Advertisement

A theoretical framework for the site-specific and frequency-dependent neuronal effects of deep brain stimulation

  • Luka Milosevic
    Correspondence
    Corresponding author. 399 Bathurst St, Room11MP301, Toronto, ON, M5T 2S8, Canada.
    Affiliations
    Krembil Brain Institute, University Health Network, Toronto, Canada

    Institute of Biomedical Engineering, University of Toronto, Toronto, Canada

    KITE, Toronto Rehabilitation Institute, University Health Network, Toronto, Canada

    CRANIA, University Health Network and University of Toronto, Toronto, Canada
    Search for articles by this author
  • Suneil K. Kalia
    Affiliations
    Krembil Brain Institute, University Health Network, Toronto, Canada

    KITE, Toronto Rehabilitation Institute, University Health Network, Toronto, Canada

    CRANIA, University Health Network and University of Toronto, Toronto, Canada

    Division of Neurosurgery, Toronto Western Hospital, University Health Network, Toronto, Canada

    Department of Surgery, University of Toronto, Toronto, Canada
    Search for articles by this author
  • Mojgan Hodaie
    Affiliations
    Krembil Brain Institute, University Health Network, Toronto, Canada

    CRANIA, University Health Network and University of Toronto, Toronto, Canada

    Division of Neurosurgery, Toronto Western Hospital, University Health Network, Toronto, Canada

    Department of Surgery, University of Toronto, Toronto, Canada
    Search for articles by this author
  • Andres M. Lozano
    Affiliations
    Krembil Brain Institute, University Health Network, Toronto, Canada

    CRANIA, University Health Network and University of Toronto, Toronto, Canada

    Division of Neurosurgery, Toronto Western Hospital, University Health Network, Toronto, Canada

    Department of Surgery, University of Toronto, Toronto, Canada
    Search for articles by this author
  • Milos R. Popovic
    Affiliations
    Institute of Biomedical Engineering, University of Toronto, Toronto, Canada

    KITE, Toronto Rehabilitation Institute, University Health Network, Toronto, Canada

    CRANIA, University Health Network and University of Toronto, Toronto, Canada
    Search for articles by this author
  • Author Footnotes
    1 indicates equal contributions.
    William D. Hutchison
    Footnotes
    1 indicates equal contributions.
    Affiliations
    CRANIA, University Health Network and University of Toronto, Toronto, Canada

    Department of Surgery, University of Toronto, Toronto, Canada

    Department of Physiology, University of Toronto, Toronto, Canada
    Search for articles by this author
  • Author Footnotes
    1 indicates equal contributions.
    Milad Lankarany
    Footnotes
    1 indicates equal contributions.
    Affiliations
    Krembil Brain Institute, University Health Network, Toronto, Canada

    Institute of Biomedical Engineering, University of Toronto, Toronto, Canada

    KITE, Toronto Rehabilitation Institute, University Health Network, Toronto, Canada
    Search for articles by this author
  • Author Footnotes
    1 indicates equal contributions.
Open AccessPublished:May 11, 2021DOI:https://doi.org/10.1016/j.brs.2021.04.022

      Highlights

      • Extracellular stimulation is brain-region-specific and frequency-dependent.
      • Neuronal stimulus responses were excitatory in thalamus & inhibitory in basal ganglia.
      • High-frequency stimulation led to neuronal suppression/a loss of site-specificity.
      • Responses to single stimuli could be predicted based on anatomy/local microcircuitry.
      • Frequency-dependant neuronal suppression could be modelled by synaptic depression.

      Abstract

      Background

      Deep brain stimulation is an established therapy for several neurological disorders; however, its effects on neuronal activity vary across brain regions and depend on stimulation settings. Understanding these variable responses can aid in the development of physiologically-informed stimulation paradigms in existing or prospective indications.

      Objective

      Provide experimental and computational insights into the brain-region-specific and frequency-dependent effects of extracellular stimulation on neuronal activity.

      Methods

      In patients with movement disorders, single-neuron recordings were acquired from the subthalamic nucleus, substantia nigra pars reticulata, ventral intermediate nucleus, or reticular thalamus during microstimulation across various frequencies (1–100 Hz) to assess single-pulse and frequency-response functions. Moreover, a biophysically-realistic computational framework was developed which generated postsynaptic responses under the assumption that electrical stimuli simultaneously activated all convergent presynaptic inputs to stimulation target neurons. The framework took into consideration the relative distributions of excitatory/inhibitory afferent inputs to model site-specific responses, which were in turn embedded within a model of short-term synaptic plasticity to account for stimulation frequency-dependence.

      Results

      We demonstrated microstimulation-evoked excitatory neuronal responses in thalamic structures (which have predominantly excitatory inputs) and inhibitory responses in basal ganglia structures (predominantly inhibitory inputs); however, higher stimulation frequencies led to a loss of site-specificity and convergence towards neuronal suppression. The model confirmed that site-specific responses could be simulated by accounting for local neuroanatomical/microcircuit properties, while suppression of neuronal activity during high-frequency stimulation was mediated by short-term synaptic depression.

      Conclusions

      Brain-region-specific and frequency-dependant neuronal responses could be simulated by considering neuroanatomical (local microcircuitry) and neurophysiological (short-term plasticity) properties.

      Keywords

      Abbreviations:

      deep brain stimulation ((DBS)), gamma aminobutyric acid ((GABA)), globus pallidus externus ((GPe)), globus pallidus internus ((GPi)), high-frequency stimulation ((HFS)), leaky integrate and fire ((LIF)), Ornstein-Uhlenbeck ((OU)), substantia nigra pars reticulata ((SNr)), subthalamic nucleus ((STN)), thalamic reticular nucleus ((Rt)), Tsodyks-Markram ((TM)), ventral intermediate nuclues ((Vim))

      Introduction

      Deep brain stimulation (DBS) is an established neuromodulatory therapy for several movement disorders [
      • Limousin P.
      • Krack P.
      • Pollak P.
      • Benazzouz A.
      • Ardouin C.
      • Hoffmann D.
      • et al.
      Electrical stimulation of the subthalamic nucleus in advanced Parkinson's disease.
      ,
      • Dallapiazza R.F.
      • Lee D.J.
      • Vloo P.D.
      • Fomenko A.
      • Hamani C.
      • Hodaie M.
      • et al.
      Outcomes from stereotactic surgery for essential tremor.
      ,
      • Hung S.W.
      • Hamani C.
      • Lozano A.M.
      • Poon Y.-Y.W.
      • Piboolnurak P.
      • Miyasaki J.M.
      • et al.
      Long-term outcome of bilateral pallidal deep brain stimulation for primary cervical dystonia.
      ] and has recently received approvals for the treatment of obsessive-compulsive disorder [
      • Menchón J.M.
      • Real E.
      • Alonso P.
      • Aparicio M.A.
      • Segalas C.
      • Plans G.
      • et al.
      A prospective international multi-center study on safety and efficacy of deep brain stimulation for resistant obsessive-compulsive disorder.
      ] and epilepsy [
      • Fisher R.
      • Salanova V.
      • Witt T.
      • Worth R.
      • Henry T.
      • Gross R.
      • et al.
      Electrical stimulation of the anterior nucleus of thalamus for treatment of refractory epilepsy.
      ]. Despite a rapidly growing interest in the development of new DBS indications [
      • Youngerman B.E.
      • Chan A.K.
      • Mikell C.B.
      • McKhann G.M.
      • Sheth S.A.
      A decade of emerging indications: deep brain stimulation in the United States.
      ], the effects of DBS on neuronal activity are not fully understood and neural responses evoked by electrical stimulation have been shown to differ across stimulation targets [
      • Basu I.
      • Robertson M.M.
      • Crocker B.
      • Peled N.
      • Farnes K.
      • Vallejo-Lopez D.I.
      • et al.
      Consistent linear and non-linear responses to invasive electrical brain stimulation across individuals and primate species with implanted electrodes.
      ]. As such, the objective of this study was to use microelectrode recordings and stimulation to demonstrate how the neuronal effects of pulsatile stimulation vary depending on the stimulation target region and the frequency of stimulation pulses being delivered. Knowledge of the site-specific and frequency-dependent ability to selectively modulate (e.g. upregulate or downregulate) neuronal output is of importance for stimulation programming and the development of physiologically-informed stimulation paradigms in existing or prospective DBS indications; and can allow the user to leverage DBS in a functionally-specific manner.
      It was previously demonstrated that single pulses of electrical stimulation to the substantia nigra pars reticulata (SNr) or globus pallidus internus (GPi) were associated with stimulation-evoked inhibitory responses, likely mediated by local GABA release [
      • Dostrovsky J.O.
      • Levy R.
      • Wu J.P.
      • Hutchison W.D.
      • Tasker R.R.
      • Lozano A.M.
      Microstimulation-induced inhibition of neuronal firing in human globus pallidus.
      ,
      • Liu L.D.
      • Prescott I.A.
      • Dostrovsky J.O.
      • Hodaie M.
      • Lozano A.M.
      • Hutchison W.D.
      Frequency-dependent effects of electrical stimulation in the globus pallidus of dystonia patients.
      ,
      • Milosevic L.
      • Kalia S.K.
      • Hodaie M.
      • Lozano A.M.
      • Fasano A.
      • Popovic M.R.
      • et al.
      Neuronal inhibition and synaptic plasticity of basal ganglia neurons in Parkinson's disease.
      ]. High-frequency stimulation (HFS) of the thalamic ventral intermediate nucleus (Vim) on the other hand elicited brief short-latency excitatory responses, likely the result of unsustained local glutamate release [
      • Milosevic L.
      • Kalia S.K.
      • Hodaie M.
      • Lozano A.M.
      • Popovic M.R.
      • Hutchison W.D.
      Physiological mechanisms of thalamic ventral intermediate nucleus stimulation for tremor suppression.
      ]. In this study, microelectrode recordings of single-neuron activity across four brain regions (Vim, thalamic reticular nucleus (Rt), subthalamic nucleus (STN), and SNr) were assessed during microstimulation across a range of frequencies. We hypothesized that (i) the effects of individual electrical stimulation pulses would vary with respect to the distribution of afferent inputs converging on target neurons (whether predominantly inhibitory or excitatory), and that based on these local neuroanatomical properties, stimulation pulses would elicit either net inhibitory or excitatory responses. Moreover, based on previous findings of HFS-induced depression of stimulus-evoked field potentials [
      • Liu L.D.
      • Prescott I.A.
      • Dostrovsky J.O.
      • Hodaie M.
      • Lozano A.M.
      • Hutchison W.D.
      Frequency-dependent effects of electrical stimulation in the globus pallidus of dystonia patients.
      ,
      • Milosevic L.
      • Kalia S.K.
      • Hodaie M.
      • Lozano A.M.
      • Fasano A.
      • Popovic M.R.
      • et al.
      Neuronal inhibition and synaptic plasticity of basal ganglia neurons in Parkinson's disease.
      ,
      • Steiner L.A.
      • Tomás F.J.B.
      • Planert H.
      • Alle H.
      • Vida I.
      • Geiger J.R.P.
      Connectivity and dynamics underlying synaptic control of the subthalamic nucleus.
      ], we hypothesized that (ii) suppression of neuronal activity during HFS is mediated by changes in short-term synaptic dynamics (i.e. depression of inhibitory and excitatory synaptic transmission).
      In addition to experimental procedures, we developed a computational framework for modelling the site-specific and frequency-dependent neuronal responses to electrical stimulation based on the above hypotheses. Previous theoretical works suggest that individual pulses of extracellular stimulation (i.e. DBS) initiate action potentials which are propagated along axons and/or their terminals [
      • Anderson R.W.
      • Farokhniaee A.
      • Gunalan K.
      • Howell B.
      • McIntyre C.C.
      Action potential initiation, propagation, and cortical invasion in the hyperdirect pathway during subthalamic deep brain stimulation.
      ,
      • McIntyre C.C.
      • Grill W.M.
      • Sherman D.L.
      • Thakor N.V.
      Cellular effects of deep brain stimulation: model-based analysis of activation and inhibition.
      ,
      • Jakobs M.
      • Fomenko A.
      • Lozano A.M.
      • Kiening K.L.
      Cellular, molecular, and clinical mechanisms of action of deep brain stimulation—a systematic review on established indications and outlook on future developments.
      ,
      • Bower K.L.
      • McIntyre C.C.
      Deep brain stimulation of terminating axons.
      ]. These axonal activations can in turn mediate synaptic transmission. Based on our first hypothesis, our computational framework considers that the postsynaptic neuronal responses to individual DBS pulses are the result of a simultaneous activation of presynaptic inputs and takes into consideration the site-specific proportions of inhibitory and excitatory inputs converging on target neurons (derived from anatomical literature). However, HFS may reduce synaptic transmission fidelity by way of synaptic depression [
      • Farokhniaee A.
      • McIntyre C.C.
      Theoretical principles of deep brain stimulation induced synaptic suppression.
      ] or axonal failure [
      • Rosenbaum R.
      • Zimnik A.
      • Zheng F.
      • Turner R.S.
      • Alzheimer C.
      • Doiron B.
      • et al.
      Axonal and synaptic failure suppress the transfer of firing rate oscillations, synchrony and information during high frequency deep brain stimulation.
      ]. Thus, in accordance with our second hypothesis, the Tsodyks-Markram (TM) model [
      • Tsodyks M.V.
      • Markram H.
      The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability.
      ] of short-term synaptic plasticity was embedded within our computational framework in order to account for changes to synaptic transmission fidelity based on the frequency of successive stimuli.

      Methods

      Experimental: Patients and neurons

      115 neurons from patients with Parkinson's disease (n = 47) or essential tremor (n = 11) were included in this study. All experiments conformed to the guidelines set by the Tri-Council Policy on Ethical Conduct for Research Involving Humans and were approved by the University Health Network Research Ethics Board. Moreover, each patient provided written informed consent prior to taking part in the studies.

      Experimental: Protocols

      Neurophysiological mapping procedures were performed during awake DBS surgeries (OFF-medication) using two closely spaced microelectrodes (600 μm apart, 0.1–0.4 MΩ impedances) [
      • Levy R.
      • Lozano A.M.
      • Hutchison W.D.
      • Dostrovsky J.O.
      Dual microelectrode technique for deep brain stereotactic surgery in humans.
      ]. Techniques for identification of Rt, STN, SNr [
      • Hutchison W.D.
      • Allan R.J.
      • Opitz H.
      • Levy R.
      • Dostrovsky J.O.
      • Lang A.E.
      • et al.
      Neurophysiological identification of the subthalamic nucleus in surgery for Parkinson's disease.
      ], and Vim [
      • Milosevic L.
      • Kalia S.K.
      • Hodaie M.
      • Lozano A.M.
      • Popovic M.R.
      • Hutchison W.D.
      Physiological mechanisms of thalamic ventral intermediate nucleus stimulation for tremor suppression.
      ,
      • Basha D.
      • Dostrovsky J.O.
      • Lopez Rios A.L.
      • Hodaie M.
      • Lozano A.M.
      • Hutchison W.D.
      Beta oscillatory neurons in the motor thalamus of movement disorder and pain patients.
      ] neurons have been previously reported. One microelectrode was used for recording single-neuron activity while a second immediately adjacent microelectrode was used to deliver stimulation at different frequencies. Recordings were obtained using two Guideline System GS3000 amplifiers (Axon Instruments, Union City, CA) and signals were digitized at ≥12.5 kHz with a CED 1401 data acquisition system (Cambridge Electronic Design, Cambridge, UK). Microstimulation was delivered using an isolated constant-current stimulator (Neuro-Amp1A, Axon Instruments, Union City, CA) with 0.3 ms biphasic pulses (cathodal followed by anodal).
      To generate stimulation frequency response functions, stimulation trains were delivered at 1 Hz (10 pulses), 2 Hz (20 pulses), 3 Hz (60 pulses), 5 Hz (50 pulses), 10 Hz (50 pulses), 20 Hz (60 pulses), 30 Hz (60 pulses), 50 Hz (50 pulses), and 100 Hz (50 pulses) using 100 μA and a 0.3 ms biphasic pulse width. This frequency response protocol was executed at 9 Vim (npatients = 5), 11 Rt (npatients = 11), 27 STN (npatients = 16), and 14 SNr (npatients = 9) recording sites. Data for STN and SNr were previously collected [
      • Milosevic L.
      • Kalia S.K.
      • Hodaie M.
      • Lozano A.M.
      • Fasano A.
      • Popovic M.R.
      • et al.
      Neuronal inhibition and synaptic plasticity of basal ganglia neurons in Parkinson's disease.
      ], whereas Vim and Rt data for this study were unique. Longer trains (>2 s) of 100Hz stimulation were also delivered to the aforementioned Vim, Rt, and SNr neurons. 100 Hz long train data for STN (44 neurons, npatients = 20) were previously collected [
      • Milosevic L.
      • Kalia S.K.
      • Hodaie M.
      • Lozano A.
      • Popovic M.R.
      • Hutchison W.
      Subthalamic suppression defines therapeutic threshold of deep brain stimulation in Parkinson's disease.
      ], as were a subset of 100 Hz and 200 Hz Vim (10 recording sites, npatients = 8) data [
      • Milosevic L.
      • Kalia S.K.
      • Hodaie M.
      • Lozano A.M.
      • Popovic M.R.
      • Hutchison W.D.
      Physiological mechanisms of thalamic ventral intermediate nucleus stimulation for tremor suppression.
      ]. Please refer to Supplementary Table 6 for data summary.

      Experimental: Offline analyses and statistics

      For artifact removal, data from the start of each stimulation artifact to just after the anodic peak (i.e. from the anodic peak or last saturated value to about 25% of the baseline amplitude) were replaced by a straight line; corresponding to a time window of ∼0.8 ms. Data were then high pass filtered (≥250 Hz) and template matching was done using a principal component analysis method in Spike2 (Cambridge Electronic Design, UK). Artifact subtraction allowed for data to be high-pass filtered without distortion in the time domain as would otherwise occur when filtering a signal containing saturated high-amplitude stimulation artifacts [
      • Bar-Gad I.
      • Elias S.
      • Vaadia E.
      • Bergman H.
      Complex locking rather than complete cessation of neuronal activity in the globus pallidus of a 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine-treated primate in response to pallidal microstimulation.
      ]. As a single action potential is ≥ 1 ms, then at most one action potential might be lost in the <1 ms artifact subtraction process. With a 0.8 ms artifact removal window, the percentage of data lost during each stimulation train corresponds to: 0.08% (1Hz), 0.16% (2Hz); 0.24% (3Hz); 0.4% (5Hz); 0.8% (10Hz); 1.6% (20Hz); 2.4% (30Hz); 4% (50Hz); 8% (100Hz). To investigate single-pulses responses, peristimulus histograms (120 ms total width, 20 ms offset, 2 ms bins) were created to encompass responses to all 50 stimuli delivered during the 5Hz train, across all neurons. The 20 ms pre-stimulus periods were compared to the 20 ms and 40 ms post-stimulus periods using Bonferroni-corrected (two comparisons) two-tailed paired t-tests, and effect sizes (Cohen's dz) were calculated. For the frequency response protocol (≤60 stimulation pulses delivered at each frequency), firing rates were measured before and during each of the stimulation trains. Kolmogorov-Smirnov tests were used to assess the null hypothesis that the data are normally distributed. One-way repeated measures ANOVA tests (stimulation frequency as a within-subject factor) were carried out, and if significant main effects were found, Bonferroni-corrected (nine comparisons) post-hoc t-tests were used to compare firing rates during the various stimulation trains to pre-stimulation baseline firing. ANOVA effect sizes (η2) and t-test effect sizes (Cohen's dz) were also determined. One neuron from the Vim group and one neuron from the Rt group were excluded from statistical analyses due to incomplete stimulation protocol (i.e. missing data points). Of note, the solid gray lines in Fig. 1B consider that each stimulation pulse generated one action potential on the efferent axon [
      • McIntyre C.C.
      • Savasta M.
      • Kerkerian-Le Goff L.
      • Vitek J.L.
      Uncovering the mechanism(s) of action of deep brain stimulation: activation, inhibition, or both.
      ], representing a situation in which the overall “neuronal output” is the summation of the somatic firing rate and a stimulus-locked efferent axon activation. However, readers should note that the statistical analyses only consider the action potential firing during periods of time that were not populated by artifacts (i.e. the activity generated at the somatic level). ANOVA analyses were carried out in the same way for both experimental (Fig. 1B) and computational (Fig. 8) results. To investigate possible time-varying responses throughout the stimulation trains, time-series histograms (2–3 s total width, no offset, 50 ms bins) were created for 5 Hz, 10 Hz, 20 Hz, 30 Hz, and long trains of 100 Hz (and 200 Hz long trains for Vim). Of note, the long train (i.e. 3 s) 100 Hz (and 200 Hz) data come from various sources since long trains of high-frequency stimulation were not initially delivered (please refer to Supplementary Table 6 for data summary). The attenuations of excitation over time in Vim and Rt during stimulation trains of ≥20 Hz were fit with double exponential functions. Histograms were also created for the shorter trains (≤1 s) of stimulation at 50 Hz and 100 Hz (0.5–1 s total width, no offset, 20 ms bins; Supplementary Fig. 1). Moreover, to investigate the prominent time-vary effects in Vim and Rt during 3 s, 100 Hz and 200 Hz stimulation trains, baseline firing was compared to the first second of stimulation and the subsequent 2 s of stimulation using Bonferroni-corrected (two comparisons) two-tailed paired t-tests.
      Fig. 1
      Fig. 1Experimental (A) peristimulus responses and (B) frequency response functions. (A) Top panels show an exemplary response to a single stimulation pulse in each structure, whereas bottom panels show groupwise firing rate (mean + standard error) peristimulus time histograms of stimulus-evoked excitatory responses for Vim (n = 9) and Rt (n = 11) and stimulus-evoked inhibitory responses for STN (n = 27) and SNr (n = 14). The average firing rates of the immediate 20 ms and 40 ms periods following stimulations pulses were significantly greater than the 20 ms pre-stimulus periods for Vim and Rt, and significantly lesser for STN and SNr (p-values of Bonferonni-corrected 2-tailed paired t-test are displayed with Cohen's dz effect sizes in parentheses). (B) Stimulation (≤60 pulses) frequency response functions show that average firing rates progressively increased in Vim and Rt as the stimulation frequency became greater, while they progressively decreased in STN and SNr. The average ± standard error baseline firing rates for Vim, Rt, STN, and SNr neurons were 32.0 ± 11 Hz, 8.2 ± 1 Hz, 39.9 ± 3 Hz, and 102.3 ± 16 Hz, respectively (dashed gray lines). Firing rates during the various stimulation trains were compared to the baseline firing rates and the p-values of Bonferroni-corrected post-hoc t-tests (2-tailed, paired) are displayed with Cohen's dz effect sizes in parentheses. ANOVA main effects for stimulation were all significant and are reported in the Results subsection “Experimental: Stimulation frequency response functions”. If one considers that each DBS pulse generates an action potential on the efferent axon, then the overall neuronal output would be the summation of the somatic firing rate and stimulation frequency; this is represented by the solid gray lines in each plot (the values on this line for 100 Hz in Vim, Rt, and STN are 100 (Hz) plus the value on the corresponding coloured line). The right anatomical panels are 12.0 mm and 14.5 mm sagittal sections (Supplementary shows the locations of the highlighted structures relative to other neuroanatomical landmarks).

      Computational: Model framework

      To model the effect of DBS pulses on the afferents of the stimulated nuclei, we used a leaky integrate and fire (LIF) single neuron model, together with a TM model of short-term synaptic plasticity [
      • Tsodyks M.
      • Pawelzik K.
      • Markram H.
      Neural networks with dynamic synapses.
      ]. Each model neuron received 500 presynaptic inputs and the proportion of excitatory and inhibitory inputs were obtained using morphological data (detailed below in “Computational: Presynaptic inputs”). In addition to these inputs, the background synaptic activity [
      • Destexhe A.
      • Rudolph M.
      • Fellous J.-M.
      • Sejnowski T.J.
      Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons.
      ] was modelled by an Ornstein-Uhlenbeck (OU) process and added to the model neuron to reproduce the impact of synaptic noise that exists in vivo [
      • Destexhe A.
      • Rudolph M.
      • Fellous J.-M.
      • Sejnowski T.J.
      Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons.
      ,
      • Destexhe A.
      • Rudolph M.
      • Paré D.
      The high-conductance state of neocortical neurons in vivo.
      ]. In accordance with our first hypothesis, each DBS single pulse simultaneously activated all presynaptic inputs (Fig. 3A). This simultaneous activation was modelled by artificially generating precise spike times which correspond to the arrival of each DBS pulse in the presynaptic inputs. We utilized our modeling framework to recreate the neuronal firing in Vim, STN, and SNr in response to stimulation trains with frequencies of 1, 2, 5, 10, 20, 30, 50, and 100 Hz. Model generation for Rt neurons was omitted to avoid redundancy since the model parameters are identical to Vim except for the parameters which underly the baseline firing rates (this is elaborated upon in detail within the “Computational: Parameter settings” subsection below).

      Computational: Presynaptic inputs

      The vast majority of inputs to the Vim are glutamatergic projections from the dentate nucleus of the cerebellum [
      • Asanuma C.
      • Thach W.T.
      • Jones E.G.
      Distribution of cerebellar terminations and their relation to other afferent terminations in the ventral lateral thalamic region of the monkey.
      ,
      • Kultas-Ilinsky K.
      • Ilinsky I.A.
      Fine structure of the ventral lateral nucleus (VL) of the Macaca mulatta thalamus: cell types and synaptology.
      ,
      • Ilinsky I.A.
      • Kultas-Ilinsky K.
      Motor thalamic circuits in primates with emphasis on the area targeted in treatment of movement disorders.
      ,
      • Kuramoto E.
      • Fujiyama F.
      • Nakamura K.C.
      • Tanaka Y.
      • Hioki H.
      • Kaneko T.
      Complementary distribution of glutamatergic cerebellar and GABAergic basal ganglia afferents to the rat motor thalamic nuclei.
      ] and reciprocal connections from cerebral cortex [
      • Stepniewska I.
      • Preuss T.M.
      • Kaas J.H.
      Thalamic connections of the primary motor cortex (M1) of owl monkeys.
      ,
      • Kakei S.
      • Na J.
      • Shinoda Y.
      Thalamic terminal morphology and distribution of single corticothalamic axons originating from layers 5 and 6 of the cat motor cortex.
      ], with less prominent inputs coming via inhibitory Rt projections [
      • Kuramoto E.
      • Fujiyama F.
      • Nakamura K.C.
      • Tanaka Y.
      • Hioki H.
      • Kaneko T.
      Complementary distribution of glutamatergic cerebellar and GABAergic basal ganglia afferents to the rat motor thalamic nuclei.
      ,
      • Ambardekar A.V.
      • Ilinsky I.A.
      • Froestl W.
      • Bowery N.G.
      • Kultas-Ilinsky K.
      Distribution and properties of GABAB antagonist [3H]CGP 62349 binding in the rhesus monkey thalamus and basal ganglia and the influence of lesions in the reticular thalamic nucleus.
      ,
      • Ilinsky I.A.
      • Ambardekar A.V.
      • Kultas-Ilinsky K.
      Organization of projections from the anterior pole of the nucleus reticularis thalami (NRT) to subdivisions of the motor thalamus: light and electron microscopic studies in the Rhesus monkey.
      ]. The Rt is a thin sheet of neurons that forms a shell around the lateral and anterior borders of the dorsal, and to some extent ventral thalamus [
      • Jones E.G.
      Some aspects of the organization of the thalamic reticular complex.
      ]. It is primarily innervated by collateral branches of glutamatergic thalamocortical and corticothalamic projections [
      • Jones E.G.
      Some aspects of the organization of the thalamic reticular complex.
      ,
      • Crabtree J.W.
      The somatotopic organization within the cat's thalamic reticular nucleus.
      ,
      • Crabtree J.W.
      The somatotopic organization within the rabbit's thalamic reticular nucleus.
      ,
      • Gonzalo-Ruiz A.
      • Lieberman A.R.
      GABAergic projections from the thalamic reticular nucleus to the anteroventral and anterodorsal thalamic nuclei of the rat.
      ,
      • Pinault D.
      The thalamic reticular nucleus: structure, function and concept.
      ], but also receives less prominent GABAergic innervation from the GPe and SNr [
      • Paré D.
      • Hazrati L.-N.
      • Parent A.
      • Steriade M.
      Substantia nigra pars reticulata projects to the reticular thalamic nucleus of the cat: a morphological and electrophysiological study.
      ,
      • Hazrati L.-N.
      • Parent A.
      Projection from the external pallidum to the reticular thalamic nucleus in the squirrel monkey.
      ,
      • Asanuma C.
      GABAergic and pallidal terminals in the thalamic reticular nucleus of squirrel monkeys.
      ]; like Vim, the majority of afferent inputs to Rt are glutamatergic. The vast majority (∼90%) of inputs to the SNr are GABAergic, projecting from the striatum and globus pallidus externus (GPe) [
      • Parent A.
      • Hazrati L.-N.
      Functional anatomy of the basal ganglia. II. The place of subthalamic nucleus and external pallidium in basal ganglia circuitry.
      ,
      • Bolam J.P.
      • Hanley J.J.
      • Booth P.a.C.
      • Bevan M.D.
      Synaptic organisation of the basal ganglia.
      ], whereas the STN receives a more homogenous convergence of GABAergic and glutamatergic inputs from the GPe [
      • Baufreton J.
      • Kirkham E.
      • Atherton J.F.
      • Menard A.
      • Magill P.J.
      • Bolam J.P.
      • et al.
      Sparse but selective and potent synaptic transmission from the globus pallidus to the subthalamic nucleus.
      ] and motor cortical areas [
      • Nambu A.
      • Tokuno H.
      • Takada M.
      Functional significance of the cortico–subthalamo–pallidal ‘hyperdirect’ pathway.
      ] respectively [
      • Parent A.
      • Hazrati L.-N.
      Functional anatomy of the basal ganglia. II. The place of subthalamic nucleus and external pallidium in basal ganglia circuitry.
      ,
      • Rinvik E.
      • Ottersen O.P.
      Terminals of subthalamonigral fibres are enriched with glutamate-like immunoreactivity: an electron microscopic, immunogold analysis in the cat.
      ]. While the mixed inputs are more homogenous in STN, electron-microscopy work suggests that GABAergic terminals nevertheless outnumber glutamatergic terminals [
      • Kita T.
      • Kita H.
      The subthalamic nucleus is one of multiple innervation sites for long-range corticofugal axons: a single-axon tracing study in the rat.
      ]. Based on the cited literature, estimates of the proportions of inhibitory and excitatory inputs were generated (Supplementary Table 1) to be used for the model.
      In the model, an ensemble of 500 LIF model neurons produced inputs to the stimulated nuclei. Each neuron received a random input (modelled by OU process of time constant 5 ms) and fired at the rate of about 5 Hz (the total average firing rate across neurons was equal to 5 ± 0.7 Hz). Each of the 500 neurons was labeled either as excitatory or inhibitory based upon estimates of the proportions of excitatory and inhibitory inputs received by Vim, STN, and SNr (Supplementary Table 1); and their spikes were fed to the stimulated nuclei through the TM model. We used an LIF neuron model (see Supplementary Tables 2 and 5 for the LIF parameters) to generate membrane potentials of the stimulated nuclei. The total synaptic current was obtained as a linear combination of presynaptic excitatory (Iexc) and inhibitory currents (Iinh):
      Isyn(t) = wexc Iexc(t) + winh Iinh(t)
      (1)


      where wexc and winh denote the weights of excitatory and inhibitory currents, respectively. These weights, together with the mean and standard deviation of the background synaptic current, were tuned to reproduce the neuronal firing rates at the baseline (DBS-OFF) as well as in response to DBS with different frequencies (Supplementary Table 2).

      Computational: Synapse model

      We utilized the TM equations to model the function of short-term synaptic plasticity:
      dudt=uτF+U(1u)δ(ttsp)
      (2)


      drdt=1rτDu+rδ(ttsp)
      (3)


      dIdt=Iτs+Au+rδ(ttsp)
      (4)


      where u indicates utilization probability, i.e., the probability of releasing neurotransmitters in synaptic cleft due to presynaptic influx of calcium ions. Upon the arrival of each presynaptic spike, tsp, u increases by U(1u)and then decays to zero by the facilitation time constant, τf. U denotes the increment of u produced by each presynaptic spike. A denotes the absolute synaptic efficacy of the synaptic connections. The vesicle depletion process – due to the release of neurotransmitters – was modelled by (2) where r denotes the fraction of available resources after neurotransmitter depletion. In contrast to the increase of u upon the arrival of each presynaptic spike, r drops and then recovers by depression time constant τD to its steady state value of 1. The competition between the depression (τD) and facilitation (τf) time constants determines the dynamics of the synapse. In the TM model, Uτf, and τD are three parameters that determine the type and dynamics of the synapse. In (4), I and τs indicate the presynaptic current and its time constant, respectively. The time constants of the excitatory and inhibitory inputs were 3 ms and 10 ms, respectively.

      Computational: Background synaptic activity

      Similar to Ref. [
      • Destexhe A.
      • Rudolph M.
      • Fellous J.-M.
      • Sejnowski T.J.
      Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons.
      ], we used OU process of the time constant of 5 ms to represent the effect of synaptic noise. The OU process can be written as:
      dxdt=x(t)μτ+a2τξ(t)
      (5)


      where ξ is a random number drawn from a Gaussian distribution with 0 average and unit variance. τ is the time constant, μ and α indicate the mean and standard deviation of variable x, respectively.

      Computational: Neuron model

      The membrane potential dynamics in an LIF model can be written as:
      dV(t)dt=(V(t)EL)+RIinj(t)τV
      (6)


      where EL = −70 mV, R = 1 MΩ, and τV = 10 ms. Iinj indicates the total injected current to the model neuron (i.e., Isyn plus background synaptic noise (5)). A spike occurspike occurs when V ≥ Vth, where Vth = - 40 mV and the reset voltage is −90 mV with an absolute refractory period of 1 ms.

      Computational: Parameter setting

      The proportions of excitatory and inhibitory neurons (Supplementary Table 1), total synaptic current (Supplementary Table 2), parameters of excitatory (Supplementary Table 3) and inhibitory (Supplementary Table 4) synapses, and time constants of membrane dynamics and synaptic currents (Supplementary Table 5) are available in the Supplementary Material. Of note, values were derived from previous experimental work for Supplementary Tables 3 and 4 [
      • Markram H.
      • Muller E.
      • Ramaswamy S.
      • Reimann M.W.
      • Abdellah M.
      • Sanchez C.A.
      • et al.
      Reconstruction and simulation of neocortical microcircuitry.
      ] as well as for Supplementary Table 5 [
      • Destexhe A.
      • Rudolph M.
      • Fellous J.-M.
      • Sejnowski T.J.
      Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons.
      ]; parameter setting for Supplementary Tables 1 and 2 are described above. Also, as previously mentioned, modelling of Rt was omitted due to redundancy as all parameters are identical to Vim except for the parameters which mediate the baseline firing rates (i.e. wexc and winh and parameters of background synaptic noise; Supplementary Table 2). Parameters for Rt modelling are nevertheless included within the Supplementary Tables.

      Resource availability

      Results

      Experimental: Responses to single stimulation pulses & stimulation frequency response functions

      The average ± standard error baseline firing rates for Vim, Rt, STN, and SNr neurons were 32.0 ± 11Hz, 8.2 ± 1Hz, 39.9 ± 3Hz, and 102.3 ± 16Hz, respectively. The responses to single stimulation pulses (Fig. 1A) showed stimulus-evoked excitatory responses for Vim and Rt, and inhibitory responses for STN and SNr. For Vim, the average firing rates of the immediate 20 ms (181.0Hz ± 33Hz; p = .002) and 40 ms (125.2 ± 25 Hz; p = .003) periods following stimulation pulses were significantly greater than the 20 ms pre-stimulus period. This was also the case for the 20 ms (186.2 ± 29Hz; p < .001) and 40 ms (120.8 ± 20Hz; p <. 001) post-stimulus periods for Rt. For STN, the average firing rates of the 20 ms (22.4 ± 3Hz; p <. 001) and 40 ms (32.6 ± 4Hz; p = .041) post-stimulus periods were significantly less than the 20 ms pre-stimulus period. This was also the case for the 20 ms (7.8 ± 3Hz; p < .001) and 40 ms (21.9 ± 7Hz; p = .003) post-stimulus periods for SNr. All statistics were corrected for multiple comparisons. Cohen's dz effect sizes are depicted in Fig. 1A.
      The stimulation frequency response functions (Fig. 1B) show excitatory responses for Vim and Rt, and inhibitory responses for STN and SNr. For Vim, neuronal firing rates progressively increased as the stimulation frequency became greater and a significant main effect of stimulation was found [F = 43.074 (9, 234), p < .001, η2 = 0.624]. Bonferroni-corrected t-tests revealed differences in neuronal firing compared to baseline at stimulation frequencies of 10 Hz (p = .038), 30 Hz (p = .041), and greater (p < .05). For Rt, neuronal firing rates also progressively increased as the stimulation frequency became greater and a significant main effect of stimulation was found [F = 31.170 (9, 117), p < .001, η2 = 0.706]. Statistically significant differences in neuronal firing compared to baseline were found at stimulation frequencies of 30Hz (p = .029) and greater (p < .05). For STN, neuronal firing rates were progressively attenuated as the stimulation frequency became greater and a significant main effect of stimulation was found [F = 26.420 (9, 91), p < .001, η2 = 0.746]. Statistically significant differences in neuronal firing compared to baseline were found at stimulation frequencies of 20 Hz (p = .029) and greater (p < .001). For SNr, neuronal firing rates also progressively attenuated as the stimulation frequency became greater and a significant main effect of stimulation was found [F = 25.890 (9, 63), p < .001, η2 = 0.787]. Statistically significant differences in neuronal firing compared to baseline were found at stimulation frequencies of 3 Hz (p < .05) and greater (p ≤ .01). Detailed post-hoc t-test statistics (all corrected for multiple comparisons within the text and figures) and Cohen's dz effect sizes are depicted in Fig. 1B.

      Experimental: Time-domain responses to stimulation

      In Vim and Rt, periodic excitatory responses were evident at 5 Hz and 10 Hz (Fig. 2). The strength of the excitatory responses attenuated over time during stimulation trains of ≥20 Hz and were modelled by double exponential decay functions (R2 values within Fig. 2). The time-series histograms for long train ≥100 Hz data (3 s) in Vim and Rt show particularly prominent time-varying responses. These stimulations elicited excitatory responses that were transient in nature and limited to start of stimulation. For Vim at 100Hz (3 s), the firing rate at baseline (41.1 ± 7 Hz) was different from the firing rate during the first 1 s of stimulation (94.8 ± 7 Hz; p = .004), but not for the subsequent 2 s of stimulation (45.4 ± 7 Hz). For Vim at 200 Hz (3 s), the firing rate at baseline (53.1 ± 8 Hz) was not different from the first 1 s of stimulation (35.9 ± 9 Hz; Fig. 2 depicts a very transient initial excitation followed by suppression) but was for the subsequent 2 s (14.0 ± 5 Hz; p = .002). For Rt at 100Hz (3 s), the firing rate at baseline (7.7 ± 1 Hz) was different from the first 1 s of stimulation (90.7 ± 14 Hz; p = .002), but not for the subsequent 2 s (4.3 ± 2 Hz). In SNr, periodic inhibitory responses were evident at 5 Hz and 10 Hz. In STN and SNr, there was an overall stationary neuronal suppressive effect with increasing frequency (rather than an effect which changed dynamically over time as was the case in Vim and Rt). Of note, the data in Fig. 2 for 5–30 Hz stimulation is the same as that presented in Fig. 1B, while the 100 Hz (and 200 Hz) data in Fig. 2 come from various sources since long trains of high-frequency stimulation were not initially delivered (please refer to Supplementary Table 6 for data summary).
      Fig. 2
      Fig. 2Experimental time-domain responses to stimulation trains. For Vim and Rt, firing rates (mean +standard error) progressively increased with increasing stimulation frequencies. Periodic excitatory responses are shown at 5 Hz and 10 Hz, however neuronal excitation declined over time with ≥20 Hz. Excitatory responses with 100 Hz long trains (≥2s) were transient, and a subsequent reduction of neuronal firing is evident after the initial excitation. In Vim, the initial excitatory response at 200 Hz is of shorter duration than at 100 Hz, and the subsequent neuronal suppressive response is stronger at 200 Hz compared to 100 Hz. In STN and SNr, firing rates progressively decreased with increasing stimulation frequencies. In SNr, periodic inhibitory responses are visible at 5 and 10 Hz. Exemplary firing rate raster data from each structure during the various stimulation trains are displayed above each of the panels. This figure is intended to demonstrate the dynamics of the firing rate as a function of time. Of note, the 100 Hz (and 200 Hz) data herein are different than the data presented in B (please refer to Supplementary for data summary).
      Fig. 3
      Fig. 3Computational (A) model framework and (B) simulated peristimulus responses. (A) To model the response to single pulses of electrical stimulation, each model neuron was assigned a certain proportion of excitatory and inhibitory presynaptic inputs/weights with proportions derived from anatomical literature. The effect of each DBS single pulse was modelled by simultaneously activating all presynaptic inputs. (B) The corresponding changes to (i) synaptic currents and (ii) somatic firing induced by the simultaneous activations are displayed (i.e. the single-pulse responses). This framework closely replicated the robust stimulus-evoked neuronal excitation in Vim and neuronal inhibition in SNr. In STN, there was a short-latency neuronal excitation which was not observed in the experimental data (though may have been occluded by the stimulation artifact) due to the high speed of excitatory synaptic transmission, followed by an inhibitory period congruent with the experimental data. F: facilitatory; D: depressive; P: pseudolinear; indicating the different types of synapses.

      Computational: Responses to single stimulation pulses

      The net changes to postsynaptic currents in response to single pulses of stimulation were modelled by simultaneous activations of all presynaptic inputs (Fig. 3Bi). These responses differed across brain regions due to differences in the proportions of excitatory and inhibitory inputs (summarized in the Methods subsection “Computational: Presynaptic inputs” and Supplementary Table 1). The simulated peristimulus firing rate histograms (i.e. the neuronal responses to the aforementioned changes to presynaptic currents) revealed stimulus-evoked excitatory responses for Vim (peak firing rate of 405.9 Hz vs. 245.1 Hz in the experimental data), inhibitory responses for SNr (minimum firing rate of 0 Hz vs. 0.7 Hz in the experimental data), and a short-latency excitatory responses (78.8 Hz peak vs. no peak in the experimental data) followed by a longer latency inhibitory response (8.4 Hz trough vs. 4.8 Hz in the experimental data) for STN (Fig. 3Bii). The lack of short-latency excitation in the experimental data for STN might be explained by discrepancies in the temporal dynamics of excitatory transmission and/or occlusion of the excitatory response by the stimulus artifact.

      Computational: Time-domain synaptic currents

      Excitatory and inhibitory synaptic currents were generated separately, along with the net (i.e. sum of excitatory and inhibitory) synaptic currents in responses to DBS pulses across a range of frequencies for each of Vim, STN, and SNr (Fig. 4). The TM model accounts for frequency-dependent changes to short-term synaptic dynamics. In all structures, the model suggests frequency-dependent depression of both excitatory and inhibitory synaptic currents. For Vim, sustained periodic excitations were seen with 5 Hz and 10 Hz, while frequency-dependent weakening of the excitatory responses with successive stimuli were observed with frequencies ≥20 Hz. Predominant inhibitory synaptic currents corroborate the strong inhibitions of somatic firing in SNr with low stimulation frequencies; whereas neuronal suppression with higher frequencies was likely the result of frequency-dependent synaptic depression. For STN, the mixed excitatory-inhibitory stimulus-evoked responses likely explain the more net-neutral somatic firing responses in experimental data with lower stimulation frequencies; whereas synaptic depression can explain the frequency-dependent suppression of somatic firing with higher stimulation frequencies.
      Fig. 4
      Fig. 4Computational time-domain synaptic currents. The three figures show excitatory, inhibitory, and total (i.e. sum of excitatory and inhibitory) synaptic currents in responses to DBS pulses across a range of frequencies with an embedded TM model to account for short-term synaptic dynamics. In all cases, the model suggests frequency-dependent depression of both excitatory and inhibitory synaptic currents. For Vim, rather stable periodic excitations are seen with 5 Hz and 10 Hz. Also corroborating experimental data, frequency-dependent weakening of the excitatory responses is observed with frequencies ≥20 Hz. Predominant inhibitory synaptic currents corroborate the strong inhibitions of somatic firing in SNr, together with frequency-dependent synaptic depression. For STN, the mixed excitatory-inhibitory stimulus-evoked responses likely explain the more net-neutral somatic firing responses in experimental data with lower stimulation frequencies, while synaptic depression can explain frequency-dependent suppression of somatic firing.

      Computational: Time-domain membrane potentials

      The membrane potentials of modelled neurons in response to DBS across a range of frequencies were generated for each of Vim (Fig. 5), STN (Fig. 6), and SNr (Fig. 7). The proportions of excitatory and inhibitory inputs (Supplementary Table 1) together with the parameters of the model neurons (Supplementary Table 2) generated baseline (DBS-OFF) firing rates which corresponded to in vivo recordings. The left side of Fig. 5 shows the simulated membrane potential (accounting also for action potential generation) before and during stimulation across a range of frequencies for Vim, whereas the right side shows an exemplary in vivo Vim neuron. Synchronous/periodic neuronal firing due to stimulus entrainment was reproduced by the model neuron for DBS at 20 Hz. The model neuron can moreover partially reproduce the transient excitatory responses at DBS onset with 50 Hz and 100 Hz stimulation and 30 Hz to some degree; however, the transient excitatory responses within the model were of shorter latency. For STN (Fig. 6), the simulated (left) neuronal firing compared to baseline decreases for DBS at ≥30 Hz, corroborating experimental data (exemplary in vivo STN neuron portrayed on the right side). Neuronal firing rates were substantially attenuated with DBS at 50 Hz and 100 Hz (as was the case experimentally) due to synaptic depression. For SNr (Fig. 7), the simulated (left) neuronal firing rate decreases dramatically beginning at 20 Hz due to the dominant inhibitory presynaptic currents, corroborating experimental data (exemplary in vivo SNr neuron portrayed on the right side). The model neuron fails to generate action potentials for DBS ≥50 Hz (as was the case experimentally) due to synaptic depression. Time-domain histograms are also presented in each figure (Fig. 5, Fig. 6, Fig. 7) which were generated by averaging the neuronal firing rates of 10 modelled neurons for each respective structure across 2 s of stimulation at each frequency.
      Fig. 5
      Fig. 5Computational time-domain membrane potential for Vim. The left panels show the membrane potential of a model Vim neuron immediately before (non-shaded) and during (shaded) DBS across a range of frequencies. The right panels are exemplary recordings from an in vivo human Vim neuron (stimulation for 50 Hz was limited to 1 s). The bottom-most panels are time-domain firing rate histograms generated by averaging across 10 model Vim neurons. Synchronous/periodic neuronal firing due to stimulus entrainment was reproduced by the model neuron for DBS at 20 Hz. The model neuron can partially generate the transient excitatory responses at DBS onset with 50 Hz and 100 Hz stimulation and 30 Hz to some degree; however, the transient excitatory responses within the model were of shorter latency.
      Fig. 6
      Fig. 6Computational time-domain membrane potential for STN. The left panels show the membrane potential of a model STN neuron immediately before (non-shaded) and during (shaded) DBS across a range of frequencies. The right panels are exemplary recordings from an in vivo human STN neuron (stimulation for 50 Hz was limited to 1 s). The bottom-most panels are time-domain firing rate histograms generated by averaging across 10 model STN neurons. The neuronal firing rate compared to baseline decreases for DBS at ≥30 Hz, corroborating experimental data. The modelled neuronal firing rates were substantially attenuated with 50 Hz and 100 Hz (as was the case experimentally) due to synaptic depression.
      Fig. 7
      Fig. 7Computational time-domain membrane potential for SNr. The left panels show the membrane potential of a model SNr neuron immediately before (non-shaded) and during (shaded) DBS across a range of frequencies. The right panels are exemplary recordings from an in vivo human SNr neuron (stimulation for 50 Hz was limited to 1 s). The bottom-most panels are time-domain firing rate histograms generated by averaging across 10 model SNr neurons. Due to the dominant inhibitory presynaptic currents, the neuronal firing rate decreases dramatically beginning at 20 Hz, corroborating experimental data. The model neuron fails to generate action potentials for DBS ≥50 Hz (as was the case experimentally) due to synaptic depression.
      Fig. 8
      Fig. 8Computational frequency response functions. The neuronal dynamics for stimulation (≤60 pulses) frequency response functions match experimental results (solid gray lines), though further tuning is required to optimize excitatory responses of Vim more precisely. The average ± standard error baseline firing rates for computational Vim, STN, and SNr neurons were 28.0 ± 0.1 Hz, 30.1 ± 0.2 Hz, and 61.7 ± 0.3 Hz, respectively (dashed gray lines). Firing rates during the various stimulation trains were compared to the baseline firing rates and the p-values of Bonferroni-corrected post-hoc t-tests (2-tailed, paired) are displayed with Cohen's dz effect sizes in parentheses. ANOVA main effects for stimulation were all significant and are reported in the Results subsection “Computational: Stimulation frequency response functions”.

      Computational: Stimulation frequency response functions

      Similar to experimental results, significant main effects of stimulation were found for Vim [F = 2400.280 (6, 54), p < .001, η2 = 0.996], STN [F = 227.963 (6, 54), p < .001, η2 = 0.962], and SNr [F = 7093.439 (6, 54), p < .001, η2 = 0.999]. 10 modelled neurons were used for each brain structure and the stimulation duration at each frequency was constrained to match experimental data within Fig. 1B. Detailed post-hoc t-test statistics (corrected for multiple comparisons) and Cohen's dz effect sizes are depicted in Fig. 8. Overall, the neuronal dynamics matched experimental results, though further tuning is required to optimize initial excitatory responses of Vim more precisely; a topic for future work.

      Discussion

      Site-specific and frequency-dependent stimulation effects

      At the somatic level, electrical stimulation is both site-specific and frequency-dependent. In Vim and Rt, neuronal activity could be upregulated, whereas in STN and SNr it was downregulated. These mechanistic disparities across brain regions are most likely explained by anatomical differences in local microcircuitries, in that the effects appeared dependent upon the relative distributions of excitatory and inhibitory inputs converging at target neurons [
      • Chiken S.
      • Nambu A.
      Disrupting neuronal transmission: mechanism of DBS?.
      ]. The experimental findings demonstrated that neuronal activity in any brain region could be suppressed either selectively in regions with a high predominance of inhibitory inputs or non-selectively if high enough stimulation frequencies were used. Neuronal excitation, however, could only be achieved when electrical stimulation was delivered to brain regions with a high predominance of glutamatergic inputs. While these bimodal effects (excitatory vs. inhibitory) with low stimulation frequencies were likely attributable to presynaptic activation, the loss of site-specificity and convergence towards neuronal suppression with sustained HFS (≥100 Hz) was most likely attributable to synaptic depression [
      • Liu L.D.
      • Prescott I.A.
      • Dostrovsky J.O.
      • Hodaie M.
      • Lozano A.M.
      • Hutchison W.D.
      Frequency-dependent effects of electrical stimulation in the globus pallidus of dystonia patients.
      ,
      • Milosevic L.
      • Kalia S.K.
      • Hodaie M.
      • Lozano A.M.
      • Fasano A.
      • Popovic M.R.
      • et al.
      Neuronal inhibition and synaptic plasticity of basal ganglia neurons in Parkinson's disease.
      ,
      • Steiner L.A.
      • Tomás F.J.B.
      • Planert H.
      • Alle H.
      • Vida I.
      • Geiger J.R.P.
      Connectivity and dynamics underlying synaptic control of the subthalamic nucleus.
      ,
      • Rosenbaum R.
      • Zimnik A.
      • Zheng F.
      • Turner R.S.
      • Alzheimer C.
      • Doiron B.
      • et al.
      Axonal and synaptic failure suppress the transfer of firing rate oscillations, synchrony and information during high frequency deep brain stimulation.
      ]. This phenomenon of short-term synaptic plasticity can be defined as a reversible decrease in synaptic efficacy, caused by the depletion of readily releasable neurotransmitter vesicle pools when successive stimuli are delivered at a fast rate; a reduction of presynaptic calcium conductance; and/or the inactivation of neurotransmitter release sites due to delayed recovery from vesicle fusion events [
      • Rosenmund C.
      • Stevens C.F.
      Definition of the readily releasable pool of vesicles at hippocampal synapses.
      ,
      • Dittman J.S.
      • Regehr W.G.
      Calcium dependence and recovery kinetics of presynaptic depression at the climbing fiber to purkinje cell synapse.
      ,
      • Zucker R.S.
      • Regehr W.G.
      Short-term synaptic plasticity.
      ,
      • Rizzoli S.O.
      • Betz W.J.
      Synaptic vesicle pools.
      ,
      • Fioravante D.
      • Regehr W.G.
      Short-term forms of presynaptic plasticity.
      ].
      Our computational model was designed to test our two main hypotheses (i) that the post-synaptic responses (i.e. neuronal output), to single pulses of electrical stimulation were mediated by the proportions of inhibitory vs. excitatory inputs to the stimulated neuron, and (ii) that weakened synaptic transmission fidelity over time with higher stimulation frequencies was mediated by short-term synaptic plasticity. As such, the biophysical modelling approach takes into consideration both anatomical (local microcircuitry) and physiological (short-term synaptic dynamics) properties. At stimulation frequencies below the threshold for synaptic depression (i.e. <20–30 Hz) [
      • Liu L.D.
      • Prescott I.A.
      • Dostrovsky J.O.
      • Hodaie M.
      • Lozano A.M.
      • Hutchison W.D.
      Frequency-dependent effects of electrical stimulation in the globus pallidus of dystonia patients.
      ,
      • Milosevic L.
      • Kalia S.K.
      • Hodaie M.
      • Lozano A.M.
      • Fasano A.
      • Popovic M.R.
      • et al.
      Neuronal inhibition and synaptic plasticity of basal ganglia neurons in Parkinson's disease.
      ], our model showed that neuronal responses were the result of a temporal summation of stimulus-evoked responses. In structures with predominantly excitatory inputs, this led to increases in neuronal output, whereas the opposite occurred in structures with predominantly inhibitory inputs. Beyond the threshold for synaptic depression, the strengths of successive stimulus-evoked responses were progressively reduced (i.e. a loss of synaptic transmission fidelity). In the Vim and Rt, with high frequencies, we observed an initial excitatory response which weakened over time. In the SNr, stimulus-evoked inhibitory responses were of sufficient magnitude to induce a substantial amount of neuronal inhibition; however, the SNr is also affected by synaptic depression, as evidenced by our previous work showing progressive, frequency-dependent decreases to the amplitudes of extracellular evoked field potentials in SNr with stimulation frequencies ≥20 Hz [
      • Milosevic L.
      • Kalia S.K.
      • Hodaie M.
      • Lozano A.M.
      • Fasano A.
      • Popovic M.R.
      • et al.
      Neuronal inhibition and synaptic plasticity of basal ganglia neurons in Parkinson's disease.
      ]. One may then assume that since synaptic depression would weaken the strength of inhibitory synaptic transmission, neuronal firing should increase via disinhibition. However, our model shows non-selective synaptic depression of both inhibitory and excitatory synaptic currents, which is supported by experimental work in rodent STN slices which demonstrated that pharmacologically-isolated excitatory and inhibitory postsynaptic potentials were both depressed during HFS [
      • Steiner L.A.
      • Tomás F.J.B.
      • Planert H.
      • Alle H.
      • Vida I.
      • Geiger J.R.P.
      Connectivity and dynamics underlying synaptic control of the subthalamic nucleus.
      ]. High-frequency DBS has therefore been considered a “functional deafferentation” [
      • Anderson T.
      • Hu B.
      • Pittman Q.
      • Kiss Z.H.T.
      Mechanisms of deep brain stimulation: an intracellular study in rat thalamus.
      ]. This would also explain the suppression of somatic firing in STN with higher stimulation frequencies, whereas the stimulus-evoked responses with lower frequencies produced rather weak net inhibitory responses due to the more homogenous distribution of excitatory and inhibitory inputs to STN.
      A recent theoretical study incorporated the TM and LIF models to characterize excitatory post-synaptic currents (EPSCs) and action potential signaling of depressive, facilitatory, and pseudolinear synapses being directly activated by DBS [
      • Farokhniaee A.
      • McIntyre C.C.
      Theoretical principles of deep brain stimulation induced synaptic suppression.
      ]. Herein, we have built upon this work by modelling both excitatory and inhibitory postsynaptic currents to generate a site-specific (i.e. dependent upon the proportion of convergent inhibitory/excitatory inputs) and frequency-dependent DBS-mediated net current elicited by each pulse. Thus, our model can capture stimulation-mediated neuronal dynamics across various brain targets and applied stimulation frequencies. Notably, each of our studies suggest that short-term synaptic depression may be a putative mechanism of high-frequency DBS. In line with these findings, previous computational work has suggested that high-frequency DBS may lead to axonal and synaptic failures which suppress the synaptic transfer of firing rate oscillations, synchrony, and rate-coded information from the STN to its synaptic targets [
      • Rosenbaum R.
      • Zimnik A.
      • Zheng F.
      • Turner R.S.
      • Alzheimer C.
      • Doiron B.
      • et al.
      Axonal and synaptic failure suppress the transfer of firing rate oscillations, synchrony and information during high frequency deep brain stimulation.
      ]; making use of a stochastic model to simulate neurotransmitter release quanta [
      • Vere-Jones D.
      Simple stochastic models for the release of quanta of transmitter from a nerve terminal.
      ]. While direct suppression of somatic activity has been shown to be therapeutic [
      • Bergman H.
      • Wichmann T.
      • DeLong M.R.
      Reversal of experimental parkinsonism by lesions of the subthalamic nucleus.
      ,
      • Wichmann T.
      • Bergman H.
      • DeLong M.R.
      The primate subthalamic nucleus. III. Changes in motor behavior and neuronal activity in the internal pallidum induced by subthalamic inactivation in the MPTP model of parkinsonism.
      ,
      • Levy R.
      • Lang A.E.
      • Dostrovsky J.O.
      • Pahapill P.
      • Romas J.
      • Saint-Cyr J.
      • et al.
      Lidocaine and muscimol microinjections in subthalamic nucleus reverse parkinsonian symptoms.
      ], orthodromic and antidromic axonal effects of electrical stimulation must also be considered [
      • McIntyre C.C.
      • Hahn P.J.
      Network perspectives on the mechanisms of deep brain stimulation.
      ]. If each DBS pulse generates an axonal action potential [
      • McIntyre C.C.
      • Grill W.M.
      • Sherman D.L.
      • Thakor N.V.
      Cellular effects of deep brain stimulation: model-based analysis of activation and inhibition.
      ], then the overall “neuronal output” should be considered as the summation of the somatic firing (that is influenced by afferent axon/axon terminal activations [
      • Bower K.L.
      • McIntyre C.C.
      Deep brain stimulation of terminating axons.
      ]) plus the direct efferent axonal activations; we have incorporated this summation within Fig. 1B. Thus, HFS applications which completely suppresses somatic firing would replace neuronal output with a more regular pattern of output corresponding to the stimulation frequency; in line with the theory of “decoupling of the axon and soma” [
      • McIntyre C.C.
      • Savasta M.
      • Kerkerian-Le Goff L.
      • Vitek J.L.
      Uncovering the mechanism(s) of action of deep brain stimulation: activation, inhibition, or both.
      ]. However, we suggest that in cases where somatic firing is not completely suppressed, such as in the STN at lower stimulation frequencies or when stimulating structures such as the Vim and Rt, the effect is a “summation” of axonal and somatic firing, rather than an explicit decoupling.

      Translational implications

      The selectively bimodal and frequency-dependent somatic responses described here should be taken into consideration in the development of novel stimulation paradigms and DBS indications. In applications of DBS which utilize a high stimulation frequency, suppression of somatic output is likely achieved (though as mentioned above, axonal activations should be considered). Stimulation paradigms which utilize low stimulation frequencies and are applied to areas of the brain with predominantly glutamatergic inputs may depend upon periodic facilitation of somatic firing, with one possible example being low-frequency pedunculopontine-DBS [
      • Moreau C.
      • Defebvre L.
      • Devos D.
      • Marchetti F.
      • Destée A.
      • Stefani A.
      • et al.
      STN versus PPN-DBS for alleviating freezing of gait: toward a frequency modulation approach?.
      ]. Low-frequency stimulation in an area of the brain with predominantly inhibitory inputs may on the other hand cause periodic inhibitions. In either case, low-frequency stimulation can induce oscillatory neuronal behaviour (as seen in Supplementary Fig. 2). Knowledge of the site-specific and frequency-dependent properties of DBS can inform the development of novel stimulation paradigms such as closed-loop stimulation for on demand upregulation or downregulation of neuronal firing, or for induction or disruption of neuronal oscillations. Indeed, stimulation parameters are often decided upon empirically. Based on the findings presented here, knowledge of the local microcircuitry (distribution of afferent inputs) inherent to the stimulated brain region (i.e. therapeutic targets of interest for DBS application) may allow us to infer/predict the stimulation frequency response properties. As such, our comprehensive computational model may represent a valuable tool for physiologically-informed stimulation programming and paradigm development in prospective DBS targets and indications, particularly as our model was developed based on in vivo experimental data from the human brain. Further clinical and physiological implications of basal ganglia, Vim, and Rt stimulation are discussed in greater detail within the Supplementary Material.

      Considerations and limitations

      Although we did not record from any structures downstream of the stimulation site, it is perhaps possible to infer the downstream effects based on the results presented here. For example, in STN stimulation, activation of the glutamatergic subthalamo-pallidal/nigral efferents may cause excitatory responses downstream [
      • Hashimoto T.
      • Elder C.M.
      • Okun M.S.
      • Patrick S.K.
      • Vitek J.L.
      Stimulation of the subthalamic nucleus changes the firing pattern of pallidal neurons.
      ,
      • Boulet S.
      • Lacombe E.
      • Carcenac C.
      • Feuerstein C.
      • Sgambato-Faure V.
      • Poupard A.
      • et al.
      Subthalamic stimulation-induced forelimb dyskinesias are linked to an increase in glutamate levels in the substantia nigra pars reticulata.
      ,
      • Galati S.
      • Mazzone P.
      • Fedele E.
      • Pisani A.
      • Peppe A.
      • Pierantozzi M.
      • et al.
      Biochemical and electrophysiological changes of substantia nigra pars reticulata driven by subthalamic stimulation in patients with Parkinson's disease.
      ], especially if lower stimulation frequencies are used; whereas with higher stimulation frequencies the downstream glutamatergic drive may in fact be weakened [
      • Tai C.-H.
      • Boraud T.
      • Bezard E.
      • Bioulac B.
      • Gross C.
      • Benazzouz A.
      Electrophysiological and metabolic evidence that high-frequency stimulation of the subthalamic nucleus bridles neuronal activity in the subthalamic nucleus and the substantia nigra reticulata.
      ,
      • Maltête D.
      • Jodoin N.
      • Karachi C.
      • Houeto J.L.
      • Navarro S.
      • Cornu P.
      • et al.
      Subthalamic stimulation and neuronal activity in the substantia nigra in Parkinson's disease.
      ,
      • Zheng F.
      • Lammert K.
      • Nixdorf-Bergweiler B.E.
      • Steigerwald F.
      • Volkmann J.
      • Alzheimer C.
      Axonal failure during high frequency stimulation of rat subthalamic nucleus.
      ] due to synaptic depression. Further studies are warranted in order to better understand the possible orthodromic (and antidromic) network phenomena of DBS [
      • Alhourani A.
      • McDowell M.M.
      • Randazzo M.J.
      • Wozny T.A.
      • Kondylis E.D.
      • Lipski W.J.
      • et al.
      Network effects of deep brain stimulation.
      ]. Moreover, studies relating to the downstream and upstream DBS effects would allow us to better understand the mechanisms of DBS applied to white matter tracts (such as forniceal-DBS). Another notable limitation of this study is that the applied stimulation trains were limited to short durations compared to that of hours, days, or longer in clinical applications. Stimulation effects over longer durations are yet to be validated and are to be considered in future work. Moreover, while this study aimed to elucidate differential mechanisms involved in stimulation of various brain structures, behavioural and clinical correlates were not assessed here directly. However, the high-frequency microstimulation applied to Vim was shown to be effective at suppressing tremor [
      • Milosevic L.
      • Kalia S.K.
      • Hodaie M.
      • Lozano A.M.
      • Popovic M.R.
      • Hutchison W.D.
      Physiological mechanisms of thalamic ventral intermediate nucleus stimulation for tremor suppression.
      ] confirming that the stimulation parameters used were clinically relevant. Moreover, the stimulation parameters used here (in particular, the 100Hz microstimulation trains) are comparable in terms of total electrical energy delivered during clinically-applied DBS macrostimulation [
      • Milosevic L.
      • Kalia S.K.
      • Hodaie M.
      • Lozano A.
      • Popovic M.R.
      • Hutchison W.
      Subthalamic suppression defines therapeutic threshold of deep brain stimulation in Parkinson's disease.
      ] though are of greater current density due to the smaller stimulating surface. Another important limitation of this work is that the explanation of site-specific mechanistic disparities based on the proportions of inhibitory/excitatory afferent inputs does not account for the possible contributions of glia [
      • Bekar L.
      • Libionka W.
      • Tian G.-F.
      • Xu Q.
      • Torres A.
      • Wang X.
      • et al.
      Adenosine is crucial for deep brain stimulation–mediated attenuation of tremor.
      ,
      • Tawfik V.L.
      • Chang S.-Y.
      • Hitti F.L.
      • Roberts D.W.
      • Leiter J.C.
      • Jovanovic S.
      • et al.
      Deep brain stimulation results in local glutamate and adenosine release: investigation into the role of astrocytes.
      ,
      • Salatino J.W.
      • Ludwig K.A.
      • Kozai T.D.Y.
      • Purcell E.K.
      Glial responses to implanted electrodes in the brain.
      ,
      • Campos A.C.P.
      • Kikuchi D.S.
      • Paschoa A.F.N.
      • Kuroki M.A.
      • Fonoff E.T.
      • Hamani C.
      • et al.
      Unraveling the role of astrocytes in subthalamic nucleus deep brain stimulation in a Parkinson's disease rat model.
      ], neuromodulatory inputs [
      • Lavoie B.
      • Smith Y.
      • Parent A.
      Dopaminergic innervation of the basal ganglia in the squirrel monkey as revealed by tyrosine hydroxylase immunohistochemistry.
      ,
      • Lavian H.
      • Loewenstern Y.
      • Madar R.
      • Almog M.
      • Bar-Gad I.
      • Okun E.
      • et al.
      Dopamine receptors in the rat entopeduncular nucleus.
      ], nor metabotropic receptor dynamics (e.g. GABAB) [
      • Xie Y.
      • Heida T.
      • Stegenga J.
      • Zhao Y.
      • Moser A.
      • Tronnier V.
      • et al.
      High-frequency electrical stimulation suppresses cholinergic accumbens interneurons in acute rat brain slices through GABAB receptors.
      ] which should be considered in future work. It is also important to note that the experimental data within this study was acquired in context of pathological circuits and may not reflect the typical responses to stimulation in a healthy individual. Moreover, Vim data was acquired from two patients with Parkinson's disease and nine with essential tremor; however, our experimental and computational analyses did not account for possible differences in baseline firing characteristics nor responses to stimulation across disease conditions. Finally, the Vim computational frequency responses require further tuning to more precisely capture stronger initial excitatory responses during HFS; a topic for future work.

      Conclusion

      The presented results demonstrate the site-specific and frequency-dependent neuronal effects of extracellular stimulation. Neuronal suppression could be achieved either by stimulus-evoked inhibitory events in structures with predominantly GABAergic inputs (STN and SNr) or non-selectively when sustained HFS was delivered. Stimulus-evoked neuronal excitatory responses were exclusive to structures with predominantly glutamatergic inputs (Vim and Rt), particularly with lower stimulation frequencies. Our computational model showed that the bimodal site-specific stimulus-evoked responses could be explained by differences in the distributions of inhibitory and excitatory inputs to the stimulated target structures, whereas convergence towards neuronal suppression with sustained HFS could be explained by synaptic depression.

      CRediT authorship contribution statement

      Luka Milosevic: Conceptualization, Methodology, Formal analysis, Investigation, Data curation, Writing – original draft. Suneil K. Kalia: Resources, Project administration, Writing – review & editing. Mojgan Hodaie: Resources, Project administration, Writing – review & editing. Andres M. Lozano: Resources, Project administration, Writing – review & editing. Milos R. Popovic: Resources, Project administration, Writing – review & editing. William D. Hutchison: Conceptualization, Investigation, Resources, Project administration, Writing – review & editing. Milad Lankarany: Methodology, Software, Formal analysis, Writing – original draft.

      Declaration of competing interest

      S.K.K., M.H., W.D.H. have received honoraria, travel funds, and/or grant support from Medtronic (not related to this work). A.M.L. has received honoraria, travel funds, and/or grant support from Medtronic , Boston Scientific , St. Jude-Abbott , and Insightec (not related to this work). M.R.P. is a shareholder in MyndTec Inc. A.M.L. is a co-founder of Functional Neuromodulation Ltd. L.M. and M.L. have no financial disclosures.

      Acknowledgements

      The authors thank Tameem Al-Ozzi for assistance in data collection and the patients for their participation.

      Appendix A. Supplementary data

      The following is the Supplementary data to this article:

      Funding

      This work was supported in part by the Natural Sciences and Engineering Research Council: Discovery Grant RGPIN-2016-06358 (M.R.P.), Dean Connor and Maris Uffelmann Donation (M.R.P.), Walter & Maria Schroeder Donation (M.R.P.), and the Dystonia Medical Research Foundation (W.D.H.).

      References

        • Limousin P.
        • Krack P.
        • Pollak P.
        • Benazzouz A.
        • Ardouin C.
        • Hoffmann D.
        • et al.
        Electrical stimulation of the subthalamic nucleus in advanced Parkinson's disease.
        N Engl J Med. 1998; 339: 1105-1111https://doi.org/10.1056/NEJM199810153391603
        • Dallapiazza R.F.
        • Lee D.J.
        • Vloo P.D.
        • Fomenko A.
        • Hamani C.
        • Hodaie M.
        • et al.
        Outcomes from stereotactic surgery for essential tremor.
        J Neurol Neurosurg Psychiatry. 2019; 90: 474-482https://doi.org/10.1136/jnnp-2018-318240
        • Hung S.W.
        • Hamani C.
        • Lozano A.M.
        • Poon Y.-Y.W.
        • Piboolnurak P.
        • Miyasaki J.M.
        • et al.
        Long-term outcome of bilateral pallidal deep brain stimulation for primary cervical dystonia.
        Neurology. 2007; 68: 457https://doi.org/10.1212/01.wnl.0000252932.71306.89
        • Menchón J.M.
        • Real E.
        • Alonso P.
        • Aparicio M.A.
        • Segalas C.
        • Plans G.
        • et al.
        A prospective international multi-center study on safety and efficacy of deep brain stimulation for resistant obsessive-compulsive disorder.
        Mol Psychiatr. 2019; 1–14https://doi.org/10.1038/s41380-019-0562-6
        • Fisher R.
        • Salanova V.
        • Witt T.
        • Worth R.
        • Henry T.
        • Gross R.
        • et al.
        Electrical stimulation of the anterior nucleus of thalamus for treatment of refractory epilepsy.
        Epilepsia. 2010; 51: 899-908https://doi.org/10.1111/j.1528-1167.2010.02536.x
        • Youngerman B.E.
        • Chan A.K.
        • Mikell C.B.
        • McKhann G.M.
        • Sheth S.A.
        A decade of emerging indications: deep brain stimulation in the United States.
        J Neurosurg. 2016; 125: 461-471https://doi.org/10.3171/2015.7.JNS142599
        • Basu I.
        • Robertson M.M.
        • Crocker B.
        • Peled N.
        • Farnes K.
        • Vallejo-Lopez D.I.
        • et al.
        Consistent linear and non-linear responses to invasive electrical brain stimulation across individuals and primate species with implanted electrodes.
        Brain Stimulat. 2019; 12: 877-892https://doi.org/10.1016/j.brs.2019.03.007
        • Dostrovsky J.O.
        • Levy R.
        • Wu J.P.
        • Hutchison W.D.
        • Tasker R.R.
        • Lozano A.M.
        Microstimulation-induced inhibition of neuronal firing in human globus pallidus.
        J Neurophysiol. 2000; 84: 570-574https://doi.org/10.1152/jn.2000.84.1.570
        • Liu L.D.
        • Prescott I.A.
        • Dostrovsky J.O.
        • Hodaie M.
        • Lozano A.M.
        • Hutchison W.D.
        Frequency-dependent effects of electrical stimulation in the globus pallidus of dystonia patients.
        J Neurophysiol. 2012; 108: 5-17https://doi.org/10.1152/jn.00527.2011
        • Milosevic L.
        • Kalia S.K.
        • Hodaie M.
        • Lozano A.M.
        • Fasano A.
        • Popovic M.R.
        • et al.
        Neuronal inhibition and synaptic plasticity of basal ganglia neurons in Parkinson's disease.
        Brain. 2018; 141: 177-190https://doi.org/10.1093/brain/awx296
        • Milosevic L.
        • Kalia S.K.
        • Hodaie M.
        • Lozano A.M.
        • Popovic M.R.
        • Hutchison W.D.
        Physiological mechanisms of thalamic ventral intermediate nucleus stimulation for tremor suppression.
        Brain. 2018; 141: 2142-2155https://doi.org/10.1093/brain/awy139
        • Steiner L.A.
        • Tomás F.J.B.
        • Planert H.
        • Alle H.
        • Vida I.
        • Geiger J.R.P.
        Connectivity and dynamics underlying synaptic control of the subthalamic nucleus.
        J Neurosci. 2019; 39: 2470-2481https://doi.org/10.1523/JNEUROSCI.1642-18.2019
        • Anderson R.W.
        • Farokhniaee A.
        • Gunalan K.
        • Howell B.
        • McIntyre C.C.
        Action potential initiation, propagation, and cortical invasion in the hyperdirect pathway during subthalamic deep brain stimulation.
        Brain Stimulat. 2018; 11: 1140-1150https://doi.org/10.1016/j.brs.2018.05.008
        • McIntyre C.C.
        • Grill W.M.
        • Sherman D.L.
        • Thakor N.V.
        Cellular effects of deep brain stimulation: model-based analysis of activation and inhibition.
        J Neurophysiol. 2004; 91: 1457-1469https://doi.org/10.1152/jn.00989.2003
        • Jakobs M.
        • Fomenko A.
        • Lozano A.M.
        • Kiening K.L.
        Cellular, molecular, and clinical mechanisms of action of deep brain stimulation—a systematic review on established indications and outlook on future developments.
        EMBO Mol Med. 2019; 11https://doi.org/10.15252/emmm.201809575
        • Bower K.L.
        • McIntyre C.C.
        Deep brain stimulation of terminating axons.
        Brain Stimulat. 2020; 13: 1863-1870https://doi.org/10.1016/j.brs.2020.09.001
        • Farokhniaee A.
        • McIntyre C.C.
        Theoretical principles of deep brain stimulation induced synaptic suppression.
        Brain Stimulat. 2019; 12: 1402-1409https://doi.org/10.1016/j.brs.2019.07.005
        • Rosenbaum R.
        • Zimnik A.
        • Zheng F.
        • Turner R.S.
        • Alzheimer C.
        • Doiron B.
        • et al.
        Axonal and synaptic failure suppress the transfer of firing rate oscillations, synchrony and information during high frequency deep brain stimulation.
        Neurobiol Dis. 2014; 62: 86-99https://doi.org/10.1016/j.nbd.2013.09.006
        • Tsodyks M.V.
        • Markram H.
        The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability.
        Proc Natl Acad Sci Unit States Am. 1997; 94: 719-723https://doi.org/10.1073/pnas.94.2.719
        • Levy R.
        • Lozano A.M.
        • Hutchison W.D.
        • Dostrovsky J.O.
        Dual microelectrode technique for deep brain stereotactic surgery in humans.
        Oper. Neurosurg. (Hagerstown). 2007; 60 (ONS-277-ONS-284)https://doi.org/10.1227/01.NEU.0000255389.85161.03
        • Hutchison W.D.
        • Allan R.J.
        • Opitz H.
        • Levy R.
        • Dostrovsky J.O.
        • Lang A.E.
        • et al.
        Neurophysiological identification of the subthalamic nucleus in surgery for Parkinson's disease.
        Ann Neurol. 1998; 44: 622-628https://doi.org/10.1002/ana.410440407
        • Basha D.
        • Dostrovsky J.O.
        • Lopez Rios A.L.
        • Hodaie M.
        • Lozano A.M.
        • Hutchison W.D.
        Beta oscillatory neurons in the motor thalamus of movement disorder and pain patients.
        Exp Neurol. 2014; 261: 782-790https://doi.org/10.1016/j.expneurol.2014.08.024
        • Milosevic L.
        • Kalia S.K.
        • Hodaie M.
        • Lozano A.
        • Popovic M.R.
        • Hutchison W.
        Subthalamic suppression defines therapeutic threshold of deep brain stimulation in Parkinson's disease.
        J Neurol Neurosurg Psychiatry. 2019; 90: 1105-1108https://doi.org/10.1136/jnnp-2019-321140
        • Bar-Gad I.
        • Elias S.
        • Vaadia E.
        • Bergman H.
        Complex locking rather than complete cessation of neuronal activity in the globus pallidus of a 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine-treated primate in response to pallidal microstimulation.
        J Neurosci. 2004; 24: 7410-7419https://doi.org/10.1523/JNEUROSCI.1691-04.2004
        • McIntyre C.C.
        • Savasta M.
        • Kerkerian-Le Goff L.
        • Vitek J.L.
        Uncovering the mechanism(s) of action of deep brain stimulation: activation, inhibition, or both.
        Clin Neurophysiol. 2004; 115: 1239-1248https://doi.org/10.1016/j.clinph.2003.12.024
        • Tsodyks M.
        • Pawelzik K.
        • Markram H.
        Neural networks with dynamic synapses.
        Neural Comput. 1998; 10: 821-835https://doi.org/10.1162/089976698300017502
        • Destexhe A.
        • Rudolph M.
        • Fellous J.-M.
        • Sejnowski T.J.
        Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons.
        Neuroscience. 2001; 107: 13-24https://doi.org/10.1016/S0306-4522(01)00344-X
        • Destexhe A.
        • Rudolph M.
        • Paré D.
        The high-conductance state of neocortical neurons in vivo.
        Nat Rev Neurosci. 2003; 4: 739-751https://doi.org/10.1038/nrn1198
        • Asanuma C.
        • Thach W.T.
        • Jones E.G.
        Distribution of cerebellar terminations and their relation to other afferent terminations in the ventral lateral thalamic region of the monkey.
        Brain Res Rev. 1983; 5: 237-265https://doi.org/10.1016/0165-0173(83)90015-2
        • Kultas-Ilinsky K.
        • Ilinsky I.A.
        Fine structure of the ventral lateral nucleus (VL) of the Macaca mulatta thalamus: cell types and synaptology.
        J Comp Neurol. 1991; 314: 319-349https://doi.org/10.1002/cne.903140209
        • Ilinsky I.A.
        • Kultas-Ilinsky K.
        Motor thalamic circuits in primates with emphasis on the area targeted in treatment of movement disorders.
        Mov Disord. 2002; 17: S9-S14https://doi.org/10.1002/mds.10137
        • Kuramoto E.
        • Fujiyama F.
        • Nakamura K.C.
        • Tanaka Y.
        • Hioki H.
        • Kaneko T.
        Complementary distribution of glutamatergic cerebellar and GABAergic basal ganglia afferents to the rat motor thalamic nuclei.
        Eur J Neurosci. 2011; 33: 95-109https://doi.org/10.1111/j.1460-9568.2010.07481.x
        • Stepniewska I.
        • Preuss T.M.
        • Kaas J.H.
        Thalamic connections of the primary motor cortex (M1) of owl monkeys.
        J Comp Neurol. 1994; 349: 558-582https://doi.org/10.1002/cne.903490405
        • Kakei S.
        • Na J.
        • Shinoda Y.
        Thalamic terminal morphology and distribution of single corticothalamic axons originating from layers 5 and 6 of the cat motor cortex.
        J Comp Neurol. 2001; 437: 170-185https://doi.org/10.1002/cne.1277
        • Ambardekar A.V.
        • Ilinsky I.A.
        • Froestl W.
        • Bowery N.G.
        • Kultas-Ilinsky K.
        Distribution and properties of GABAB antagonist [3H]CGP 62349 binding in the rhesus monkey thalamus and basal ganglia and the influence of lesions in the reticular thalamic nucleus.
        Neuroscience. 1999; 93: 1339-1347https://doi.org/10.1016/S0306-4522(99)00282-1
        • Ilinsky I.A.
        • Ambardekar A.V.
        • Kultas-Ilinsky K.
        Organization of projections from the anterior pole of the nucleus reticularis thalami (NRT) to subdivisions of the motor thalamus: light and electron microscopic studies in the Rhesus monkey.
        J Comp Neurol. 1999; 409: 369-384https://doi.org/10.1002/(SICI)1096-9861(19990705)409:3<369::AID-CNE3>3.0.CO;2-H
        • Jones E.G.
        Some aspects of the organization of the thalamic reticular complex.
        J Comp Neurol. 1975; 162: 285-308https://doi.org/10.1002/cne.901620302
        • Crabtree J.W.
        The somatotopic organization within the cat's thalamic reticular nucleus.
        Eur J Neurosci. 1992; 4: 1352-1361https://doi.org/10.1111/j.1460-9568.1992.tb00160.x
        • Crabtree J.W.
        The somatotopic organization within the rabbit's thalamic reticular nucleus.
        Eur J Neurosci. 1992; 4: 1343-1351https://doi.org/10.1111/j.1460-9568.1992.tb00159.x
        • Gonzalo-Ruiz A.
        • Lieberman A.R.
        GABAergic projections from the thalamic reticular nucleus to the anteroventral and anterodorsal thalamic nuclei of the rat.
        J Chem Neuroanat. 1995; 9: 165-174https://doi.org/10.1016/0891-0618(95)00078-X
        • Pinault D.
        The thalamic reticular nucleus: structure, function and concept.
        Brain Res Rev. 2004; 46: 1-31https://doi.org/10.1016/j.brainresrev.2004.04.008
        • Paré D.
        • Hazrati L.-N.
        • Parent A.
        • Steriade M.
        Substantia nigra pars reticulata projects to the reticular thalamic nucleus of the cat: a morphological and electrophysiological study.
        Brain Res. 1990; 535: 139-146https://doi.org/10.1016/0006-8993(90)91832-2
        • Hazrati L.-N.
        • Parent A.
        Projection from the external pallidum to the reticular thalamic nucleus in the squirrel monkey.
        Brain Res. 1991; 550: 142-146https://doi.org/10.1016/0006-8993(91)90418-U
        • Asanuma C.
        GABAergic and pallidal terminals in the thalamic reticular nucleus of squirrel monkeys.
        Exp Brain Res. 1994; 101: 439-451https://doi.org/10.1007/BF00227337
        • Parent A.
        • Hazrati L.-N.
        Functional anatomy of the basal ganglia. II. The place of subthalamic nucleus and external pallidium in basal ganglia circuitry.
        Brain Res Rev. 1995; 20: 128-154https://doi.org/10.1016/0165-0173(94)00008-D
        • Bolam J.P.
        • Hanley J.J.
        • Booth P.a.C.
        • Bevan M.D.
        Synaptic organisation of the basal ganglia.
        J Anat. 2000; 196: 527-542https://doi.org/10.1046/j.1469-7580.2000.19640527.x
        • Baufreton J.
        • Kirkham E.
        • Atherton J.F.
        • Menard A.
        • Magill P.J.
        • Bolam J.P.
        • et al.
        Sparse but selective and potent synaptic transmission from the globus pallidus to the subthalamic nucleus.
        J Neurophysiol. 2009; 102: 532-545https://doi.org/10.1152/jn.00305.2009
        • Nambu A.
        • Tokuno H.
        • Takada M.
        Functional significance of the cortico–subthalamo–pallidal ‘hyperdirect’ pathway.
        Neurosci Res. 2002; 43: 111-117https://doi.org/10.1016/S0168-0102(02)00027-5
        • Rinvik E.
        • Ottersen O.P.
        Terminals of subthalamonigral fibres are enriched with glutamate-like immunoreactivity: an electron microscopic, immunogold analysis in the cat.
        J Chem Neuroanat. 1993; 6: 19-30https://doi.org/10.1016/0891-0618(93)90004-N
        • Kita T.
        • Kita H.
        The subthalamic nucleus is one of multiple innervation sites for long-range corticofugal axons: a single-axon tracing study in the rat.
        J Neurosci. 2012; 32: 5990-5999https://doi.org/10.1523/JNEUROSCI.5717-11.2012
        • Markram H.
        • Muller E.
        • Ramaswamy S.
        • Reimann M.W.
        • Abdellah M.
        • Sanchez C.A.
        • et al.
        Reconstruction and simulation of neocortical microcircuitry.
        Cell. 2015; 163: 456-492https://doi.org/10.1016/j.cell.2015.09.029
        • Destexhe A.
        • Rudolph M.
        • Fellous J.-M.
        • Sejnowski T.J.
        Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons.
        Neuroscience. 2001; 107: 13-24https://doi.org/10.1016/S0306-4522(01)00344-X
        • Chiken S.
        • Nambu A.
        Disrupting neuronal transmission: mechanism of DBS?.
        Front Syst Neurosci. 2014; 8https://doi.org/10.3389/fnsys.2014.00033
        • Rosenmund C.
        • Stevens C.F.
        Definition of the readily releasable pool of vesicles at hippocampal synapses.
        Neuron. 1996; 16: 1197-1207https://doi.org/10.1016/S0896-6273(00)80146-4
        • Dittman J.S.
        • Regehr W.G.
        Calcium dependence and recovery kinetics of presynaptic depression at the climbing fiber to purkinje cell synapse.
        J Neurosci. 1998; 18: 6147-6162https://doi.org/10.1523/JNEUROSCI.18-16-06147.1998
        • Zucker R.S.
        • Regehr W.G.
        Short-term synaptic plasticity.
        Annu Rev Physiol. 2002; 64: 355-405https://doi.org/10.1146/annurev.physiol.64.092501.114547
        • Rizzoli S.O.
        • Betz W.J.
        Synaptic vesicle pools.
        Nat Rev Neurosci. 2005; 6: 57-69https://doi.org/10.1038/nrn1583
        • Fioravante D.
        • Regehr W.G.
        Short-term forms of presynaptic plasticity.
        Curr Opin Neurobiol. 2011; 21: 269-274https://doi.org/10.1016/j.conb.2011.02.003
        • Anderson T.
        • Hu B.
        • Pittman Q.
        • Kiss Z.H.T.
        Mechanisms of deep brain stimulation: an intracellular study in rat thalamus.
        J Physiol. 2004; 559: 301-313https://doi.org/10.1113/jphysiol.2004.064998
        • Vere-Jones D.
        Simple stochastic models for the release of quanta of transmitter from a nerve terminal.
        Aust J Stat. 1966; 8: 53-63https://doi.org/10.1111/j.1467-842X.1966.tb00164.x
        • Bergman H.
        • Wichmann T.
        • DeLong M.R.
        Reversal of experimental parkinsonism by lesions of the subthalamic nucleus.
        Science. 1990; 249: 1436-1438https://doi.org/10.1126/science.2402638
        • Wichmann T.
        • Bergman H.
        • DeLong M.R.
        The primate subthalamic nucleus. III. Changes in motor behavior and neuronal activity in the internal pallidum induced by subthalamic inactivation in the MPTP model of parkinsonism.
        J Neurophysiol. 1994; 72: 521-530https://doi.org/10.1152/jn.1994.72.2.521
        • Levy R.
        • Lang A.E.
        • Dostrovsky J.O.
        • Pahapill P.
        • Romas J.
        • Saint-Cyr J.
        • et al.
        Lidocaine and muscimol microinjections in subthalamic nucleus reverse parkinsonian symptoms.
        Brain. 2001; 124: 2105-2118https://doi.org/10.1093/brain/124.10.2105
        • McIntyre C.C.
        • Hahn P.J.
        Network perspectives on the mechanisms of deep brain stimulation.
        Neurobiol Dis. 2010; 38: 329-337https://doi.org/10.1016/j.nbd.2009.09.022
        • Moreau C.
        • Defebvre L.
        • Devos D.
        • Marchetti F.
        • Destée A.
        • Stefani A.
        • et al.
        STN versus PPN-DBS for alleviating freezing of gait: toward a frequency modulation approach?.
        Mov Disord. 2009; 24: 2164-2166https://doi.org/10.1002/mds.22743
        • Hashimoto T.
        • Elder C.M.
        • Okun M.S.
        • Patrick S.K.
        • Vitek J.L.
        Stimulation of the subthalamic nucleus changes the firing pattern of pallidal neurons.
        J Neurosci. 2003; 23: 1916-1923https://doi.org/10.1523/JNEUROSCI.23-05-01916.2003
        • Boulet S.
        • Lacombe E.
        • Carcenac C.
        • Feuerstein C.
        • Sgambato-Faure V.
        • Poupard A.
        • et al.
        Subthalamic stimulation-induced forelimb dyskinesias are linked to an increase in glutamate levels in the substantia nigra pars reticulata.
        J Neurosci. 2006; 26: 10768-10776https://doi.org/10.1523/JNEUROSCI.3065-06.2006
        • Galati S.
        • Mazzone P.
        • Fedele E.
        • Pisani A.
        • Peppe A.
        • Pierantozzi M.
        • et al.
        Biochemical and electrophysiological changes of substantia nigra pars reticulata driven by subthalamic stimulation in patients with Parkinson's disease.
        Eur J Neurosci. 2006; 23: 2923-2928https://doi.org/10.1111/j.1460-9568.2006.04816.x
        • Tai C.-H.
        • Boraud T.
        • Bezard E.
        • Bioulac B.
        • Gross C.
        • Benazzouz A.
        Electrophysiological and metabolic evidence that high-frequency stimulation of the subthalamic nucleus bridles neuronal activity in the subthalamic nucleus and the substantia nigra reticulata.
        Faseb J. 2003; 17: 1820-1830https://doi.org/10.1096/fj.03-0163com
        • Maltête D.
        • Jodoin N.
        • Karachi C.
        • Houeto J.L.
        • Navarro S.
        • Cornu P.
        • et al.
        Subthalamic stimulation and neuronal activity in the substantia nigra in Parkinson's disease.
        J Neurophysiol. 2007; 97: 4017-4022https://doi.org/10.1152/jn.01104.2006
        • Zheng F.
        • Lammert K.
        • Nixdorf-Bergweiler B.E.
        • Steigerwald F.
        • Volkmann J.
        • Alzheimer C.
        Axonal failure during high frequency stimulation of rat subthalamic nucleus.
        J Physiol. 2011; 589: 2781-2793https://doi.org/10.1113/jphysiol.2011.205807
        • Alhourani A.
        • McDowell M.M.
        • Randazzo M.J.
        • Wozny T.A.
        • Kondylis E.D.
        • Lipski W.J.
        • et al.
        Network effects of deep brain stimulation.
        J Neurophysiol. 2015; 114: 2105-2117https://doi.org/10.1152/jn.00275.2015
        • Bekar L.
        • Libionka W.
        • Tian G.-F.
        • Xu Q.
        • Torres A.
        • Wang X.
        • et al.
        Adenosine is crucial for deep brain stimulation–mediated attenuation of tremor.
        Nat Med. 2008; 14: 75-80https://doi.org/10.1038/nm1693
        • Tawfik V.L.
        • Chang S.-Y.
        • Hitti F.L.
        • Roberts D.W.
        • Leiter J.C.
        • Jovanovic S.
        • et al.
        Deep brain stimulation results in local glutamate and adenosine release: investigation into the role of astrocytes.
        Neurosurgery. 2010; 67: 367-375https://doi.org/10.1227/01.NEU.0000371988.73620.4C
        • Salatino J.W.
        • Ludwig K.A.
        • Kozai T.D.Y.
        • Purcell E.K.
        Glial responses to implanted electrodes in the brain.
        Nat. Biomed. Eng. 2017; 1: 862-877https://doi.org/10.1038/s41551-017-0154-1
        • Campos A.C.P.
        • Kikuchi D.S.
        • Paschoa A.F.N.
        • Kuroki M.A.
        • Fonoff E.T.
        • Hamani C.
        • et al.
        Unraveling the role of astrocytes in subthalamic nucleus deep brain stimulation in a Parkinson's disease rat model.
        Cell Mol Neurobiol. 2020; https://doi.org/10.1007/s10571-019-00784-3
        • Lavoie B.
        • Smith Y.
        • Parent A.
        Dopaminergic innervation of the basal ganglia in the squirrel monkey as revealed by tyrosine hydroxylase immunohistochemistry.
        J Comp Neurol. 1989; 289: 36-52https://doi.org/10.1002/cne.902890104
        • Lavian H.
        • Loewenstern Y.
        • Madar R.
        • Almog M.
        • Bar-Gad I.
        • Okun E.
        • et al.
        Dopamine receptors in the rat entopeduncular nucleus.
        Brain Struct Funct. 2018; 223: 2673-2684https://doi.org/10.1007/s00429-018-1657-6
        • Xie Y.
        • Heida T.
        • Stegenga J.
        • Zhao Y.
        • Moser A.
        • Tronnier V.
        • et al.
        High-frequency electrical stimulation suppresses cholinergic accumbens interneurons in acute rat brain slices through GABAB receptors.
        Eur J Neurosci. 2014; 40: 3653-3662https://doi.org/10.1111/ejn.12736