Direct electrical stimulation can modulate the activity of brain networks for the treatment of several neurological and neuropsychiatric disorders and for restoring lost function. However, precise neuromodulation in an individual requires the accurate modelling and prediction of the effects of stimulation on the activity of their large-scale brain networks. Here, we report the development of dynamic input–output models that predict multiregional dynamics of brain networks in response to temporally varying patterns of ongoing microstimulation. In experiments with two awake rhesus macaques, we show that the activities of brain networks are modulated by changes in both stimulation amplitude and frequency, that they exhibit damping and oscillatory response dynamics, and that variabilities in prediction accuracy and in estimated response strength across brain regions can be explained by an at-rest functional connectivity measure computed without stimulation. Input–output models of brain dynamics may enable precise neuromodulation for the treatment of disease and facilitate the investigation of the functional organization of large-scale brain networks.
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Suppression of seizure in childhood absence epilepsy using robust control of deep brain stimulation: a simulation study
Scientific Reports Open Access 10 January 2023
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The main data supporting the results in this study are available within the paper and its Supplementary Information. The raw and analysed datasets generated during the study are too large to be publicly shared, but are available for research purposes from the corresponding author on reasonable request.
The custom computer code in this study is available at https://github.com/ShanechiLab/DynamicStimulation.
Shanechi, M. M. Brain–machine interfaces from motor to mood. Nat. Neurosci. 22, 1554–1564 (2019).
Hoang, K. B., Cassar, I. R., Grill, W. M. & Turner, D. A. Biomarkers and stimulation algorithms for adaptive brain stimulation. Front. Neurosci. 11, 564 (2017).
Lo, M. C. & Widge, A. S. Closed-loop neuromodulation systems: next-generation treatments for psychiatric illness. Int. Rev. Psychiatry 29, 191–204 (2017).
Ashkan, K., Rogers, P., Bergman, H. & Ughratdar, I. Insights into the mechanisms of deep brain stimulation. Nat. Rev. Neurol. 13, 548–554 (2017).
Deuschl, G. & Agid, Y. Subthalamic neurostimulation for Parkinson’s disease with early fluctuations: balancing the risks and benefits. Lancet Neurol. 12, 1025–1034 (2013).
Fisher, R. et al. Electrical stimulation of the anterior nucleus of thalamus for treatment of refractory epilepsy. Epilepsia 51, 899–908 (2010).
Boccard, S. G., Pereira, E. A. & Aziz, T. Z. Deep brain stimulation for chronic pain. J. Clin. Neurosci. 22, 1537–1543 (2015).
Dandekar, M., Fenoy, A., Carvalho, A., Soares, J. & Quevedo, J. Deep brain stimulation for treatment-resistant depression: an integrative review of preclinical and clinical findings and translational implications. Mol. Psychiatry 23, 1094 (2018).
Koning, P. P., de, Figee, M., Munckhof, P., van den, Schuurman, P. R. & Denys, D. Current status of deep brain stimulation for obsessive–compulsive disorder: a clinical review of different targets. Curr. Psychiatry Rep. 13, 274–282 (2011).
Williams, Z. M. & Eskandar, E. N. Selective enhancement of associative learning by microstimulation of the anterior caudate. Nat. Neurosci. 9, 562 (2006).
Chang, E. F., Kurteff, G. & Wilson, S. M. Selective interference with syntactic encoding during sentence production by direct electrocortical stimulation of the inferior frontal gyrus. J. Cogn. Neurosci. 30, 411–420 (2018).
Whitmire, C. J., Millard, D. C. & Stanley, G. B. Thalamic state control of cortical paired-pulse dynamics. J. Neurophysiol. 117, 163–177 (2016).
Rao, V. R. et al. Direct electrical stimulation of lateral orbitofrontal cortex acutely improves mood in individuals with symptoms of depression. Curr. Biol. 28, 3893–3902 (2018).
Hartevelt, T. Jvan et al. Neural plasticity in human brain connectivity: the effects of long term deep brain stimulation of the subthalamic nucleus in Parkinson’s disease. PLoS ONE 9, e86496 (2014).
Saenger, V. M. et al. Uncovering the underlying mechanisms and whole-brain dynamics of deep brain stimulation for Parkinson’s disease. Sci. Rep. 7, 9882 (2017).
Basu, I. et al. Consistent linear and non-linear responses to invasive electrical brain stimulation across individuals and primate species with implanted electrodes. Brain Stimul. 12, 877–892 (2019).
Crowther, L. J. et al. A quantitative method for evaluating cortical responses to electrical stimulation. J. Neurosci. Methods 311, 67–75 (2019).
Yang, Y., Connolly, A. T. & Shanechi, M. M. A control-theoretic system identification framework and a real-time closed-loop clinical simulation testbed for electrical brain stimulation. J. Neural Eng. 15, 066007 (2018).
Osorio, I. et al. An introduction to contingent (closed-loop) brain electrical stimulation for seizure blockage, to ultra-short-term clinical trials, and to multidimensional statistical analysis of therapeutic efficacy. J. Clin. Neurophysiol. 18, 533–544 (2001).
Little, S. et al. Bilateral adaptive deep brain stimulation is effective in Parkinson’s disease. J. Neurol. Neurosurg. Psychiatry 87, 717–721 (2016).
Shirvalkar, P., Veuthey, T. L., Dawes, H. E. & Chang, E. F. Closed-loop deep brain stimulation for refractory chronic pain. Front. Comput. Neurosci. 12, 18 (2018).
Sani, O. G. et al. Mood variations decoded from multi-site intracranial human brain activity. Nat. Biotechnol. 36, 954–961 (2018).
Kirkby, L. A. et al. An amygdala–hippocampus subnetwork that encodes variation in human mood. Cell 175, 1688–1700 (2018).
Etkin, A. & Wager, T. D. Functional neuroimaging of anxiety: a meta-analysis of emotional processing in PTSD, social anxiety disorder, and specific phobia. Am. J. Psychiatry 164, 1476–1488 (2007).
Kupfer, D. J., Frank, E. & Phillips, M. L. Major depressive disorder: new clinical, neurobiological, and treatment perspectives. Lancet 379, 1045–1055 (2012).
Williams, L. M. Defining biotypes for depression and anxiety based on large-scale circuit dysfunction: a theoretical review of the evidence and future directions for clinical translation. Depress. Anxiety 34, 9–24 (2017).
Montgomery, E. B. & Baker, K. B. Mechanisms of deep brain stimulation and future technical developments. Neurol. Res. 22, 259–266 (2000).
Rubin, J. E. & Terman, D. High frequency stimulation of the subthalamic nucleus eliminates pathological thalamic rhythmicity in a computational model. J. Comput. Neurosci. 16, 211–235 (2004).
McIntyre, C. C. & Hahn, P. J. Network perspectives on the mechanisms of deep brain stimulation. Neurobiol. Dis. 38, 329–337 (2010).
Hahn, P. J. & McIntyre, C. C. Modeling shifts in the rate and pattern of subthalamopallidal network activity during deep brain stimulation. J. Comput. Neurosci. 28, 425–441 (2010).
Santaniello, S. et al. Therapeutic mechanisms of high-frequency stimulation in Parkinson’s disease and neural restoration via loop-based reinforcement. Proc. Natl Acad. Sci. USA 112, E586–E595 (2015).
Stefanescu, R. A., Shivakeshavan, R. & Talathi, S. S. Computational models of epilepsy. Seizure 21, 748–759 (2012).
Sritharan, D. & Sarma, S. V. Fragility in dynamic networks: application to neural networks in the epileptic cortex. Neural Comput. 26, 2294–2327 (2014).
Feng, X. J., Shea-Brown, E., Greenwald, B., Kosut, R. & Rabitz, H. Optimal deep brain stimulation of the subthalamic nucleus–a computational study. J. Comput. Neurosci. 23, 265–282 (2007).
Brocker, D. T. et al. Optimized temporal pattern of brain stimulation designed by computational evolution. Sci. Transl. Med. 9, eaah3532 (2017).
Liu, J., Khalil, H. K. & Oweiss, K. G. Model-based analysis and control of a network of basal ganglia spiking neurons in the normal and parkinsonian states. J. Neural Eng. 8, 045002 (2011).
Santaniello, S., Fiengo, G., Glielmo, L. & Grill, W. M. Closed-loop control of deep brain stimulation: a simulation study. IEEE Trans. Neural Syst. Rehabil. Eng. 19, 15–24 (2011).
Millard, D. C., Wang, Q., Gollnick, C. A. & Stanley, G. B. System identification of the nonlinear dynamics in the thalamocortical circuit in response to patterned thalamic microstimulation in vivo. J. Neural Eng. 10, 066011 (2013).
Bolus, M., Willats, A., Whitmire, C., Rozell, C. & Stanley, G. Design strategies for dynamic closed-loop optogenetic neurocontrol in vivo. J. Neural Eng. 15, 026011 (2018).
Basu, I. et al. A neural mass model to predict electrical stimulation evoked responses in human and non-human primate brain. J. Neural Eng. 15, 066012 (2018).
Khambhati, A. N. et al. Functional control of electrophysiological network architecture using direct neurostimulation in humans. Netw. Neuroscience 3, 848–877 (2019).
Stiso, J. et al. White matter network architecture guides direct electrical stimulation through optimal state transitions. Cell Rep. 28, 2554–2566 (2019).
Hsieh, H.-L., Wong, Y. T., Pesaran, B. & Shanechi, M. M. Multiscale modeling and decoding algorithms for spike-field activity. J. Neural Eng. 16, 016018 (2018).
de Hemptinne, C. et al. Therapeutic deep brain stimulation reduces cortical phase-amplitude coupling in Parkinson’s disease. Nat. Neurosci. 18, 779–786 (2015).
Kondabolu, K. et al. Striatal cholinergic interneurons generate beta and gamma oscillations in the corticostriatal circuit and produce motor deficits. Proc. Natl Acad. Sci. USA 113, E3159–E3168 (2016).
Pasqualetti, F., Zampieri, S. & Bullo, F. Controllability metrics, limitations and algorithms for complex networks. IEEE Trans. Control Netw. Syst. 1, 40–52 (2014).
Gu, S. et al. Controllability of structural brain networks. Nat. Commun. 6, 8414 (2015).
Muldoon, S. F. et al. Stimulation-based control of dynamic brain networks. PLoS Comput. Biol. 12, e1005076 (2016).
Tang, E. et al. Developmental increases in white matter network controllability support a growing diversity of brain dynamics. Nat. Commun. 8, 1252 (2017).
Medaglia, J. D. et al. Network controllability in the inferior frontal gyrus relates to controlled language variability and susceptibility to TMS. J. Neurosci. 38, 6399–6410 (2018).
Pesaran, B. et al. Investigating large-scale brain dynamics using field potential recordings: analysis and interpretation. Nat. Neurosci. 21, 903–919 (2018).
Ljung, L. System Identification (Prentice Hall, 1999).
Tass, P. A. A model of desynchronizing deep brain stimulation with a demand-controlled coordinated reset of neural subpopulations. Biol. Cybern. 89, 81–88 (2003).
Tass, P. A. & Hauptmann, C. Therapeutic modulation of synaptic connectivity with desynchronizing brain stimulation. Int. J. Psychophysiol. 64, 53–61 (2007).
Tass, P. A. et al. Coordinated reset has sustained aftereffects in Parkinsonian monkeys. Ann. Neurol. 72, 816–820 (2012).
Barrat, A., Barthelemy, M., Pastor-Satorras, R. & Vespignani, A. The architecture of complex weighted networks. Proc. Natl Acad. Sci. USA 101, 3747–3752 (2004).
Van Wijk, B. C., Stam, C. J. & Daffertshofer, A. Comparing brain networks of different size and connectivity density using graph theory. PLoS ONE 5, e13701 (2010).
Sani, O. G., Abbaspourazad, H., Wong, Y. T., Pesaran, B. & Shanechi, M. M. Modeling behaviorally relevant neural dynamics enabled by preferential subspace identification. Nat. Neurosci. 24, 140–149 (2021).
Herzfeld, D. J., Kojima, Y., Soetedjo, R. & Shadmehr, R. Encoding of action by the Purkinje cells of the cerebellum. Nature 526, 439 (2015).
Churchland, M. M. et al. Neural population dynamics during reaching. Nature 487, 51 (2012).
Anumanchipalli, G. K., Chartier, J. & Chang, E. F. Speech synthesis from neural decoding of spoken sentences. Nature 568, 493–498 (2019).
Vaz, A. P., Inati, S. K., Brunel, N. & Zaghloul, K. A. Coupled ripple oscillations between the medial temporal lobe and neocortex retrieve human memory. Science 363, 975–978 (2019).
Markowitz, D. A., Curtis, C. E. & Pesaran, B. Multiple component networks support working memory in prefrontal cortex. Proc. Natl Acad. Sci. USA 112, 11084–11089 (2015).
Denfield, G. H., Ecker, A. S., Shinn, T. J., Bethge, M. & Tolias, A. S. Attentional fluctuations induce shared variability in macaque primary visual cortex. Nat. Commun. 9, 2654 (2018).
Han, X., Xian, S. X. & Moore, T. Dynamic sensitivity of area V4 neurons during saccade preparation. Proc. Natl Acad. Sci. USA 106, 13046–13051 (2009).
Jamali, M. et al. Dorsolateral prefrontal neurons mediate subjective decisions and their variation in humans. Nat. Neurosci. 22, 1010–1020 (2019).
Zavala, B. A., Jang, A. I. & Zaghloul, K. A. Human subthalamic nucleus activity during non-motor decision making. eLife 6, e31007 (2017).
Herzfeld, D. J., Kojima, Y., Soetedjo, R. & Shadmehr, R. Encoding of error and learning to correct that error by the Purkinje cells of the cerebellum. Nat. Neurosci. 21, 736–743 (2018).
Zheng, H. J., Wang, Q. & Stanley, G. B. Adaptive shaping of cortical response selectivity in the vibrissa pathway. J. Neurophysiol. 113, 3850–3865 (2015).
Froudarakis, E. et al. Population code in mouse V1 facilitates readout of natural scenes through increased sparseness. Nat. Neurosci. 17, 851–857 (2014).
Susilaradeya, D. et al. Extrinsic and intrinsic dynamics in movement intermittency. eLife 8, e40145 (2019).
Hall, T. M., Carvalho, Fde & Jackson, A. A common structure underlies low-frequency cortical dynamics in movement, sleep, and sedation. Neuron 83, 1185–1199 (2014).
Abbaspourazad, H., Choudhury, M., Wong, Y. T., Pesaran, B. & Shanechi, M. M. Multiscale low-dimensional motor cortical state dynamics predict naturalistic reach-and-grasp behavior. Nat. Commun. (in the press).
Shenoy, K. V. & Carmena, J. M. Combining decoder design and neural adaptation in brain-machine interfaces. Neuron 84, 665–680 (2014).
Abbaspourazad, H., Hsieh, H.-L. & Shanechi, M. M. A multiscale dynamical modeling and identification framework for spike-field activity. IEEE Trans. Neural Syst. Rehabil. Eng. 27, 1128–1138 (2019).
Kao, J. C. et al. Single-trial dynamics of motor cortex and their applications to brain-machine interfaces. Nat. Commun. 6, 7759 (2015).
Irwin, Z. et al. Neural control of finger movement via intracortical brain–machine interface. J. Neural Eng. 14, 066004 (2017).
Vaskov, A. K. et al. Cortical decoding of individual finger group motions using ReFIT Kalman filter. Front. Neurosci. 12, 751 (2018).
Keller, C. J. et al. Mapping human brain networks with cortico-cortical evoked potentials. Phil. Trans. R. Soc. B 369, 20130528 (2014).
Holtzheimer, P. E. et al. Subcallosal cingulate deep brain stimulation for treatment-resistant depression: a multisite, randomised, sham-controlled trial. Lancet Psychiat. 4, 839–849 (2017).
Dougherty, D. D. et al. A randomized sham-controlled trial of deep brain stimulation of the ventral capsule/ventral striatum for chronic treatment-resistant depression. Biol. Psychiatry 78, 240–248 (2015).
Ezzyat, Y. et al. Closed-loop stimulation of temporal cortex rescues functional networks and improves memory. Nat. Commun. 9, 365 (2018).
Deadwyler, S. A. et al. A cognitive prosthesis for memory facilitation by closed-loop functional ensemble stimulation of hippocampal neurons in primate brain. Exp. Neurol. 287, 452–460 (2017).
Zanos, S., Richardson, A. G., Shupe, L., Miles, F. P. & Fetz, E. E. The Neurochip-2: an autonomous head-fixed computer for recording and stimulating in freely behaving monkeys. IEEE Trans. Neural Syst. Rehabil. Eng. 19, 427–435 (2011).
Zanos, S., Rembado, I., Chen, D. & Fetz, E. E. Phase-locked stimulation during cortical beta oscillations produces bidirectional synaptic plasticity in awake monkeys. Curr. Biol. 28, 2515–2526 (2018).
Etkin, A. et al. Using fMRI connectivity to define a treatment-resistant form of post-traumatic stress disorder. Sci. Transl. Med. 11, eaal3236 (2019).
Ahmadipour, P., Yang, Y., Chang, E. F. & Shanechi, M. M. Adaptive tracking of human ECoG network dynamics. J. Neural Eng. https://doi.org/10.1088/1741-2552/abae42 (2020).
Mazzoni, A. et al. Computing the local field potential (LFP) from integrate-and-fire network models. PLoS Comput. Biol. 11, e1004584 (2015).
Tehovnik, E., Tolias, A., Sultan, F., Slocum, W. & Logothetis, N. Direct and indirect activation of cortical neurons by electrical microstimulation. J. Neurophysiol. 96, 512–521 (2006).
Haber, S. N. in Decision Neuroscience: An Integrative Perspective (eds Dreher, J.-C. & Tremblay, L.) 3–19 (Elsevier, 2017).
Choi, J., Goncharov, V., Kleinbart, J., Orsborn, A. & Pesaran, B. Monkey-MIMMS: Towards automated cellular resolution large-scale two-photon microscopy in the awake macaque monkey. In 40th Conf. Proc. IEEE Eng. Med. Biol. Soc. 3013–3016 (IEEE, 2018).
Kleinbart, J. E. et al. A modular implant system for multimodal recording and manipulation of the primate brain. In 40th Conf. Proc. IEEE Eng. Med. Biol. Soc. 3362–3365 (IEEE, 2018).
Bighamian, R., Wong, Y. T., Pesaran, B. & Shanechi, M. M. Sparse model-based estimation of functional dependence in high-dimensional field and spike multiscale networks. J. Neural Eng. 16, 056022 (2019).
Wang, C. & Shanechi, M. M. Estimating multiscale direct causality graphs in neural spike-field networks. IEEE Trans. Neural Syst. Rehabil. Eng. 27, 857–866 (2019).
Yang, Y., Sani, O., Chang, E. F. & Shanechi, M. M. Dynamic network modeling and dimensionality reduction for human ECoG activity. J. Neural Eng. 16, 056014 (2019).
Garcia, L., d Alessandro, G., Bioulac, B. & Hammond, C. High-frequency stimulation in Parkinson’s disease: more or less? Trends Neurosci. 28, 209–216 (2005).
Qiao, S., Brown, K. A., Orsborn, A. L., Ferrentino, B. & Pesaran, B. Development of semi-chronic microdrive system for large-scale circuit mapping in macaque mesolimbic and basal ganglia systems. In 38th Conf. Proc. IEEE Eng. Med. Biol. Soc. 5825–5828 (IEEE, 2016).
Dotson, N. M., Hoffman, S. J., Goodell, B. & Gray, C. M. A large-scale semi-chronic microdrive recording system for non-human primates. Neuron 96, 769–782 (2017).
Yang, Y. et al. Developing a personalized closed-loop controller of medically-induced coma in a rodent model. J. Neural Eng. 16, 036022 (2019).
Yang, Y. & Shanechi, M. M. An adaptive and generalizable closed-loop system for control of medically induced coma and other states of anesthesia. J. Neural Eng. 13, 066019 (2016).
Lilly, J. C., Hughes, J. R., Alvord, E. C. Jr & Galkin, T. W. Brief, noninjurious electric waveform for stimulation of the brain. Science 121, 468–469 (1955).
Herrington, T. M., Cheng, J. J. & Eskandar, E. N. Mechanisms of deep brain stimulation. J. Neurophysiol. 115, 19–38 (2015).
Hashimoto, T., Elder, C. M. & Vitek, J. L. A template subtraction method for stimulus artifact removal in high-frequency deep brain stimulation. J. Neurosci. Methods 113, 181–186 (2002).
Erez, Y., Tischler, H., Moran, A. & Bar-Gad, I. Generalized framework for stimulus artifact removal. J. Neurosci. Methods 191, 45–59 (2010).
Babadi, B. & Brown, E. N. A review of multitaper spectral analysis. IEEE Trans. Biomed. Eng. 61, 1555–1564 (2014).
Schwartz, A. B., Cui, X. T., Weber, D. J. & Moran, D. W. Brain-controlled interfaces: movement restoration with neural prosthetics. Neuron 52, 205–220 (2006).
Thakor, N. V. Translating the brain-machine interface. Sci. Transl. Med. 5, 210ps17 (2013).
So, K., Dangi, S., Orsborn, A. L., Gastpar, M. C. & Carmena, J. M. Subject-specific modulation of local field potential spectral power during brain–machine interface control in primates. J. Neural Eng. 11, 026002 (2014).
Stavisky, S. D., Kao, J. C., Nuyujukian, P., Ryu, S. I. & Shenoy, K. V. A high performing brain–machine interface driven by low-frequency local field potentials alone and together with spikes. J. Neural Eng. 12, 036009 (2015).
Sarnthein, J. & Jeanmonod, D. High thalamocortical theta coherence in patients with Parkinson’s disease. J. Neurosci. 27, 124–131 (2007).
Neumann, W.-J. et al. Subthalamic synchronized oscillatory activity correlates with motor impairment in patients with Parkinson’s disease. Mov. Disord. 31, 1748–1751 (2016).
Wijk, B. Cvan et al. Subthalamic nucleus phase–amplitude coupling correlates with motor impairment in Parkinson’s disease. Clin. Neurophysiol. 127, 2010–2019 (2016).
Van Overschee, P. & De Moor, B. Subspace Identification for Linear Systems: Theory, Implementation and Applications (Springer Science & Business Media, 2012).
Schalk, G. et al. Decoding two-dimensional movement trajectories using electrocorticographic signals in humans. J. Neural Eng. 4, 264 (2007).
Pistohl, T., Ball, T., Schulze-Bonhage, A., Aertsen, A. & Mehring, C. Prediction of arm movement trajectories from ECoG-recordings in humans. J. Neurosci. Methods 167, 105–114 (2008).
Bansal, A. K., Truccolo, W., Vargas-Irwin, C. E. & Donoghue, J. P. Decoding 3D reach and grasp from hybrid signals in motor and premotor cortices: spikes, multiunit activity, and local field potentials. J. Neurophysiol. 107, 1337–1355 (2011).
Benjamini, Y. & Hochberg, Y. Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. R. Stat. Soc. B 57, 289–300 (1995).
Zhang, Q. Using wavelet network in nonparametric estimation. IEEE Trans. Neural Netw. 8, 227–236 (1997).
Akaike, H. in Selected Papers of Hirotugu Akaike (eds Parzen, E. et al.) 199–213 (Springer, 1998).
We acknowledge support of the Army Research Office under contract W911NF-16-1-0368 (to M.M.S.) as part of the collaboration between the US Department of Defense, the UK Ministry of Defence and the UK Engineering and Physical Research Council under the Multidisciplinary University Research Initiative. We also acknowledge support of US National Institutes of Health BRAIN grant R01-NS104923 (to B.P. and M.M.S.). Finally, the we acknowledge the Defense Advanced Research Projects Agency under Cooperative Agreement Number W911NF-14-2-0043 (to M.M.S. and B.P.), issued by the Army Research Office contracting office in support of the DARPA SUBNETS programme. The views, opinions and/or findings expressed are those of the author(s) and should not be interpreted as representing the official views or policies of the Department of Defense or the US Government. We thank B. Goodell, C. Gray, J. E. Kleinbart and A. Orsborn for assistance with chamber and microdrive system design; S. Frey and B. Hynes for custom modifications to the Brainsight system; R. Shewcraft, J. Choi, M. Rubiano, Y. Jang and O. Martin for help with animal preparation and care; and K. Brown for help with MRI analysis.
The authors declare no competing interests.
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Yang, Y., Qiao, S., Sani, O.G. et al. Modelling and prediction of the dynamic responses of large-scale brain networks during direct electrical stimulation. Nat Biomed Eng 5, 324–345 (2021). https://doi.org/10.1038/s41551-020-00666-w
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