatic nerves to measure the speed of recovery of A fibres from block carryover. Block carryover is the process by which nerve excitability remains suppressed temporarily after High Frequency Alternative (HFAC) block is turned off following its application. In this series of experiments 5 rat sciatic nerves were extracted and prepared for ex-vivo stimulation and recording in a specially designed perfusion chamber. For each nerve repeated HFAC block and concurrent stimulation trials were carried out to observe block carryover after signal shutoff. The nerve was allowed to recover fully between each trial. Time to recovery from block was measured by monitoring for when relative nerve activity returned to within 90% of baseline levels measured at the start of each trial. HFAC block carryover duration was found to be dependent on accumulated dose by statistical test for two different HFAC durations. The carryover property of HFAC block on A fibres could enable selective stimulation of autonomic nerve fibres such as C fibres for the duration of carryover. Block carryover is particularly relevant to potential chronic clinical applications of block as it reduces power requirements for stimulation to provide the blocking effect. This work characterizes this process toward the creation of a model describing its behavior.

The cortical evoked potential corresponds with deep brain stimulation efficacy in rats

Deep brain stimulation (DBS) of the subthalamic nucleus (STN) antidromically activates the motor cortex (M1), and this cortical activation appears to play a role in the treatment of hypokinetic motor behaviors (Gradinaru V, Mogri M, Thompson KR, Henderson JM, Deisseroth K. Science 324: 354-359, 2009; Yu C, Cassar IR, Sambangi J, Grill WM. J Neurosci 40: 4323-4334, 2020). The synchronous antidromic activation takes the form of a short-latency cortical evoked potential (cEP) in electrocorticography (ECoG) recordings of M1. We assessed the utility of the cEP as a biomarker for STN DBS in unilateral 6-hydroxydopamine-lesioned female Sprague Dawley rats, with stimulating electrodes implanted in the STN and the ECoG recorded above M1. We quantified the correlations of the cEP magnitude and latency with changes in motor behavior from DBS and compared them to the correlation between motor behaviors and several commonly used spectral-based biomarkers. The cEP features correlated strongly with motor behaviors and were highly consistent across animals, whereas the spectral biomarkers correlated weakly with motor behaviors and were highly variable across animals. The cEP may thus be a useful biomarker for assessing the therapeutic efficacy of DBS parameters, as its features strongly correlate with motor behavior, it is consistent across time and subjects, it can be recorded under anesthesia, and it is simple to quantify with a large signal-to-noise ratio, enabling rapid, real-time evaluation. Additionally, our work provides further evidence that antidromic cortical activation mediates changes in motor behavior from STN DBS and that the dependence of DBS efficacy on stimulation frequency may be related to antidromic spike failure.NEW & NOTEWORTHY We characterize a new potential biomarker for deep brain stimulation (DBS), the cortical evoked potential (cEP), and demonstrate that it exhibits a robust correlation with motor behaviors as a function of stimulation frequency. The cEP may thus be a useful clinical biomarker for changes in motor behavior. This work also provides insight into the cortical mechanisms of DBS, suggesting that motor behaviors are strongly affected by the rate of antidromic spike failure during DBS.

Neuromodulation using ultra low frequency current waveform reversibly blocks axonal conduction and chronic pain

Chronic pain remains a leading cause of disability worldwide, and there is still a clinical reliance on opioids despite the medical side effects associated with their use and societal impacts associated with their abuse. An alternative approach is the use of electrical neuromodulation to produce analgesia. Direct current can block action potential propagation but leads to tissue damage if maintained. We have developed a form of ultra low frequency (ULF) biphasic current and studied its effects. In anesthetized rats, this waveform produced a rapidly developing and completely reversible conduction block in >85% of spinal sensory nerve fibers excited by peripheral stimulation. Sustained ULF currents at lower amplitudes led to a slower onset but reversible conduction block. Similar changes were seen in an animal model of neuropathic pain, where ULF waveforms blocked sensory neuron ectopic activity, known to be an important driver of clinical neuropathic pain. Using a computational model, we showed that prolonged ULF currents could induce accumulation of extracellular potassium, accounting for the slowly developing block observed in rats. Last, we tested the analgesic effects of epidural ULF currents in 20 subjects with chronic leg and back pain. Pain ratings improved by 90% after 2 weeks. One week after explanting the electrodes, pain ratings reverted to 72% of pretreatment screening value. We conclude that epidural spinal ULF neuromodulation represents a promising therapy for treating chronic pain.

A tridomain model for potassium clearance in optic nerve of Necturus

Complex fluids flow in complex ways in complex structures. Transport of water and various organic and inorganic molecules in the central nervous system are important in a wide range of biological and medical processes. However, the exact driving mechanisms are often not known. In this work, we investigate flows induced by action potentials in an optic nerve as a prototype of the central nervous system. Different from traditional fluid dynamics problems, flows in biological tissues such as the central nervous system are coupled with ion transport. They are driven by osmosis created by concentration gradient of ionic solutions, which in turn influence the transport of ions. Our mathematical model is based on the known structural and biophysical properties of the experimental system used by the Harvard group Orkand et al. Asymptotic analysis and numerical computation show the significant role of water in convective ion transport. The full model (including water) and the electrodiffusion model (excluding water) are compared in detail to reveal an interesting interplay between water and ion transport. In the full model, convection due to water flow dominates inside the glial domain. This water flow in the glia contributes significantly to the spatial buffering of potassium in the extracellular space. Convection in the extracellular domain does not contribute significantly to spatial buffering. Electrodiffusion is the dominant mechanism for flows confined to the extracellular domain.

Adjust Neuronal Reactions to Pulses of High-Frequency Stimulation with Designed Inter-Pulse-Intervals in Rat Hippocampus In Vivo

Sequences of electrical pulses have been applied in the brain to treat certain disorders. In recent years, altering inter-pulse-interval (IPI) regularly or irregularly in real time has emerged as a promising way to modulate the stimulation effects. However, algorithms to design IPI sequences are lacking. This study proposed a novel strategy to design pulse sequences with varying IPI based on immediate neuronal reactions. Firstly, to establish the correlationship between the neuronal reactions with varying IPIs, high-frequency stimulations with varying IPI in the range of 5–10 ms were applied at the alveus of the hippocampal CA1 region of anesthetized rats in vivo. Antidromically-evoked population spikes (APS) following each IPI were recorded and used as a biomarker to evaluate neuronal reactions to each pulse. A linear mapping model was established to estimate the varied APS amplitudes by the two preceding IPIs. Secondly, the mapping model was used to derive an algorithm for designing an IPI sequence that would be applied for generating a desired neuronal reaction pre-defined by a particular APS distribution. Finally, examples of stimulations with different IPI sequences designed by the algorithm were verified by rat experiments. The results showed that the designed IPI sequences were able to reproduce the desired APS responses of different distributions in the hippocampal stimulations. The novel algorithm of IPI design provides a potential way to obtain various stimulation effects for brain stimulation therapies.

Cortical hemodynamic mapping of subthalamic nucleus deep brain stimulation in Parkinsonian patients, using high-density functional near-infrared spectroscopy

Subthalamic nucleus deep brain stimulation (STN-DBS) is an effective treatment for idiopathic Parkinson's disease. Despite recent progress, the mechanisms responsible for the technique's effectiveness have yet to be fully elucidated. The purpose of the present study was to gain new insights into the interactions between STN-DBS and cortical network activity. We therefore combined high-resolution functional near-infrared spectroscopy with low-resolution electroencephalography in seven Parkinsonian patients on STN-DBS, and measured cortical haemodynamic changes at rest and during hand movement in the presence and absence of stimulation (the ON-stim and OFF-stim conditions, respectively) in the off-drug condition. The relative changes in oxyhaemoglobin [HbO], deoxyhaemoglobin [HbR], and total haemoglobin [HbT] levels were analyzed continuously. At rest, the [HbO], [HbR], and [HbT] over the bilateral sensorimotor (SM), premotor (PM) and dorsolateral prefrontal (DLPF) cortices decreased steadily throughout the duration of stimulation, relative to the OFF-stim condition. During hand movement in the OFF-stim condition, [HbO] increased and [HbR] decreased concomitantly over the contralateral SM cortex (as a result of neurovascular coupling), and [HbO], [HbR], and [HbT] increased concomitantly in the dorsolateral prefrontal cortex (DLPFC)-suggesting an increase in blood volume in this brain area. During hand movement with STN-DBS, the increase in [HbO] was over the contralateral SM and PM cortices was significantly lower than in the OFF-stim condition, as was the decrease in [HbO] and [HbT] in the DLPFC. Our results indicate that STN-DBS is associated with a reduction in blood volume over the SM, PM and DLPF cortices, regardless of whether or not the patient is performing a task. This particular effect on cortical networks might explain not only STN-DBS's clinical effectiveness but also some of the associated adverse effects.

The Effect of Spinal Cord Stimulation Frequency on the Neural Response and Perceived Sensation in Patients With Chronic Pain

Background

The effect of spinal cord stimulation (SCS) amplitude on the activation of dorsal column fibres has been widely studied through the recording of Evoked Compound Action Potentials (ECAPs), the sum of all action potentials elicited by an electrical stimulus applied to the fibres. ECAP amplitude grows linearly with stimulus current after a threshold, and a larger ECAP results in a stronger stimulus sensation for patients. This study investigates the effect of stimulus frequency on both the ECAP amplitude as well as the perceived stimulus sensation in patients undergoing SCS therapy for chronic back and/or leg pain.

Methods

Patients suffering with chronic neuropathic lower-back and/or lower-limb pain undergoing an epidural SCS trial were recruited. Patients were implanted according to standard practice, having two 8-contact leads (8 mm inter-electrode spacing) which overlapped 2–4 contacts around the T9/T10 interspace. Both lead together thus spanning about three vertebral levels. Neurophysiological recordings were taken during the patient’s trial phase at two routine follow-ups using a custom external stimulator capable of recording ECAPs in real-time from all non-stimulating contacts. Stimulation was performed at various vertebral levels, varying the frequency (ranging from 2 to 455 Hz) while all other stimulating variables were kept constant. During the experiments subjects were asked to rate the stimulation-induced sensation (paraesthesia) on a scale from 0 to 10.

Results

Frequency response curves showed an inverse relationship between stimulation sensation strength and ECAP amplitude, with higher frequencies generating smaller ECAPs but stronger stimulation-induced paraesthesia (at constant stimulation amplitude). Both relationships followed logarithmic trends against stimulus frequency meaning that the effects on ECAP amplitude and sensation are larger for smaller frequencies.

Conclusion

This work supports the hypothesis that SCS-induced paraesthesia is conveyed through both frequency coding and population coding, fitting known psychophysics of tactile sensory information processing. The inverse relationship between ECAP amplitude and sensation for increasing frequencies at fixed stimulus amplitude questions common assumptions of monotonic relationships between ECAP amplitude and sensation strength.

The Appearance Order of Varying Intervals Introduces Extra Modulation Effects on Neuronal Firing Through Non-linear Dynamics of Sodium Channels During High-Frequency Stimulations

Electrical pulse stimulation in the brain has shown success in treating several brain disorders with constant pulse frequency or constant inter-pulse interval (IPI). Varying IPI may offer a variety of novel stimulation paradigms and may extend the clinical applications. However, a lack of understanding of neuronal responses to varying IPI limits its informed applications. In this study, to investigate the effects of varying IPI, we performed both rat experiments and computational modeling by applying high-frequency stimulation (HFS) to efferent axon fibers of hippocampal pyramidal cells. Antidromically evoked population spikes (PSs) were used to evaluate the neuronal responses to pulse stimulations with different IPI patterns including constant IPI, gradually varying IPI, and randomly varying IPI. All the varying IPI sequences were uniformly distributed in the same interval range of 10 to 5 ms (i.e., 100 to 200 Hz). The experimental results showed that the mean correlation coefficient of PS amplitudes to the lengths of preceding IPI during HFS with random IPI (0.72 ± 0.04, n = 7 rats) was significantly smaller than the corresponding correlation coefficient during HFS with gradual IPI (0.92 ± 0.03, n = 7 rats, P < 0.001, t-test). The PS amplitudes induced by the random IPI covered a wider range, over twice as much as that induced by the gradual IPI, indicating additional effects induced by merely changing the appearance order of IPI. The computational modeling reproduced these experimental results and provided insights into these modulatory effects through the mechanism of non-linear dynamics of sodium channels and potassium accumulation in the narrow peri-axonal space. The simulation results showed that the HFS-induced increase of extracellular potassium ([K⁺] _o ) elevated the membrane potential of axons, delayed the recovery course of sodium channels that were repeatedly activated and inactivated during HFS, and resulted in intermittent neuronal firing. Because of non-linear membrane dynamics, random IPI recruited more neurons to fire together following specific sub-sequences of pulses than gradual IPI, thereby widening the range of PS amplitudes. In conclusion, the study demonstrated novel HFS effects of neuronal modulation induced by merely changing the appearance order of the same group of IPI of pulses, which may inform the development of new stimulation patterns to meet different demands for treating various brain diseases.

Myelinated axon physiology and regulation of neural circuit function

The study of structural and functional plasticity in the central nervous system (CNS) to date has focused primarily on that of neurons and synapses. However, more recent studies implicate glial cells as key regulators of neural circuit function. Among these, the myelinating glia of the CNS, oligodendrocytes, have been shown to be responsive to extrinsic signals including neuronal activity, and in turn, tune neurophysiological function. Due to the fact that myelin fundamentally alters the conduction properties of axons, much attention has focused on how dynamic regulation of myelination might represent a form of functional plasticity. Here, we highlight recent research that indicates that it is not only myelin, but essentially all the function-regulating components of the myelinated axon that are responsive to neuronal activity. For example, the axon initial segment, nodes of Ranvier, heminodes, axonal termini, and the morphology of the axon itself all exhibit the potential to respond to neuronal activity, and in so doing might underpin specific functional outputs. We also highlight emerging evidence that the myelin sheath itself has a rich physiology capable of influencing axonal physiology. We suggest that to fully understand nervous system plasticity we need to consider the fact that myelinated axon is an integrated functional unit and adaptations that influence the entire functional unit are likely to underpin modifications to neural circuit function.

Simulation Study of Intermittent Responses of Neuronal Populations to Axonal High-Frequency Stimulation

Deep brain stimulation (DBS) have shown a promising future for treating various brain disorders. Studies have indicated that the high frequency stimulation (HFS) used in DBS could cause a partial block in axons thereby attenuating the responses of axon fibers to the pulses of HFS. The attenuated response of axons might play a desynchronization role in modulating activity of neuronal populations. To investigate the detail behavior of individual axons under HFS, we created a computational model of neuronal populations including 1250 neurons. Each neuron consisted of a myelinated axon, an axonal initial segment, a soma and dendrites. A 10-s HFS sequence with 100 Hz pulses was applied to the axon layer by a bipolar stimulation electrode. The membrane potentials and the extracellular potassium concentration [K⁺]_o at axons and at somata during the stimulation were investigated. The results showed that the simulation model with a mechanism of potassium accumulation could reproduce the attenuated responses of neuronal populations to persistent axonal HFS in rat experiments. The elevation of [K⁺]_o during HFS resulted in an increase of basic membrane potentials and then generated a depolarization block in the axonal membrane thereby attenuating the responses of neuronal populations. The depolarization block in axons included both complete block (~26%) and intermittent block (~74%), which generated desynchronized firing among axons in fibers and travelled to the cell bodies to induce desynchronized firing in somata. The simulation results may provide important information for revealing the modulation mechanisms of axonal HFS in the therapy of brain stimulation.

Small Changes in Inter-Pulse-Intervals Can Cause Synchronized Neuronal Firing During High-Frequency Stimulations in Rat Hippocampus

Deep brain stimulation (DBS) traditionally utilizes electrical pulse sequences with a constant frequency, i.e., constant inter-pulse-interval (IPI), to treat certain brain disorders in clinic. Stimulation sequences with varying frequency have been investigated recently to improve the efficacy of existing DBS therapy and to develop new treatments. However, the effects of such sequences are inconclusive. The present study tests the hypothesis that stimulations with varying IPI can generate neuronal activity markedly different from the activity induced by stimulations with constant IPI. And, the crucial factor causing the distinction is the relative differences in IPI lengths rather than the absolute lengths of IPI nor the average lengths of IPI. In rat experiments in vivo, responses of neuronal populations to applied stimulation sequences were collected during stimulations with both constant IPI (control) and random IPI. The stimulations were applied in the efferent fibers antidromically (in alveus) or in the afferent fibers orthodromically (in Schaffer collaterals) of pyramidal cells, the principal cells of hippocampal CA1 region. Amplitudes and areas of population spike (PS) waveforms were used to evaluate the neuronal responses induced by different stimulation paradigms. During the periods of both antidromic and orthodromic high-frequency stimulation (HFS), the HFS with random IPI induced synchronous neuronal firing with large PS even if the lengths of random IPI were limited to a small range of 5-10 ms, corresponding to a frequency range 100-200 Hz. The large PS events did not appear during control stimulations with a constant frequency at 100, 200, or 130 Hz (i.e., the mean frequency of HFS with random IPI uniformly distributed within 5-10 ms). Presumably, nonlinear dynamics in neuronal responses to random IPI might cause the generation of synchronous firing under the situation without any long pauses in HFS sequences. The results indicate that stimulations with random IPI can generate salient impulses to brain tissues and modulate the synchronization of neuronal activity, thereby providing potential stimulation paradigms for extending DBS therapy in treating more brain diseases, such as disorders of consciousness and vegetative states.

Simulation Study of Intermittent Axonal Block and Desynchronization Effect Induced by High-Frequency Stimulation of Electrical Pulses

Deep brain stimulation (DBS) has been successfully used in treating neural disorders in brain, such as Parkinson’s disease and epilepsy. However, the precise mechanisms of DBS remain unclear. Regular DBS therapy utilizes high-frequency stimulation (HFS) of electrical pulses. Among all of neuronal elements, axons are mostly inclined to be activated by electrical pulses. Therefore, the response of axons may play an important role in DBS treatment. To study the axonal responses during HFS, we developed a computational model of myelinated axon to simulate sequences of action potentials generated in single and multiple axons (an axon bundle) by stimulations. The stimulations are applied extracellularly by a point source of current pulses with a frequency of 50–200 Hz. Additionally, our model takes into account the accumulation of potassium ions in the peri-axonal spaces. Results show that the increase of extracellular potassium generates intermittent depolarization block in the axons during HFS. Under the state of alternate block and recovery, axons fire action potentials at a rate far lower than the frequency of stimulation pulses. In addition, the degree of axonal block is highly related to the distance between the axons and the stimulation point. The differences in the degree of block for individual axons in a bundle result in desynchronized firing among the axons. Stimulations with higher frequency and/or greater intensity can induce axonal block faster and increase the desynchronization effect on axonal firing. Presumably, the desynchronized axonal activity induced by HFS could generate asynchronous activity in the population of target neurons downstream thereby suppressing over-synchronized firing of neurons in pathological conditions. The desynchronization effect generated by intermittent activation of axons may be crucial for DBS therapy. The present study provides new insights into the mechanisms of DBS, which is significant for advancing the application of DBS.

Axonal Stimulations With a Higher Frequency Generate More Randomness in Neuronal Firing Rather Than Increase Firing Rates in Rat Hippocampus

Deep brain stimulation (DBS) has been used for treating many brain disorders. Clinical applications of DBS commonly require high-frequency stimulations (HFS, ∼100 Hz) of electrical pulses to obtain therapeutic efficacy. It is not clear whether the electrical energy of HFS functions other than generating firing of action potentials in neuronal elements. To address the question, we investigated the reactions of downstream neurons to pulse sequences with a frequency in the range 50-200 Hz at afferent axon fibers in the hippocampal CA1 region of anesthetized rats. The results show that the mean rates of neuronal firing induced by axonal HFS were similar even for an up to fourfold difference (200:50) in the number and thereby in the energy of electrical pulses delivered. However, HFS with a higher pulse frequency (100 or 200 Hz) generated more randomness in the firing pattern of neurons than a lower pulse frequency (50 Hz), which were quantitatively evaluated by the significant changes of two indexes, namely, the peak coefficients and the duty ratios of excitatory phase of neuronal firing, induced by different frequencies (50-200 Hz). The findings indicate that a large portion of the HFS energy might function to generate a desynchronization effect through a possible mechanism of intermittent depolarization block of neuronal membranes. The present study addresses the demand of high frequency for generating HFS-induced desynchronization in neuronal activity, which may play important roles in DBS therapy.

Computational Modeling of Ultrasonic Subthalamic Nucleus Stimulation

OBJECTIVE

To explore the potential of ultrasonic modulation of plateau-potential generating subthalamic nucleus neurons (STN), by modeling their interaction with continuous and pulsed ultrasonic waves.

METHODS

A computational model for ultrasonic stimulation of the STN is created by combining the Otsuka-model with the bilayer sonophore model. The neuronal response to continuous and pulsed ultrasonic waves is computed in parallel for a range of frequencies, duty cycles, pulse repetition frequencies, and intensities.

RESULTS

Ultrasonic intensity in continuous-wave stimulation determines the firing pattern of the STN. Three observed spiking modes in order of increasing intensity are low frequency spiking, high frequency spiking with significant spike-frequency and spike-amplitude adaptation, and a silenced mode. Continuous-wave stimulation has little capability to manipulate the saturated spiking rate in the high frequency spiking mode. In contrast, STN firing rates induced by pulsed ultrasound insonication will saturate to the pulse repetition frequency with short latencies, for sufficiently large intensity and repetition frequency.

CONCLUSION

Computational results show that the activity of plateau-potential generating STN can be modulated by selection of the stimulus parameters. Low intensities result in repetitive firing, while higher intensities silence the STN. Pulsed ultrasonic stimulation results in a shorter saturation latency and is able to modulate spiking rates.

SIGNIFICANCE

Stimulation or suppresion of the STN is important in the treatment of Parkinson's disease, e.g., in deep brain stimulation. This explorative study on ultrasonic modulation of the STN, could be a step in the direction of minimally invasive alternatives to conventional deep brain stimulation.

Oligodendrocytes control potassium accumulation in white matter and seizure susceptibility

The inwardly rectifying K⁺ channel K_ir4.1 is broadly expressed by CNS glia and deficits in K_ir4.1 lead to seizures and myelin vacuolization. However, the role of oligodendrocyte K_ir4.1 channels in controlling myelination and K⁺ clearance in white matter has not been defined. Here, we show that selective deletion of K_ir4.1 from oligodendrocyte progenitors (OPCs) or mature oligodendrocytes did not impair their development or disrupt the structure of myelin. However, mice lacking oligodendrocyte K_ir4.1 channels exhibited profound functional impairments, including slower clearance of extracellular K⁺ and delayed recovery of axons from repetitive stimulation in white matter, as well as spontaneous seizures, a lower seizure threshold, and activity-dependent motor deficits. These results indicate that K_ir4.1 channels in oligodendrocytes play an important role in extracellular K⁺ homeostasis in white matter, and that selective loss of this channel from oligodendrocytes is sufficient to impair K⁺ clearance and promote seizures.

High frequency stimulation of afferent fibers generates asynchronous firing in the downstream neurons in hippocampus through partial block of axonal conduction

Deep brain stimulation (DBS) is effective for treating neurological disorders in clinic. However, the therapeutic mechanisms of high-frequency stimulation (HFS) of DBS have not yet been elucidated. Previous studies have suggested that HFS-induced changes in axon conduction could have important contributions to the DBS effects and desiderate further studies. To investigate the effects of prolonged HFS of afferent axons on the firing of downstream neurons, HFS trains of 100 and 200Hz were applied on the Schaffer collaterals of the hippocampal CA1 region in anaesthetized rats. Single unit activity of putative pyramidal cells and interneurons in the downstream region was analyzed during the late periods of prolonged HFS when the axonal conduction was blocked. The results show that the firing rates of both pyramidal cells and interneurons increased rather than decreased during the period of axon block. However, the firing rates were far smaller than the stimulation frequency of HFS. In addition, the firing pattern of pyramidal cells changed from typical bursts during baseline recordings into regular single spikes during HFS periods. Furthermore, the HFS produced asynchronous firing in the downstream neurons in contrast to the synchronous firing induced by single pulses. Presumably, the HFS-induced block of axonal conduction was not complete. During the period of partial block, individual axons could recover intermittently and independently, and drive the downstream neurons to fire in an asynchronous pattern. This axonal mechanism of HFS provides a novel explanation for how DBS could replace an original pattern of neuronal activity by a HFS-modulated asynchronous firing in the target region thereby generating the therapeutic effects of DBS.

Kilohertz Frequency Deep Brain Stimulation Is Ineffective at Regularizing the Firing of Model Thalamic Neurons

Deep brain stimulation (DBS) is an established therapy for movement disorders, including tremor, dystonia, and Parkinson's disease, but the mechanisms of action are not well understood. Symptom suppression by DBS typically requires stimulation frequencies ≥100 Hz, but when the frequency is increased above ~2 kHz, the effectiveness in tremor suppression declines (Benabid et al., 1991). We sought to test the hypothesis that the decline in efficacy at high frequencies is associated with desynchronization of the activity generated within a population of stimulated neurons. Regularization of neuronal firing is strongly correlated with tremor suppression by DBS, and desynchronization would disrupt the regularization of neuronal activity. We implemented computational models of CNS axons with either deterministic or stochastic membrane dynamics, and quantified the response of populations of model nerve fibers to extracellular stimulation at different frequencies and amplitudes. As stimulation frequency was increased from 2 to 80 Hz the regularity of neuronal firing increased (as assessed with direct estimates of entropy), in accord with the clinical effects on tremor of increasing stimulation frequency (Kuncel et al., 2006). Further, at frequencies between 80 and 500 Hz, increasing the stimulation amplitude (i.e., the proportion of neurons activated by the stimulus) increased the regularity of neuronal activity across the population, in accord with the clinical effects on tremor of stimulation amplitude (Kuncel et al., 2007). However, at stimulation frequencies above 1 kHz the regularity of neuronal firing declined due to irregular patterns of action potential generation and conduction block. The reductions in neuronal regularity that occurred at high frequencies paralleled the previously reported decline in tremor reduction and may be responsible for the loss of efficacy of DBS at very high frequencies. This analysis provides further support for the hypothesis that effective DBS masks the intrinsic patterns of activity in the stimulated neurons and replaces it with regularized firing.

Computational analysis of kilohertz frequency spinal cord stimulation for chronic pain management

BACKGROUND

Kilohertz frequency spinal cord stimulation (KHFSCS) is an emerging therapy for treating refractory neuropathic pain. Although KHFSCS has the potential to improve the lives of patients experiencing debilitating pain, its mechanisms of action are unknown and thus it is difficult to optimize its development. Therefore, the goal of this study was to use a computer model to investigate the direct effects of KHFSCS on specific neural elements of the spinal cord.

METHODS

This computer model consisted of two main components: (1) finite element models of the electric field generated by KHFSCS and (2) multicompartment cable models of axons in the spinal cord. Model analysis permitted systematic investigation into a number of variables (e.g., dorsal cerebrospinal fluid thickness, lead location, fiber collateralization, and fiber size) and their corresponding effects on excitation and conduction block thresholds during KHFSCS.

RESULTS

The results of this study suggest that direct excitation of large-diameter dorsal column or dorsal root fibers require high stimulation amplitudes that are at the upper end or outside of the range used in clinical KHFSCS (i.e., 0.5 to 5 mA). Conduction block was only possible within the clinical range for a thin dorsal cerebrospinal fluid layer.

CONCLUSIONS

These results suggest that clinical KHFSCS may not function through direct activation or conduction block of dorsal column or dorsal root fibers. Although these results should be validated with further studies, the authors propose that additional concepts and/or alternative hypotheses should be considered when examining the pain relief mechanisms of KHFSCS.

Deep Brain Stimulation

High-frequency deep brain stimulation (DBS) is an effective treatment for some movement disorders. Though mechanisms underlying DBS are still unclear, commonly accepted theories include a “functional inhibition” of neuronal cell bodies and the excitation of axonal projections near the electrodes. It is becoming clear, however, that the paradoxical dissociation “local inhibition” and “distant excitation” is far more complex than initially thought. Despite an initial increase in neuronal activity following stimulation, cells are often unable to maintain normal ionic concentrations, particularly those of sodium and potassium. Based on currently available evidence, we proposed an alternative hypothesis. Increased extracellular concentrations of potassium during DBS may change the dynamics of both cells and axons, contributing not only to the intermittent excitation and inhibition of these elements but also to interrupt abnormal pathological activity. In this article, we review mechanisms through which high extracellular potassium may mediate some of the effects of DBS.

Fidelity of frequency and phase entrainment of circuit-level spike activity during DBS

High-frequency stimulation is known to entrain spike activity downstream and upstream of several clinical deep brain stimulation (DBS) targets, including the cerebellar-receiving area of thalamus (VPLo), subthalamic nucleus (STN), and globus pallidus (GP). Less understood are the fidelity of entrainment to each stimulus pulse, whether entrainment patterns are stationary over time, and how responses differ among DBS targets. In this study, three rhesus macaques were implanted with a single DBS lead in VPLo, STN, or GP. Single-unit spike activity was recorded in the resting state in motor cortex during VPLo DBS, in GP during STN DBS, and in STN and pallidal-receiving area of motor thalamus (VLo) during GP DBS. VPLo DBS induced time-locked spike activity in 25% (n = 15/61) of motor cortex cells, with entrained cells following 7.5 ± 7.4% of delivered pulses. STN DBS entrained spike activity in 26% (n = 8/27) of GP cells, which yielded time-locked spike activity for 8.7 ± 8.4% of stimulus pulses. GP DBS entrained 67% (n = 14/21) of STN cells and 32% (n = 19/59) of VLo cells, which showed a higher fraction of pulses effectively inhibiting spike activity (82.0 ± 9.6% and 86.1 ± 16.6%, respectively). Latency of phase-locked spike activity increased over time in motor cortex (58%, VPLo DBS) and to a lesser extent in GP (25%, STN DBS). In contrast, the initial inhibitory phase observed in VLo and STN during GP DBS remained stable following stimulation onset. Together, these data suggest that circuit-level entrainment is low-pass filtered during high-frequency stimulation, most notably for glutamatergic pathways. Moreover, phase entrainment is not stationary or consistent at the circuit level for all DBS targets.

Astrocyte glycogen as an emergency fuel under conditions of glucose deprivation or intense neural activity

Energy metabolism in the brain is a complex process that is incompletely understood. Although glucose is agreed as the main energy support of the brain, the role of glucose is not clear, which has led to controversies that can be summarized as follows: the fate of glucose, once it enters the brain is unclear. It is not known the form in which glucose enters the cells (neurons and glia) within the brain, nor the degree of metabolic shuttling of glucose derived metabolites between cells, with a key limitation in our knowledge being the extent of oxidative metabolism, and how increased tissue activity alters this. Glycogen is present within the brain and is derived from glucose. Glycogen is stored in astrocytes and acts to provide short-term delivery of substrates to neural elements, although it may also contribute an important component to astrocyte metabolism. The roles played by glycogen awaits further study, but to date its most important role is in supporting neural elements during increased firing activity, where signaling molecules, proposed to be elevated interstitial K(+), indicative of elevated neural firing rates, activate glycogen phosphorylase leading to increased production of glycogen derived substrate.

Blocking central pathways in the primate motor system using high-frequency sinusoidal current

Electrical stimulation with high-frequency (2-10 kHz) sinusoidal currents has previously been shown to produce a transient and complete nerve block in the peripheral nervous system. Modeling and in vitro studies suggest that this is due to a prolonged local depolarization across a broad section of membrane underlying the blocking electrode. Previous work has used cuff electrodes wrapped around the peripheral nerve to deliver the blocking stimulus. We extended this technique to central motor pathways, using a single metal microelectrode to deliver focal sinusoidal currents to the corticospinal tract at the cervical spinal cord in anesthetized adult baboons. The extent of conduction block was assessed by stimulating a second electrode caudal to the blocking site and recording the antidromic field potential over contralateral primary motor cortex. The maximal block achieved was 99.6%, similar to findings of previous work in peripheral fibers, and the optimal frequency for blocking was 2 kHz. Block had a rapid onset, being complete as soon as the transient activation associated with the start of the sinusoidal current was over. High-frequency block was also successfully applied to the pyramidal tract at the medulla, ascending sensory pathways in the dorsal columns, and the descending systems of the medial longitudinal fasciculus. High-frequency sinusoidal stimulation produces transient, reversible lesions in specific target locations and therefore could be a useful alternative to permanent tissue transection in some experimental paradigms. It also could help to control or prevent some of the hyperactivity associated with chronic neurological disorders.

High frequency stimulation extends the refractory period and generates axonal block in the rat hippocampus

BACKGROUND

The therapeutic mechanisms of deep brain stimulations (DBS) are not fully understood. Axonal block induced by high frequency stimulation (HFS) has been suggested as one possible underlying mechanism of DBS.

OBJECTIVE

To investigate the mechanism of the generation of HFS-induced axonal block.

METHODS

High frequency pulse trains were applied to the fiber tracts of alveus and Schaffer collaterals in the hippocampal CA1 neurons in anaesthetized rats at 50, 100 and 200 Hz. The amplitude changes of antidromic-evoked population spikes (APS) were measured to determine the degree of axonal block. The amplitude ratio of paired-pulse evoked APS was used to assess the changes of refractory period.

RESULTS

There were two distinct recovery stages of axonal block following the termination of HFS. One frequency-dependent faster phase followed by another frequency-independent slower phase. Experiments with specially designed temporal patterns of stimulation showed that HFS produced an extension of the duration of axonal refractory period thereby causing a fast recovery phase of the axonal block. Thus, prolonged gaps inserted within HFS trains could eliminate the axonal block and induced large population spikes and even epileptiform activity in the upstream or downstream regions.

CONCLUSIONS

Extension of refractory period plays an important role on HFS induced axonal block. Stimulation pattern with properly designed pauses could be beneficial for different requirements of excitation or inhibition in DBS therapies.

Closing the loop of deep brain stimulation

High-frequency deep brain stimulation is used to treat a wide range of brain disorders, like Parkinson's disease. The stimulated networks usually share common electrophysiological signatures, including hyperactivity and/or dysrhythmia. From a clinical perspective, HFS is expected to alleviate clinical signs without generating adverse effects. Here, we consider whether the classical open-loop HFS fulfills these criteria and outline current experimental or theoretical research on the different types of closed-loop DBS that could provide better clinical outcomes. In the first part of the review, the two routes followed by HFS-evoked axonal spikes are explored. In one direction, orthodromic spikes functionally de-afferent the stimulated nucleus from its downstream target networks. In the opposite direction, antidromic spikes prevent this nucleus from being influenced by its afferent networks. As a result, the pathological synchronized activity no longer propagates from the cortical networks to the stimulated nucleus. The overall result can be described as a reversible functional de-afferentation of the stimulated nucleus from its upstream and downstream nuclei. In the second part of the review, the latest advances in closed-loop DBS are considered. Some of the proposed approaches are based on mathematical models, which emphasize different aspects of the parkinsonian basal ganglia: excessive synchronization, abnormal firing-rate rhythms, and a deficient thalamo-cortical relay. The stimulation strategies are classified depending on the control-theory techniques on which they are based: adaptive and on-demand stimulation schemes, delayed and multi-site approaches, stimulations based on proportional and/or derivative control actions, optimal control strategies. Some of these strategies have been validated experimentally, but there is still a large reservoir of theoretical work that may point to ways of improving practical treatment.

Axonal and synaptic failure suppress the transfer of firing rate oscillations, synchrony and information during high frequency deep brain stimulation

High frequency deep brain stimulation (DBS) of the subthalamic nucleus (STN) is a widely used treatment for Parkinson's disease, but its effects on neural activity in basal ganglia circuits are not fully understood. DBS increases the excitation of STN efferents yet decouples STN spiking patterns from the spiking patterns of STN synaptic targets. We propose that this apparent paradox is resolved by recent studies showing an increased rate of axonal and synaptic failures in STN projections during DBS. To investigate this hypothesis, we combine in vitro and in vivo recordings to derive a computational model of axonal and synaptic failure during DBS. Our model shows that these failures induce a short term depression that suppresses the synaptic transfer of firing rate oscillations, synchrony and rate-coded information from STN to its synaptic targets. In particular, our computational model reproduces the widely reported suppression of parkinsonian β oscillations and synchrony during DBS. Our results support the idea that short term depression is a therapeutic mechanism of STN DBS that works as a functional lesion by decoupling the somatic spiking patterns of STN neurons from spiking activity in basal ganglia output nuclei.

Focal axonal swellings and associated ultrastructural changes attenuate conduction velocity in central nervous system axons: a computer modeling study

The constancy of action potential conduction in the central nervous system (CNS) relies on uniform axon diameter coupled with fidelity of the overlying myelin providing high-resistance, low capacitance insulation. Whereas the effects of demyelination on conduction have been extensively studied/modeled, equivalent studies on the repercussions for conduction of axon swelling, a common early pathological feature of (potentially reversible) axonal injury, are lacking. The recent description of experimentally acquired morphological and electrical properties of small CNS axons and oligodendrocytes prompted us to incorporate these data into a computer model, with the aim of simulating the effects of focal axon swelling on action potential conduction. A single swelling on an otherwise intact axon, as occurs in optic nerve axons of Cnp1 null mice caused a small decrease in conduction velocity. The presence of single swellings on multiple contiguous internodal regions (INR), as likely occurs in advanced disease, caused qualitatively similar results, except the dimensions of the swellings required to produce equivalent attenuation of conduction were significantly decreased. Our simulations of the consequences of metabolic insult to axons, namely, the appearance of multiple swollen regions, accompanied by perturbation of overlying myelin and increased axolemmal permeability, contained within a single INR, revealed that conduction block occurred when the dimensions of the simulated swellings were within the limits of those measured experimentally, suggesting that multiple swellings on a single axon could contribute to axonal dysfunction, and that increased axolemmal permeability is the decisive factor that promotes conduction block.

Extracellular sheets and tunnels modulate glutamate diffusion in hippocampal neuropil

Although the extracellular space in the neuropil of the brain is an important channel for volume communication between cells and has other important functions, its morphology on the micron scale has not been analyzed quantitatively owing to experimental limitations. We used manual and computational techniques to reconstruct the 3D geometry of 180 μm(3) of rat CA1 hippocampal neuropil from serial electron microscopy and corrected for tissue shrinkage to reflect the in vivo state. The reconstruction revealed an interconnected network of 40-80 nm diameter tunnels, formed at the junction of three or more cellular processes, spanned by sheets between pairs of cell surfaces with 10-40 nm width. The tunnels tended to occur around synapses and axons, and the sheets were enriched around astrocytes. Monte Carlo simulations of diffusion within the reconstructed neuropil demonstrate that the rate of diffusion of neurotransmitter and other small molecules was slower in sheets than in tunnels. Thus, the non-uniformity found in the extracellular space may have specialized functions for signaling (sheets) and volume transmission (tunnels).

Post stimulus effects of high frequency biphasic electrical current on a fibre's conductibility in isolated frog nerves

OBJECTIVE

High frequency biphasic (HFB) electrical currents are widely used in nerve blocking studies. Their safety margins largely remain unknown and need to be investigated.

APPROACH

This study, exploring the post stimulus effects of HFB electrical currents on a nerve's conductibility, was performed on bullfrog sciatic nerves. Both compound action potentials (CAPs) and differential CAPs (DCAPs, i.e. control CAPs subtracted by CAPs following HFB currents) were obtained, and N1 and N2 components, which were the first and second upward components of DCAPs, were used for analyses of the effects introduced by HFB electrical stimulation.

MAIN RESULTS

First, HFB currents of 10 kHz at a completely blocking threshold were applied for 5 s. The maximum amplitudes and conducting velocities of the CAPs were significantly (P < 0.02) decreased within the observed period (60 s) following HFB currents. The DCAPs displayed clear N1 and N2 components, demonstrating respectively the losses of the fibres' normal conductibility and the appearances of new delayed conductions. Decreases of N1 amplitudes along time, regarded as the recovery of the nerve's conductibility, exhibited two distinct phases: a fast one lasting several seconds and a slow one lasting longer than 5 min. Further tests showed a linear relationship between the HFB stimulation durations and recovering periods of N1 amplitudes. Supra-threshold blocking did not cause higher N1 amplitudes.

SIGNIFICANCE

This study indicates that HFB electrical currents lead to long lasting post stimulus reduction of a nerve's conductibility, which might relate to potential nerve injuries. A possible mechanism, focusing on changes in intracellular and periaxonal ionic concentrations, was proposed to underlie the reduction of the nerve's conductibility and potential nerve injuries. Greater caution and stimulation protocols with greater safety margins should be explored when utilizing HFB electrical current to block nerve conductions.

Functional disconnection of axonal fibers generated by high frequency stimulation in the hippocampal CA1 region in-vivo

High frequency stimulation (HFS) applied in the brain has been shown to be efficient for treating several brain disorders, such as Parkinson's disease and epilepsy. But the mechanisms underlying HFS are not clear. In particular, the effect of HFS on axons has been intriguing since axonal propagation plays an important role in the functional outcome of HFS. In order to study the potential effect of axonal block by HFS in-vivo, both orthodromic- and antidromic-HFS (O-HFS, A-HFS) with biphasic pulses were applied to the hippocampal CA1 region in anaesthetized rats. Changes in the amplitude and latency of orthodromic- and antidromic-population spikes within 1-min long period of stimulation at 50, 100 and 200 Hz HFS were analyzed. The results show that except for a short onset period, activity evoked by O-HFS with a frequency over 100 Hz could not be sustained. For A-HFS at frequencies over 100 Hz, the amplitudes and the latencies of antidromic population spike (APS) greatly decreased and increased respectively. Significantly larger changes in APS latency were observed in HFS than those generated at low frequency, suggesting a suppression of axon conduction by HFS. Furthermore, the CA1 somata remained excitable while failing to respond to excitation from orthodromic or antidromic HFS. Taken together, these results show that HFS produces an axonal block of both afferent and efferent fibers localized to the area of stimulation since it does not affect the excitability of CA1 somata. This effect of HFS on axons causes a functional disconnection of axonal pathways that is reversible and temporary. The reversible disconnection or temporary deafferentation between putative therapeutic targets could have extensive implication for various clinical applications of HFS to treat brain diseases.

Block of peripheral pain response by high-frequency sinusoidal stimulation

OBJECTIVES

Pain due to peripheral neuropathy is extremely difficult to treat as drugs often become less and less effective over the course of a patient's life. In order to augment such treatments, electrical stimulation has become relatively common, in the form of transcutaneous electrical nerve stimulation, peripheral nerve stimulation, and spinal cord stimulation. Unfortunately, these treatments are only effective in a subset of chronic pain patients.

MATERIALS AND METHODS

A rabbit sural-gastrocnemius reflex model of pain was used, in which reflex twitches were elicited using 0.3-Hz 100-μs pulses applied to the sural nerve. This stimulation induces a small electromyogram (EMG) twitch recorded from the gastrocnemius with about 1-msec delay. When pain stimuli are applied on the heel of the foot, the amplitude of the reflex-induced EMG response increased by 4.7 ± 2.5-fold (p < 0.005). Sinusoidal stimulation (high-frequency stimulation) was applied (130 Hz) through a tripolar cuff placed distally on the sural nerve to block the C-fiber activity induced by heel pain.

RESULTS

The stimulation paradigm was able to successfully and reversibly block pain signals as measured by the lack of potentiation of the reflex in 100% of the five nerves tested (no significant difference in reflex response, p > 0.5), with thresholds between 500 and 900 μApp .

CONCLUSIONS

Complete, reversible block of pain-induced reflex potentiation was obtained in all five nerves tested. This method could be applicable to the control of pain in patients with peripheral neuropathy.

Elevated potassium provides an ionic mechanism for deep brain stimulation in the hemiparkinsonian rat

The mechanism of high-frequency stimulation used in deep brain stimulation (DBS) for Parkinson's disease (PD) has not been completely elucidated. Previously, high-frequency stimulation of the rat entopeduncular nucleus, a basal ganglia output nucleus, elicited an increase in [K(+)](e) to 18 mm, in vitro. In this study, we assessed whether elevated K(+) can elicit DBS-like therapeutic effects in hemiparkinsonian rats by employing the limb-use asymmetry test and the self-adjusting stepping test. We then identified how these effects were meditated with in-vivo and in-vitro electrophysiology. Forelimb akinesia improved in hemiparkinsonian rats undergoing both tests after 20 mm KCl injection into the substantia nigra pars reticulata (SNr) or the subthalamic nucleus. In the SNr, neuronal spiking activity decreased from 38.2 ± 1.2 to 14.6 ± 1.6 Hz and attenuated SNr beta-frequency (12-30 Hz) oscillations after K(+) treatment. These oscillations are commonly associated with akinesia/bradykinesia in patients with PD and animal models of PD. Pressure ejection of 20 mm KCl onto SNr neurons in vitro caused a depolarisation block and sustained quiescence of SNr activity. In conclusion, our data showed that elevated K(+) injection into the hemiparkinsonian rat SNr improved forelimb akinesia, which coincided with a decrease in SNr neuronal spiking activity and desynchronised activity in SNr beta frequency, and subsequently an overall increase in ventral medial thalamic neuronal activity. Moreover, these findings also suggest that elevated K(+) may provide an ionic mechanism that can contribute to the therapeutic effects of DBS for the motor treatment of advanced PD.

Desynchronizing effect of high-frequency stimulation in a generic cortical network model

Transcranial electrical stimulation (TCES) and deep brain stimulation are two different applications of electrical current to the brain used in different areas of medicine. Both have a similar frequency dependence of their efficiency, with the most pronounced effects around 100 Hz. We apply superthreshold electrical stimulation, specifically depolarizing DC current, interrupted at different frequencies, to a simple model of a population of cortical neurons which uses phenomenological descriptions of neurons by Izhikevich and synaptic connections on a similar level of sophistication. With this model, we are able to reproduce the optimal desynchronization around 100 Hz, as well as to predict the full frequency dependence of the efficiency of desynchronization, and thereby to give a possible explanation for the action mechanism of TCES.

Mechanisms of deep brain stimulation for obsessive compulsive disorder: effects upon cells and circuits

Deep brain stimulation (DBS) has emerged as a safe, effective, and reversible treatment for a number of movement disorders. This has prompted investigation of its use for other applications including psychiatric disorders. In recent years, DBS has been introduced for the treatment of obsessive compulsive disorder (OCD), which is characterized by recurrent unwanted thoughts or ideas (obsessions) and repetitive behaviors or mental acts performed in order to relieve these obsessions (compulsions). Abnormal activity in cortico-striato-thalamo-cortical (CSTC) circuits including the orbitofrontal cortex (OFC), anterior cingulate cortex (ACC), ventral striatum, and mediodorsal (MD) thalamus has been implicated in OCD. To this end a number of DBS targets including the anterior limb of the internal capsule (ALIC), ventral capsule/ventral striatum (VC/VS), ventral caudate nucleus, subthalamic nucleus (STN), and nucleus accumbens (NAc) have been investigated for the treatment of OCD. Despite its efficacy and widespread use in movement disorders, the mechanism of DBS is not fully understood, especially as it relates to psychiatric disorders. While initially thought to create a functional lesion akin to ablative procedures, it is increasingly clear that DBS may induce clinical benefit through activation of axonal fibers spanning the CSTC circuits, alteration of oscillatory activity within this network, and/or release of critical neurotransmitters. In this article we review how the use of DBS for OCD informs our understanding of both the mechanisms of DBS and the circuitry of OCD. We review the literature on DBS for OCD and discuss potential mechanisms of action at the neuronal level as well as the broader circuit level.

Dynamics and sensitivity analysis of high-frequency conduction block

The local delivery of extracellular high-frequency stimulation (HFS) has been shown to be a fast acting and quickly reversible method of blocking neural conduction and is currently being pursued for several clinical indications. However, the mechanism for this type of nerve block remains unclear. In this study, we investigate two hypotheses: (1) depolarizing currents promote conduction block via inactivation of sodium channels and (2) the gating dynamics of the fast sodium channel are the primary determinate of minimal blocking frequency. Hypothesis 1 was investigated using a combined modeling and experimental study to investigate the effect of depolarizing and hyperpolarizing currents on high-frequency block. The results of the modeling study show that both depolarizing and hyperpolarizing currents play an important role in conduction block and that the conductance to each of three ionic currents increases relative to resting values during HFS. However, depolarizing currents were found to promote the blocking effect, and hyperpolarizing currents were found to diminish the blocking effect. Inward sodium currents were larger than the sum of the outward currents, resulting in a net depolarization of the nodal membrane. Our experimental results support these findings and closely match results from the equivalent modeling scenario: intra-peritoneal administration of the persistent sodium channel blocker ranolazine resulted in an increase in the amplitude of HFS required to produce conduction block in rats, confirming that depolarizing currents promote the conduction block phenomenon. Hypothesis 2 was investigated using a spectral analysis of the channel gating variables in a single-fiber axon model. The results of this study suggested a relationship between the dynamical properties of specific ion channel gating elements and the contributions of corresponding conductances to block onset. Specifically, we show that the dynamics of the fast sodium inactivation gate are too slow to track the high-frequency changes in membrane potential during HFS, and that the behavior of the fast sodium current was dominated by the low-frequency depolarization of the membrane. As a result, in the blocked state, only 5.4% of nodal sodium channels were found to be in the activatable state in the node closest to the blocking electrode, resulting in conduction block. Moreover, we find that the corner frequency for the persistent sodium channel activation gate corresponds to the frequency below which high-frequency stimuli of arbitrary amplitude are incapable of inducing conduction block.

Axonal failure during high frequency stimulation of rat subthalamic nucleus

Deep brain stimulation (DBS) has been established as an effective surgical therapy for advanced Parkinson's disease (PD) and gains increasing acceptance for otherwise intractable neuropsychiatric diseases such as major depression or obsessive–compulsive disorders. In PD, DBS targets predominantly the subthalamic nucleus (STN) and relieves motor deficits only at high frequency (>100 Hz). In contrast to the well-documented clinical efficacy of DBS, its underlying principle remains enigmatic spawning a broad and, in part, contradictory spectrum of suggested synaptic and non-synaptic mechanisms within and outside STN. Here we focused on a crucial, but largely neglected issue in this controversy, namely the axonal propagation of DBS within and away from STN. In rat brain slices preserving STN projections to substantia nigra (SN) and entopeduncular nucleus (EP, the rodent equivalent of internal globus pallidus), STN-DBS disrupted synaptic excitation onto target neurons through an unexpected failure of axonal signalling. The rapid onset and, upon termination of DBS, recovery of this effect was highly reminiscent of the time course of DBS in the clinical setting. We propose that DBS-induced suppression of axonal projections from and to STN serves to shield basal ganglia circuitry from pathological activity arising in or amplified by this nucleus.

Morphological and electrical properties of oligodendrocytes in the white matter of the corpus callosum and cerebellum

In the central nervous system, electrical signals passing along nerve cells are speeded by cells called oligodendrocytes, which wrap the nerve cells with a fatty layer called myelin. This layer is important for rapid information processing, and is often lost in disease, causing mental or physical impairment in multiple sclerosis, stroke, cerebral palsy and spinal cord injury. The myelin speeds the information flow in two ways, by decreasing the capacitance of the nerve cell and by increasing its membrane resistance, but little is known about the latter aspect of myelin function. By recording electrically from oligodendrocytes and imaging their morphology we characterised the geometry and, for the first time, the resistance of myelin in the brain. This revealed differences between the properties of oligodendrocytes in two brain areas and established that the resistance of myelin is sufficiently high to prevent significant slowing of the nerve electrical signal by current leakage through the myelin.

Excitation block in a nerve fibre model owing to potassium-dependent changes in myelin resistance

The myelinated nerve fibre is formed by an axon and Schwann cells or oligodendrocytes that sheath the axon by winding around it in tight myelin layers. Repetitive stimulation of a fibre is known to result in accumulation of extracellular potassium ions, especially between the axon and the myelin. Uptake of potassium leads to Schwann cell swelling and myelin restructuring that impacts the electrical properties of the myelin. In order to further understand the dynamic interaction that takes place between the myelin and the axon, we have modelled submyelin potassium accumulation and related changes in myelin resistance during prolonged high-frequency stimulation. We predict that potassium-mediated decrease in myelin resistance leads to a functional excitation block with various patterns of altered spike trains. The patterns are found to depend on stimulation frequency and amplitude and to range from no block (less than 100 Hz) to a complete block (greater than 500 Hz). The transitional patterns include intermittent periodic block with interleaved spiking and non-spiking intervals of different relative duration as well as an unstable regime with chaotic switching between the spiking and non-spiking states. Intermittent conduction blocks are accompanied by oscillations of extracellular potassium. The mechanism of conductance block based on myelin restructuring complements the already known and modelled block via hyperpolarization mediated by the axonal sodium pump and potassium depolarization.

Effect of nerve cuff electrode geometry on onset response firing in high-frequency nerve conduction block

The delivery of high-frequency alternating currents has been shown to produce a focal and reversible conduction block in whole nerve and is a potential therapeutic option for various diseases and disorders involving pathological or undesired neurological activity. However, delivery of high-frequency alternating current to a nerve produces a finite burst of neuronal firing, called the onset response, before the nerve is blocked. Reduction or elimination of the onset response is very important to moving this type of nerve block into clinical applications since the onset response is likely to result in undesired muscle contraction and pain. This paper describes a study of the effect of nerve cuff electrode geometry (specifically, bipolar contact separation distance), and waveform amplitude on the magnitude and duration of the onset response. Electrode geometry and waveform amplitude were both found to affect these measures. The magnitude and duration of the onset response showed a monotonic relationship with bipolar separation distance and amplitude. The duration of the onset response varied by as much as 820% on average for combinations of different electrode geometries and waveform amplitudes. Bipolar electrodes with a contact separation distance of 0.5 mm resulted in the briefest onset response on average. Furthermore, the data presented in this study provide some insight into a biophysical explanation for the onset response. These data suggest that the onset response consists of two different phases: one phase which is responsive to experimental variables such as electrode geometry and waveform amplitude, and one which is not and appears to be inherent to the transition to the blocked state. This study has implications for nerve block electrode and stimulation parameter selection for clinical therapy systems and basic neurophysiology studies.

Potassium diffusive coupling in neural networks

Conventional neural networks are characterized by many neurons coupled together through synapses. The activity, synchronization, plasticity and excitability of the network are then controlled by its synaptic connectivity. Neurons are surrounded by an extracellular space whereby fluctuations in specific ionic concentration can modulate neuronal excitability. Extracellular concentrations of potassium ([K(+)](o)) can generate neuronal hyperexcitability. Yet, after many years of research, it is still unknown whether an elevation of potassium is the cause or the result of the generation, propagation and synchronization of epileptiform activity. An elevation of potassium in neural tissue can be characterized by dispersion (global elevation of potassium) and lateral diffusion (local spatial gradients). Both experimental and computational studies have shown that lateral diffusion is involved in the generation and the propagation of neural activity in diffusively coupled networks. Therefore, diffusion-based coupling by potassium can play an important role in neural networks and it is reviewed in four sections. Section 2 shows that potassium diffusion is responsible for the synchronization of activity across a mechanical cut in the tissue. A computer model of diffusive coupling shows that potassium diffusion can mediate communication between cells and generate abnormal and/or periodic activity in small (section sign 3) and in large networks of cells (section sign 4). Finally, in section sign 5, a study of the role of extracellular potassium in the propagation of axonal signals shows that elevated potassium concentration can block the propagation of neural activity in axonal pathways. Taken together, these results indicate that potassium accumulation and diffusion can interfere with normal activity and generate abnormal activity in neural networks.

Modeling action potential generation during single and dual electrode stimulation of CA3 axons in hippocampal slice

Despite widespread use of electrical stimulation of hippocampal brain slices, the precise sites of action potential initiation and propagation are unknown. To better understand these sites, we modeled axon recruitment by coupling stimulation-induced electric potential fields to biophysical models of CA3 axon arbors in mouse hippocampal brain slices. Geometrically realistic CA3 axon arbors were generated from prior anatomic observations. For single electrode stimulation, 95% of initiation sites were no further than 135microm away and propagation sites were no further than 875microm. Using dual electrode stimulation, additional axon arbor pieces were recruited, an effect that increased with distance between stimulating electrodes.

High frequency stimulation can block axonal conduction

High frequency stimulation (HFS) is used to control abnormal neuronal activity associated with movement, seizure, and psychiatric disorders. Yet, the mechanisms of its therapeutic action are not known. Although experimental results have shown that HFS suppresses somatic activity, other data has suggested that HFS could generate excitation of axons. Moreover it is unclear what effect the stimulation has on tissue surrounding the stimulation electrode. Electrophysiological and computational modeling literature suggests that HFS can drive axons at the stimulus frequency. Therefore, we tested the hypothesis that unlike cell bodies, axons are driven by pulse train HFS. This hypothesis was tested in fibers of the hippocampus both in-vivo and in-vitro. Our results indicate that although electrical stimulation could activate and drive axons at low frequencies (0.5-25 Hz), as the stimulus frequency increased, electrical stimulation failed to continuously excite axonal activity. Fiber tracts were unable to follow extracellular pulse trains above 50 Hz in-vitro and above 125 Hz in-vivo. The number of cycles required for failure was frequency dependent but independent of stimulus amplitude. A novel in-vitro preparation was developed, in which, the alveus was isolated from the remainder of the hippocampus slice. The isolated fiber tract was unable to follow pulse trains above 75 Hz. Reversible conduction block occurred at much higher stimulus amplitudes, with pulse train HFS (>150 Hz) preventing propagation through the site of stimulation. This study shows that pulse train HFS affects axonal activity by: (1) disrupting HFS evoked excitation leading to partial conduction block of activity through the site of HFS; and (2) generating complete conduction block of secondary evoked activity, as HFS amplitude is increased. These results are relevant for the interpretation of the effects of HFS for the control of abnormal neural activity such as epilepsy and Parkinson's disease.