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Basic Research|Articles in Press

Modeling Instantaneous Firing Rate of Deep Brain Stimulation Target Neuronal Ensembles in the Basal Ganglia and Thalamus

  • Yupeng Tian
    Affiliations
    Krembil Research Institute – University Health Network, Toronto, ON, Canada

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

    KITE Research Institute, Toronto Rehabilitation Institute - University Health Network, Toronto, ON, Canada

    CRANIA, University Health Network and University of Toronto, Toronto, ON, Canada
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  • Matthew J.H. Murphy
    Affiliations
    Department of Mathematics, University of Toronto, Toronto, ON, Canada
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  • Leon A. Steiner
    Affiliations
    Krembil Research Institute – University Health Network, Toronto, ON, Canada

    Berlin Institute of Health, Berlin, Germany

    Department of Surgery, University of Toronto, Toronto, ON, Canada

    Department of Neurology, Charité-Universitätsmedizin Berlin, Berlin, Germany
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  • Suneil K. Kalia
    Affiliations
    Krembil Research Institute – University Health Network, Toronto, ON, Canada

    KITE Research Institute, Toronto Rehabilitation Institute - University Health Network, Toronto, ON, Canada

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

    Department of Surgery, University of Toronto, Toronto, ON, Canada

    Division of Neurosurgery, Toronto Western Hospital, University Health Network, Toronto, ON, Canada
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  • Mojgan Hodaie
    Affiliations
    Krembil Research Institute – University Health Network, Toronto, ON, Canada

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

    Department of Surgery, University of Toronto, Toronto, ON, Canada

    Division of Neurosurgery, Toronto Western Hospital, University Health Network, Toronto, ON, Canada
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  • Andres M. Lozano
    Affiliations
    Krembil Research Institute – University Health Network, Toronto, ON, Canada

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

    Department of Surgery, University of Toronto, Toronto, ON, Canada

    Division of Neurosurgery, Toronto Western Hospital, University Health Network, Toronto, ON, Canada
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  • William D. Hutchison
    Affiliations
    CRANIA, University Health Network and University of Toronto, Toronto, ON, Canada

    Department of Surgery, University of Toronto, Toronto, ON, Canada

    Department of Physiology, University of Toronto, Toronto, ON, Canada
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  • Milos R. Popovic
    Affiliations
    Institute of Biomedical Engineering, University of Toronto, Toronto, ON, Canada

    KITE Research Institute, Toronto Rehabilitation Institute - University Health Network, Toronto, ON, Canada

    CRANIA, University Health Network and University of Toronto, Toronto, ON, Canada
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  • Luka Milosevic
    Affiliations
    Krembil Research Institute – University Health Network, Toronto, ON, Canada

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

    KITE Research Institute, Toronto Rehabilitation Institute - University Health Network, Toronto, ON, Canada

    CRANIA, University Health Network and University of Toronto, Toronto, ON, Canada
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  • Milad Lankarany
    Correspondence
    Address correspondence to: Milad Lankarany, PhD, The Krembil Research Institute–University Health Network, 60 Leonard Ave, Toronto, M5T 0S8 ON, Canada.
    Affiliations
    Krembil Research Institute – University Health Network, Toronto, ON, Canada

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

    KITE Research Institute, Toronto Rehabilitation Institute - University Health Network, Toronto, ON, Canada

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

    Department of Physiology, University of Toronto, Toronto, ON, Canada
    Search for articles by this author

      Abstract

      Objective

      Deep brain stimulation (DBS) is an effective treatment for movement disorders, including Parkinson disease and essential tremor. However, the underlying mechanisms of DBS remain elusive. Despite the capability of existing models in interpreting experimental data qualitatively, there are very few unified computational models that quantitatively capture the dynamics of the neuronal activity of varying stimulated nuclei—including subthalamic nucleus (STN), substantia nigra pars reticulata (SNr), and ventral intermediate nucleus (Vim)—across different DBS frequencies.

      Materials and Methods

      Both synthetic and experimental data were used in the model fitting; the synthetic data were generated by an established spiking neuron model that was reported in our previous work, and the experimental data were provided using single-unit microelectrode recordings (MERs) during DBS (microelectrode stimulation). Based on these data, we developed a novel mathematical model to represent the firing rate of neurons receiving DBS, including neurons in STN, SNr, and Vim—across different DBS frequencies. In our model, the DBS pulses were filtered through a synapse model and a nonlinear transfer function to formulate the firing rate variability. For each DBS-targeted nucleus, we fitted a single set of optimal model parameters consistent across varying DBS frequencies.

      Results

      Our model accurately reproduced the firing rates observed and calculated from both synthetic and experimental data. The optimal model parameters were consistent across different DBS frequencies.

      Conclusions

      The result of our model fitting was in agreement with experimental single-unit MER data during DBS. Reproducing neuronal firing rates of different nuclei of the basal ganglia and thalamus during DBS can be helpful to further understand the mechanisms of DBS and to potentially optimize stimulation parameters based on their actual effects on neuronal activity.

      Keywords

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      References

        • Lebouvier T.
        • Chaumette T.
        • Paillusson S.
        • et al.
        The second brain and Parkinson’s disease.
        Eur J Neurosci. 2009; 30: 735-741https://doi.org/10.1111/j.1460-9568.2009.06873.x
        • van Albada S.J.
        • Gray R.T.
        • Drysdale P.M.
        • Robinson P.A.
        Mean-field modeling of the basal ganglia-thalamocortical system. II Dynamics of parkinsonian oscillations.
        J Theor Biol. 2009; 257: 664-688https://doi.org/10.1016/j.jtbi.2008.12.013
        • Yousif N.
        • Mace M.
        • Pavese N.
        • Borisyuk R.
        • Nandi D.
        • Bain P.
        A network model of local field potential activity in essential tremor and the impact of deep brain stimulation.
        PLoS Comput Biol. 2017; 13e1005326https://doi.org/10.1371/journal.pcbi.1005326
        • Blomstedt P.
        • Sandvik U.
        • Tisch S.
        Deep brain stimulation in the posterior subthalamic area in the treatment of essential tremor.
        Mov Disord. 2010; 25: 1350-1356
        • Milosevic L.
        • Kalia S.K.
        • Hodaie M.
        • et al.
        A theoretical framework for the site-specific and frequency-dependent neuronal effects of deep brain stimulation.
        Brain Stimul. 2021; 14: 807-821https://doi.org/10.1016/j.brs.2021.04.022
        • Limousin P.
        • Krack P.
        • Pollak P.
        • 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.
        • De Vloo P.D.
        • 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.
        • et al.
        Long-term outcome of bilateral pallidal deep brain stimulation for primary cervical dystonia.
        Neurology. 2007; 68: 457-459https://doi.org/10.1212/01.wnl.0000252932.71306.89
        • Menchón J.M.
        • Real E.
        • Alonso P.
        • et al.
        A prospective international multi-center study on safety and efficacy of deep brain stimulation for resistant obsessive-compulsive disorder.
        Mol Psychiatry. 2021; 26: 1234-1247https://doi.org/10.1038/s41380-019-0562-6
        • Laxton A.W.
        • Lozano A.M.
        Deep brain stimulation for the treatment of Alzheimer disease and dementias.
        World Neurosurg. 2013; 80: S28.e1-S28.e8https://doi.org/10.1016/j.wneu.2012.06.028
        • Fisher R.
        • Salanova V.
        • Witt T.
        • 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
        • Boutet A.
        • Madhavan R.
        • Elias G.J.B.
        • et al.
        Predicting optimal deep brain stimulation parameters for Parkinson’s disease using functional MRI and machine learning.
        Nat Commun. 2021; 12: 3043https://doi.org/10.1038/s41467-021-23311-9
        • Rosenbaum R.
        • Zimnik A.
        • Zheng F.
        • 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
        • Farokhniaee A.
        • McIntyre C.C.
        Theoretical principles of deep brain stimulation induced synaptic suppression.
        Brain Stimul. 2019; 12: 1402-1409https://doi.org/10.1016/j.brs.2019.07.005
        • Steiner L.A.
        • Barreda 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
        • Milosevic L.
        • Kalia S.K.
        • Hodaie M.
        • et al.
        Neuronal inhibition and synaptic plasticity of basal ganglia neurons in Parkinson’s disease.
        Brain. 2018; 141: 177-190
        • Steiner L.A.
        • Kühn A.A.
        • Geiger J.R.P.
        • et al.
        Persistent synaptic inhibition of the subthalamic nucleus by high frequency stimulation.
        Brain Stimul. 2022; 15: 1223-1232https://doi.org/10.1016/j.brs.2022.08.020
        • Jercog D.
        • Roxin A.
        • Barthó P.
        • Luczak A.
        • Compte A.
        • de la Rocha J.
        UP-DOWN cortical dynamics reflect state transitions in a bistable network.
        eLife. 2017; 6e22425https://doi.org/10.7554/eLife.22425
        • Hennequin G.
        • Ahmadian Y.
        • Rubin D.B.
        • Lengyel M.
        • Miller K.D.
        The dynamical regime of sensory cortex: stable dynamics around a single stimulus-tuned attractor account for patterns of noise variability.
        Neuron. 2018; 98: 846-860.e5https://doi.org/10.1016/j.neuron.2018.04.017
        • Lim S.
        • McKee J.L.
        • Woloszyn L.
        • et al.
        Inferring learning rules from distributions of firing rates in cortical neurons.
        Nat Neurosci. 2015; 18: 1804-1810https://doi.org/10.1038/nn.4158
        • Murphy B.K.
        • Miller K.D.
        Balanced amplification: a new mechanism of selective amplification of neural activity patterns.
        Neuron. 2009; 61: 635-648https://doi.org/10.1016/j.neuron.2009.02.005
        • van Albada S.J.
        • Robinson P.A.
        Mean-field modeling of the basal ganglia-thalamocortical system. I Firing rates in healthy and parkinsonian states.
        J Theor Biol. 2009; 257: 642-663https://doi.org/10.1016/j.jtbi.2008.12.018
        • Gigante G.
        • Deco G.
        • Marom S.
        • Del Giudice P.D.
        Network events on multiple space and time scales in cultured neural networks and in a stochastic rate model.
        PLoS Comp Biol. 2015; 11e1004547https://doi.org/10.1371/journal.pcbi.1004547
        • Farokhniaee A.
        • Lowery M.M.
        Cortical network effects of subthalamic deep brain stimulation in a thalamo-cortical microcircuit model.
        J Neural Eng. 2021; 18https://doi.org/10.1088/1741-2552/abee50
        • Yousif N.
        • Bain P.G.
        • Nandi D.
        • Borisyuk R.
        A population model of deep brain stimulation in movement disorders from circuits to cells.
        Front Hum Neurosci. 2020; 14: 55https://doi.org/10.3389/fnhum.2020.00055
        • Wilson H.R.
        • Cowan J.D.
        Excitatory and inhibitory interactions in localized populations of model neurons.
        Biophys J. 1972; 12: 1-24https://doi.org/10.1016/S0006-3495(72)86068-5
        • Tsodyks M.
        • Pawelzik K.
        • Markram H.
        Neural networks with dynamic synapses.
        Neural Comput. 1998; 10: 821-835https://doi.org/10.1162/089976698300017502
        • Tsodyks M.
        • Wu S.
        Short-term synaptic plasticity.
        Scholarpedia. 2013; 8: 3153https://doi.org/10.4249/scholarpedia.3153
        • Ghanbari A.
        • Malyshev A.
        • Volgushev M.
        • Stevenson I.H.
        Estimating short-term synaptic plasticity from pre-and postsynaptic spiking.
        PLoS Comp Biol. 2017; 13e1005738
        • Sporns O.
        • Chialvo D.R.
        • Kaiser M.
        • Hilgetag C.C.
        Organization, development and function of complex brain networks.
        Trends Cogn Sci. 2004; 8: 418-425https://doi.org/10.1016/j.tics.2004.07.008
        • Nelder J.A.
        • Mead R.
        A simplex method for function minimization.
        Comput J. 1965; 7: 308-313https://doi.org/10.1093/comjnl/7.4.308
        • Lagarias J.C.
        • Reeds J.A.
        • Wright M.H.
        • Wright P.E.
        Convergence properties of the Nelder--Mead simplex method in low dimensions.
        SIAM J Optim. 1998; 9: 112-147https://doi.org/10.1137/S1052623496303470
        • Shimazaki H.
        • Shinomoto S.
        A method for selecting the bin size of a time histogram.
        Neural Comput. 2007; 19: 1503-1527https://doi.org/10.1162/neco.2007.19.6.1503
        • Reed C.M.
        • Mosher C.P.
        • Chandravadia N.
        • Chung J.M.
        • Mamelak A.N.
        • Rutishauser U.
        Extent of single-neuron activity modulation by hippocampal interictal discharges predicts declarative memory disruption in humans.
        J Neurosci. 2020; 40: 682-693https://doi.org/10.1523/JNEUROSCI.1380-19.2019
        • Mansouri F.A.
        • Buckley M.J.
        • Tanaka K.
        The essential role of primate orbitofrontal cortex in conflict-induced executive control adjustment.
        J Neurosci. 2014; 34: 11016-11031https://doi.org/10.1523/JNEUROSCI.1637-14.2014
        • Koirala N.
        • Serrano L.
        • Paschen S.
        • et al.
        Mapping of subthalamic nucleus using microelectrode recordings during deep brain stimulation.
        Sci Rep. 2020; 1019241https://doi.org/10.1038/s41598-020-74196-5
        • Kinfe T.M.
        • Vesper J.
        The impact of multichannel microelectrode recording (MER) in deep brain stimulation of the basal ganglia.
        Acta Neurochir Suppl. 2013; 117: 27-33https://doi.org/10.1007/978-3-7091-1482-7_5
        • Maggio F.
        • Pasciuto T.
        • Paffi A.
        • et al.
        Micro vs macro electrode DBS stimulation: a dosimetric study.
        Annu Int Conf IEEE Eng Med Biol Soc. 2010; 2010: 2057-2060https://doi.org/10.1109/IEMBS.2010.5626487
        • Lafreniere-Roula M.
        • Hutchison W.D.
        • Lozano A.M.
        • Hodaie M.
        • Dostrovsky J.O.
        Microstimulation-induced inhibition as a tool to aid targeting the ventral border of the subthalamic nucleus.
        J Neurosurg. 2009; 111: 724-728https://doi.org/10.3171/2009.3.JNS09111
        • Sirica D.
        • Hewitt A.L.
        • Tarolli C.G.
        • et al.
        Neurophysiological biomarkers to optimize deep brain stimulation in movement disorders.
        Neurodegener Dis Manag. 2021; 11: 315-328https://doi.org/10.2217/nmt-2021-0002
        • Arcot Desai S.
        • Gutekunst C.A.
        • Potter S.M.
        • Gross R.E.
        Deep brain stimulation macroelectrodes compared to multiple microelectrodes in rat hippocampus.
        Front Neuroeng. 2014; 7: 16https://doi.org/10.3389/fneng.2014.00016
        • 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: 2142-2155
        • Wang Y.
        • Markram H.
        • Goodman P.H.
        • Berger T.K.
        • Ma J.
        • Goldman-Rakic P.S.
        Heterogeneity in the pyramidal network of the medial prefrontal cortex.
        Nat Neurosci. 2006; 9: 534-542https://doi.org/10.1038/nn1670
        • Markram H.
        • Muller E.
        • Ramaswamy S.
        • et al.
        Reconstruction and simulation of neocortical microcircuitry.
        Cell. 2015; 163: 456-492https://doi.org/10.1016/j.cell.2015.09.029
        • Molnar G.F.
        • Pilliar A.
        • Lozano A.M.
        • Dostrovsky J.O.
        Differences in neuronal firing rates in pallidal and cerebellar receiving areas of thalamus in patients with Parkinson’s disease, essential tremor, and pain.
        J Neurophysiol. 2005; 93: 3094-3101https://doi.org/10.1152/jn.00881.2004
        • Remple M.S.
        • Bradenham C.H.
        • Kao C.C.
        • Charles P.D.
        • Neimat J.S.
        • Konrad P.E.
        Subthalamic nucleus neuronal firing rate increases with Parkinson’s disease progression.
        Mov Disord. 2011; 26: 1657-1662https://doi.org/10.1002/mds.23708
        • Mallet N.
        • Pogosyan A.
        • Márton L.F.
        • Bolam J.P.
        • Brown P.
        • Magill P.J.
        Parkinsonian beta oscillations in the external globus pallidus and their relationship with subthalamic nucleus activity.
        J Neurosci. 2008; 28: 14245-14258https://doi.org/10.1523/JNEUROSCI.4199-08.2008
        • Kovaleski R.F.
        • Callahan J.W.
        • Chazalon M.
        • Wokosin D.L.
        • Baufreton J.
        • Bevan M.D.
        Dysregulation of external globus pallidus-subthalamic nucleus network dynamics in parkinsonian mice during cortical slow-wave activity and activation.
        J Physiol. 2020; 598: 1897-1927https://doi.org/10.1113/JP279232
        • Yamada-Hanff J.
        • Bean B.P.
        Persistent sodium current drives conditional pacemaking in CA1 pyramidal neurons under muscarinic stimulation.
        J Neurosci. 2013; 33: 15011-15021https://doi.org/10.1523/JNEUROSCI.0577-13.2013
        • Raman I.M.
        • Bean B.P.
        Resurgent sodium current and action potential formation in dissociated cerebellar Purkinje neurons.
        J Neurosci. 1997; 17: 4517-4526https://doi.org/10.1523/JNEUROSCI.17-12-04517.1997
        • Anderson J.S.
        • Lampl I.
        • Gillespie D.C.
        • Ferster D.
        The contribution of noise to contrast invariance of orientation tuning in cat visual cortex.
        Science. 2000; 290: 1968-1972https://doi.org/10.1126/science.290.5498.1968
        • Rauch A.
        • La Camera G.
        • Luscher H.R.
        • Senn W.
        • Fusi S.
        Neocortical pyramidal cells respond as integrate-and-fire neurons to in vivo-like input currents.
        J Neurophysiol. 2003; 90: 1598-1612https://doi.org/10.1152/jn.00293.2003
        • Izhikevich E.M.
        • Edelman G.M.
        Large-scale model of mammalian thalamocortical systems.
        Proc Natl Acad Sci U S A. 2008; 105: 3593-3598https://doi.org/10.1073/pnas.0712231105
        • Schwalger T.
        • Chizhov A.V.
        Mind the last spike – firing rate models for mesoscopic populations of spiking neurons.
        Curr Opin Neurobiol. 2019; 58: 155-166https://doi.org/10.1016/j.conb.2019.08.003
        • Schmidt S.L.
        • Brocker D.T.
        • Swan B.D.
        • Turner D.A.
        • Grill W.M.
        Evoked potentials reveal neural circuits engaged by human deep brain stimulation.
        Brain Stimul. 2020; 13: 1706-1718https://doi.org/10.1016/j.brs.2020.09.028
        • Steffen J.K.
        • Reker P.
        • Mennicken F.K.
        • et al.
        Bipolar directional deep brain stimulation in essential and parkinsonian tremor.
        Neuromodulation. 2020; 23: 543-549https://doi.org/10.1111/ner.13109
        • Masuda H.
        • Shirozu H.
        • Ito Y.
        • Fukuda M.
        • Fujii Y.
        Surgical strategy for directional deep brain stimulation.
        Neurol Med Chir (Tokyo). 2022; 62: 1-12https://doi.org/10.2176/nmc.ra.2021-0214
        • Murray Sherman S.
        • Guillery R.W.
        Chapter II - The nerve cells of the thalamus.
        in: Murray Sherman S. Guillery R.W. Exploring the Thalamus. Academic Press, 2001: 19-58https://doi.org/10.1016/B978-012305460-9/50016-2
        • Ohara P.T.
        • Chazal G.
        • Ralston H.J.
        Ultrastructural analysis of gaba-immunoreactive elements in the monkey thalamic ventrobasal complex.
        J Comp Neurol. 1989; 283: 541-558https://doi.org/10.1002/cne.902830408
        • Fleming J.E.
        • Dunn E.
        • Lowery M.M.
        Simulation of closed-loop deep brain stimulation control schemes for suppression of pathological beta oscillations in Parkinson’s disease.
        Front Neurosci. 2020; 14: 166https://doi.org/10.3389/fnins.2020.00166
        • Engert F.
        • Bonhoeffer T.
        Dendritic spine changes associated with hippocampal long-term synaptic plasticity.
        Nature. 1999; 399: 66-70https://doi.org/10.1038/19978
        • Kullmann D.M.
        • Lamsa K.P.
        Long-term synaptic plasticity in hippocampal interneurons.
        Nat Rev Neurosci. 2007; 8: 687-699https://doi.org/10.1038/nrn2207
        • Paulsen O.
        • Sejnowski T.J.
        Natural patterns of activity and long-term synaptic plasticity.
        Curr Opin Neurobiol. 2000; 10: 172-179
        • Chiu C.Q.
        • Barberis A.
        • Higley M.J.
        Preserving the balance: diverse forms of long-term GABAergic synaptic plasticity.
        Nat Rev Neurosci. 2019; 20: 272-281https://doi.org/10.1038/s41583-019-0141-5
        • Palacios-Filardo J.
        • Mellor J.R.
        Neuromodulation of hippocampal long-term synaptic plasticity.
        Curr Opin Neurobiol. 2019; 54: 37-43https://doi.org/10.1016/j.conb.2018.08.009
        • Grado L.L.
        • Johnson M.D.
        • Netoff T.I.
        Bayesian adaptive dual control of deep brain stimulation in a computational model of Parkinson’s disease.
        PLoS Comp Biol. 2018; 14e1006606https://doi.org/10.1371/journal.pcbi.1006606
        • Picillo M.
        • Lozano A.M.
        • Kou N.
        • Puppi Munhoz R.
        • Fasano A.
        Programming deep brain stimulation for Parkinson’s disease: the Toronto Western Hospital algorithms.
        Brain Stimul. 2016; 9: 425-437https://doi.org/10.1016/j.brs.2016.02.004
        • Liu C.
        • Zhao G.
        • Meng Z.
        • et al.
        Closing the loop of DBS using the beta oscillations in cortex.
        Cogn Neurodyn. 2021; 15: 1157-1167https://doi.org/10.1007/s11571-021-09690-1
        • Merola A.
        • Zibetti M.
        • Artusi C.A.
        • et al.
        80 Hz versus 130 Hz subthalamic nucleus deep brain stimulation: effects on involuntary movements.
        Parkinsonism Relat Disord. 2013; 19: 453-456https://doi.org/10.1016/j.parkreldis.2013.01.006