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Ter Horst J, Boillot M, Cohen MX, Englitz B. Decreased Beta Power and OFC-STN Phase Synchronization during Reactive Stopping in Freely Behaving Rats. J Neurosci 2024; 44:e0463242024. [PMID: 38866485 PMCID: PMC11308328 DOI: 10.1523/jneurosci.0463-24.2024] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2024] [Revised: 04/30/2024] [Accepted: 05/24/2024] [Indexed: 06/14/2024] Open
Abstract
During natural behavior, an action often needs to be suddenly stopped in response to an unexpected sensory input-referred to as reactive stopping. Reactive stopping has been mostly investigated in humans, which led to hypotheses about the involvement of different brain structures, in particular the hyperdirect pathway. Here, we directly investigate the contribution and interaction of two key regions of the hyperdirect pathway, the orbitofrontal cortex (OFC) and subthalamic nucleus (STN), using dual-area, multielectrode recordings in male rats performing a stop-signal task. In this task, rats have to initiate movement to a go-signal, and occasionally stop their movement to the go-signal side after a stop-signal, presented at various stop-signal delays. Both the OFC and STN show near-simultaneous field potential reductions in the beta frequency range (12-30 Hz) compared with the period preceding the go-signal and the movement period. These transient reductions (∼200 ms) only happen during reactive stopping, which is when the stop-signal was received after action initiation, and are well timed after stop-signal onset and before the estimated time of stopping. Phase synchronization analysis also showed a transient attenuation of synchronization between the OFC and STN in the beta range during reactive stopping. The present results provide the first direct quantification of local neural oscillatory activity in the OFC and STN and interareal synchronization specifically timed during reactive stopping.
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Affiliation(s)
- Jordi Ter Horst
- Donders Institute for Brain, Cognition and Behaviour, Department of Cognitive Neuroscience, Radboud University Medical Center, Nijmegen 6525 EN, The Netherlands
- Donders Institute for Brain, Cognition and Behaviour, Radboud University, Nijmegen 6525 EN, The Netherlands
| | - Morgane Boillot
- Donders Institute for Brain, Cognition and Behaviour, Department of Cognitive Neuroscience, Radboud University Medical Center, Nijmegen 6525 EN, The Netherlands
- Donders Institute for Brain, Cognition and Behaviour, Radboud University, Nijmegen 6525 EN, The Netherlands
| | - Michael X Cohen
- Donders Institute for Brain, Cognition and Behaviour, Department of Cognitive Neuroscience, Radboud University Medical Center, Nijmegen 6525 EN, The Netherlands
- Donders Institute for Brain, Cognition and Behaviour, Radboud University, Nijmegen 6525 EN, The Netherlands
| | - Bernhard Englitz
- Donders Institute for Brain, Cognition and Behaviour, Radboud University, Nijmegen 6525 EN, The Netherlands
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2
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Steiner LA, Crompton D, Sumarac S, Vetkas A, Germann J, Scherer M, Justich M, Boutet A, Popovic MR, Hodaie M, Kalia SK, Fasano A, Hutchison Wd WD, Lozano AM, Lankarany M, Kühn AA, Milosevic L. Neural signatures of indirect pathway activity during subthalamic stimulation in Parkinson's disease. Nat Commun 2024; 15:3130. [PMID: 38605039 PMCID: PMC11009243 DOI: 10.1038/s41467-024-47552-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Accepted: 04/02/2024] [Indexed: 04/13/2024] Open
Abstract
Deep brain stimulation (DBS) of the subthalamic nucleus (STN) produces an electrophysiological signature called evoked resonant neural activity (ERNA); a high-frequency oscillation that has been linked to treatment efficacy. However, the single-neuron and synaptic bases of ERNA are unsubstantiated. This study proposes that ERNA is a subcortical neuronal circuit signature of DBS-mediated engagement of the basal ganglia indirect pathway network. In people with Parkinson's disease, we: (i) showed that each peak of the ERNA waveform is associated with temporally-locked neuronal inhibition in the STN; (ii) characterized the temporal dynamics of ERNA; (iii) identified a putative mesocircuit architecture, embedded with empirically-derived synaptic dynamics, that is necessary for the emergence of ERNA in silico; (iv) localized ERNA to the dorsal STN in electrophysiological and normative anatomical space; (v) used patient-wise hotspot locations to assess spatial relevance of ERNA with respect to DBS outcome; and (vi) characterized the local fiber activation profile associated with the derived group-level ERNA hotspot.
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Affiliation(s)
- Leon A Steiner
- Krembil Brain Institute, University Health Network, Toronto, ON, M5T 1M8, Canada
- Department of Neurology, Charité-Universitätsmedizin Berlin, Berlin, 10117, Germany
- Berlin Institute of Health (BIH), Berlin, 10178, Germany
| | - David Crompton
- Krembil Brain Institute, University Health Network, Toronto, ON, M5T 1M8, Canada
- Institute of Biomedical Engineering, University of Toronto, Toronto, ON, M5S 3G9, Canada
| | - Srdjan Sumarac
- Krembil Brain Institute, University Health Network, Toronto, ON, M5T 1M8, Canada
- Institute of Biomedical Engineering, University of Toronto, Toronto, ON, M5S 3G9, Canada
| | - Artur Vetkas
- Krembil Brain Institute, University Health Network, Toronto, ON, M5T 1M8, Canada
- Division of Neurosurgery, Toronto Western Hospital, Toronto, ON, M5T 2S8, Canada
| | - Jürgen Germann
- Krembil Brain Institute, University Health Network, Toronto, ON, M5T 1M8, Canada
- Division of Neurosurgery, Toronto Western Hospital, Toronto, ON, M5T 2S8, Canada
- Department of Surgery, University of Toronto, Toronto, ON, M5G 2C4, Canada
| | - Maximilian Scherer
- Krembil Brain Institute, University Health Network, Toronto, ON, M5T 1M8, Canada
- Institute of Biomedical Engineering, University of Toronto, Toronto, ON, M5S 3G9, Canada
| | - Maria Justich
- Krembil Brain Institute, University Health Network, Toronto, ON, M5T 1M8, Canada
- Department of Neurology, University of Toronto, Toronto, ON, M5S 3H2, Canada
- Edmond J. Safra Program in Parkinson's Disease, Morton and Gloria Shulman Movement Disorders Clinic, Toronto Western Hospital, Toronto, ON, M5T 2S8, Canada
| | - Alexandre Boutet
- Joint Department of Medical Imaging, University of Toronto, Toronto, ON, M5G 1×6, Canada
| | - Milos R Popovic
- Institute of Biomedical Engineering, University of Toronto, Toronto, ON, M5S 3G9, Canada
- KITE Research Institute, University Health Network, Toronto, ON, M5G 2A2, Canada
- Center for Advancing Neurotechnological Innovation to Application (CRANIA), Toronto, ON, M5T 2S8, Canada
| | - Mojgan Hodaie
- Krembil Brain Institute, University Health Network, Toronto, ON, M5T 1M8, Canada
- Division of Neurosurgery, Toronto Western Hospital, Toronto, ON, M5T 2S8, Canada
- Department of Surgery, University of Toronto, Toronto, ON, M5G 2C4, Canada
- Center for Advancing Neurotechnological Innovation to Application (CRANIA), Toronto, ON, M5T 2S8, Canada
- Institute of Medical Sciences, University of Toronto, Toronto, ON, M5S 1A8, Canada
| | - Suneil K Kalia
- Krembil Brain Institute, University Health Network, Toronto, ON, M5T 1M8, Canada
- Division of Neurosurgery, Toronto Western Hospital, Toronto, ON, M5T 2S8, Canada
- Department of Surgery, University of Toronto, Toronto, ON, M5G 2C4, Canada
- KITE Research Institute, University Health Network, Toronto, ON, M5G 2A2, Canada
- Center for Advancing Neurotechnological Innovation to Application (CRANIA), Toronto, ON, M5T 2S8, Canada
- Institute of Medical Sciences, University of Toronto, Toronto, ON, M5S 1A8, Canada
| | - Alfonso Fasano
- Krembil Brain Institute, University Health Network, Toronto, ON, M5T 1M8, Canada
- Department of Neurology, University of Toronto, Toronto, ON, M5S 3H2, Canada
- Edmond J. Safra Program in Parkinson's Disease, Morton and Gloria Shulman Movement Disorders Clinic, Toronto Western Hospital, Toronto, ON, M5T 2S8, Canada
- Center for Advancing Neurotechnological Innovation to Application (CRANIA), Toronto, ON, M5T 2S8, Canada
- Institute of Medical Sciences, University of Toronto, Toronto, ON, M5S 1A8, Canada
| | - William D Hutchison Wd
- Krembil Brain Institute, University Health Network, Toronto, ON, M5T 1M8, Canada
- Department of Surgery, University of Toronto, Toronto, ON, M5G 2C4, Canada
- Center for Advancing Neurotechnological Innovation to Application (CRANIA), Toronto, ON, M5T 2S8, Canada
- Department of Physiology, University of Toronto, Toronto, ON, M5S 1A8, Canada
| | - Andres M Lozano
- Krembil Brain Institute, University Health Network, Toronto, ON, M5T 1M8, Canada
- Division of Neurosurgery, Toronto Western Hospital, Toronto, ON, M5T 2S8, Canada
- Department of Surgery, University of Toronto, Toronto, ON, M5G 2C4, Canada
- Center for Advancing Neurotechnological Innovation to Application (CRANIA), Toronto, ON, M5T 2S8, Canada
- Institute of Medical Sciences, University of Toronto, Toronto, ON, M5S 1A8, Canada
| | - Milad Lankarany
- Krembil Brain Institute, University Health Network, Toronto, ON, M5T 1M8, Canada
- Institute of Biomedical Engineering, University of Toronto, Toronto, ON, M5S 3G9, Canada
- Center for Advancing Neurotechnological Innovation to Application (CRANIA), Toronto, ON, M5T 2S8, Canada
| | - Andrea A Kühn
- Department of Neurology, Charité-Universitätsmedizin Berlin, Berlin, 10117, Germany
| | - Luka Milosevic
- Krembil Brain Institute, University Health Network, Toronto, ON, M5T 1M8, Canada.
- Institute of Biomedical Engineering, University of Toronto, Toronto, ON, M5S 3G9, Canada.
- KITE Research Institute, University Health Network, Toronto, ON, M5G 2A2, Canada.
- Center for Advancing Neurotechnological Innovation to Application (CRANIA), Toronto, ON, M5T 2S8, Canada.
- Institute of Medical Sciences, University of Toronto, Toronto, ON, M5S 1A8, Canada.
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Neumann WJ, Steiner LA, Milosevic L. Neurophysiological mechanisms of deep brain stimulation across spatiotemporal resolutions. Brain 2023; 146:4456-4468. [PMID: 37450573 PMCID: PMC10629774 DOI: 10.1093/brain/awad239] [Citation(s) in RCA: 11] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Revised: 06/04/2023] [Accepted: 06/28/2023] [Indexed: 07/18/2023] Open
Abstract
Deep brain stimulation is a neuromodulatory treatment for managing the symptoms of Parkinson's disease and other neurological and psychiatric disorders. Electrodes are chronically implanted in disease-relevant brain regions and pulsatile electrical stimulation delivery is intended to restore neurocircuit function. However, the widespread interest in the application and expansion of this clinical therapy has preceded an overarching understanding of the neurocircuit alterations invoked by deep brain stimulation. Over the years, various forms of neurophysiological evidence have emerged which demonstrate changes to brain activity across spatiotemporal resolutions; from single neuron, to local field potential, to brain-wide cortical network effects. Though fruitful, such studies have often led to debate about a singular putative mechanism. In this Update we aim to produce an integrative account of complementary instead of mutually exclusive neurophysiological effects to derive a generalizable concept of the mechanisms of deep brain stimulation. In particular, we offer a critical review of the most common historical competing theories, an updated discussion on recent literature from animal and human neurophysiological studies, and a synthesis of synaptic and network effects of deep brain stimulation across scales of observation, including micro-, meso- and macroscale circuit alterations.
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Affiliation(s)
- Wolf-Julian Neumann
- Movement Disorder and Neuromodulation Unit, Department of Neurology, Charité - Universitätsmedizin Berlin, Berlin 10117, Germany
| | - Leon A Steiner
- Movement Disorder and Neuromodulation Unit, Department of Neurology, Charité - Universitätsmedizin Berlin, Berlin 10117, Germany
- Department of Clinical and Computational Neuroscience, Krembil Brain Institute, University Health Network, Toronto M5T 1M8, Canada
| | - Luka Milosevic
- Department of Clinical and Computational Neuroscience, Krembil Brain Institute, University Health Network, Toronto M5T 1M8, Canada
- Institute of Biomedical Engineering, Institute of Medical Sciences, and CRANIA Neuromodulation Institute, University of Toronto, Toronto M5S 3G9, Canada
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Kromer JA, Bokil H, Tass PA. Synaptic network structure shapes cortically evoked spatio-temporal responses of STN and GPe neurons in a computational model. Front Neuroinform 2023; 17:1217786. [PMID: 37675246 PMCID: PMC10477454 DOI: 10.3389/fninf.2023.1217786] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2023] [Accepted: 07/31/2023] [Indexed: 09/08/2023] Open
Abstract
Introduction The basal ganglia (BG) are involved in motor control and play an essential role in movement disorders such as hemiballismus, dystonia, and Parkinson's disease. Neurons in the motor part of the BG respond to passive movement or stimulation of different body parts and to stimulation of corresponding cortical regions. Experimental evidence suggests that the BG are organized somatotopically, i.e., specific areas of the body are associated with specific regions in the BG nuclei. Signals related to the same body part that propagate along different pathways converge onto the same BG neurons, leading to characteristic shapes of cortically evoked responses. This suggests the existence of functional channels that allow for the processing of different motor commands or information related to different body parts in parallel. Neurological disorders such as Parkinson's disease are associated with pathological activity in the BG and impaired synaptic connectivity, together with reorganization of somatotopic maps. One hypothesis is that motor symptoms are, at least partly, caused by an impairment of network structure perturbing the organization of functional channels. Methods We developed a computational model of the STN-GPe circuit, a central part of the BG. By removing individual synaptic connections, we analyzed the contribution of signals propagating along different pathways to cortically evoked responses. We studied how evoked responses are affected by systematic changes in the network structure. To quantify the BG's organization in the form of functional channels, we suggested a two-site stimulation protocol. Results Our model reproduced the cortically evoked responses of STN and GPe neurons and the contributions of different pathways suggested by experimental studies. Cortical stimulation evokes spatio-temporal response patterns that are linked to the underlying synaptic network structure. Our two-site stimulation protocol yielded an approximate functional channel width. Discussion/conclusion The presented results provide insight into the organization of BG synaptic connectivity, which is important for the development of computational models. The synaptic network structure strongly affects the processing of cortical signals and may impact the generation of pathological rhythms. Our work may motivate further experiments to analyze the network structure of BG nuclei and their organization in functional channels.
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Affiliation(s)
- Justus A. Kromer
- Department of Neurosurgery, Stanford University, Stanford, CA, United States
| | - Hemant Bokil
- Boston Scientific Neuromodulation, Valencia, CA, United States
| | - Peter A. Tass
- Department of Neurosurgery, Stanford University, Stanford, CA, United States
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Xiao C, Ji YW, Luan YW, Jia T, Yin C, Zhou CY. Differential modulation of subthalamic projection neurons by short-term and long-term electrical stimulation in physiological and parkinsonian conditions. Acta Pharmacol Sin 2022; 43:1928-1939. [PMID: 34880404 PMCID: PMC9343451 DOI: 10.1038/s41401-021-00811-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2021] [Accepted: 10/31/2021] [Indexed: 11/09/2022] Open
Abstract
The subthalamic nucleus (STN) is one of the best targets for therapeutic deep brain stimulation (DBS) to control motor symptoms in Parkinson's disease. However, the precise circuitry underlying the effects of STN-DBS remains unclear. To understand how electrical stimulation affects STN projection neurons, we used a retrograde viral vector (AAV-retro-hSyn-eGFP) to label STN neurons projecting to the substantia nigra pars reticulata (SNr) (STN-SNr neurons) or the globus pallidus interna (GPi) (STN-GPi neurons) in mice, and performed whole-cell patch-clamp recordings from these projection neurons in ex vivo brain slices. We found that STN-SNr neurons exhibited stronger responses to depolarizing stimulation than STN-GPi neurons. In most STN-SNr and STN-GPi neurons, inhibitory synaptic inputs predominated over excitatory inputs and electrical stimulation at 20-130 Hz inhibited these neurons in the short term; its longer-term effects varied. 6-OHDA lesion of the nigrostriatal dopaminergic pathway significantly reduced inhibitory synaptic inputs in STN-GPi neurons, but did not change synaptic inputs in STN-SNr neurons; it enhanced short-term electrical-stimulation-induced inhibition in STN-SNr neurons but reversed the effect of short-term electrical stimulation on the firing rate in STN-GPi neurons from inhibitory to excitatory; in both STN-SNr and STN-GPi neurons, it increased the inhibition but attenuated the enhancement of firing rate induced by long-term electrical stimulation. Our results suggest that STN-SNr and STN-GPi neurons differ in their synaptic inputs, their responses to electrical stimulation, and their modification under parkinsonian conditions; STN-GPi neurons may play important roles in both the pathophysiology and therapeutic treatment of Parkinson's disease.
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Affiliation(s)
- Cheng Xiao
- Jiangsu Province Key Laboratory of Anesthesiology, School of Anesthesiology, Xuzhou Medical University, Xuzhou, 221004, China. .,Jiangsu Province Key Laboratory of Anesthesia and Analgesia Application Technology, Xuzhou Medical University, Xuzhou, 221004, China. .,NMPA Key Laboratory for Research and Evaluation of Narcotic and Psychotropic Drugs, School of Anesthesiology, Xuzhou Medical University, Xuzhou, 221004, China.
| | - Ya-wei Ji
- grid.417303.20000 0000 9927 0537Jiangsu Province Key Laboratory of Anesthesiology, School of Anesthesiology, Xuzhou Medical University, Xuzhou, 221004 China
| | - Yi-wen Luan
- grid.417303.20000 0000 9927 0537Jiangsu Province Key Laboratory of Anesthesiology, School of Anesthesiology, Xuzhou Medical University, Xuzhou, 221004 China ,grid.460176.20000 0004 1775 8598Department of Anesthesiology, Wuxi People’s Hospital, Wuxi, 214023 China
| | - Tao Jia
- grid.417303.20000 0000 9927 0537Jiangsu Province Key Laboratory of Anesthesiology, School of Anesthesiology, Xuzhou Medical University, Xuzhou, 221004 China
| | - Cui Yin
- grid.417303.20000 0000 9927 0537Jiangsu Province Key Laboratory of Anesthesiology, School of Anesthesiology, Xuzhou Medical University, Xuzhou, 221004 China ,grid.417303.20000 0000 9927 0537Jiangsu Province Key Laboratory of Anesthesia and Analgesia Application Technology, Xuzhou Medical University, Xuzhou, 221004 China ,grid.417303.20000 0000 9927 0537NMPA Key Laboratory for Research and Evaluation of Narcotic and Psychotropic Drugs, School of Anesthesiology, Xuzhou Medical University, Xuzhou, 221004 China
| | - Chun-yi Zhou
- grid.417303.20000 0000 9927 0537Jiangsu Province Key Laboratory of Anesthesiology, School of Anesthesiology, Xuzhou Medical University, Xuzhou, 221004 China ,grid.417303.20000 0000 9927 0537Jiangsu Province Key Laboratory of Anesthesia and Analgesia Application Technology, Xuzhou Medical University, Xuzhou, 221004 China ,grid.417303.20000 0000 9927 0537NMPA Key Laboratory for Research and Evaluation of Narcotic and Psychotropic Drugs, School of Anesthesiology, Xuzhou Medical University, Xuzhou, 221004 China
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6
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Spiliotis K, Starke J, Franz D, Richter A, Köhling R. Deep brain stimulation for movement disorder treatment: exploring frequency-dependent efficacy in a computational network model. BIOLOGICAL CYBERNETICS 2022; 116:93-116. [PMID: 34894291 PMCID: PMC8866393 DOI: 10.1007/s00422-021-00909-2] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/20/2020] [Accepted: 10/31/2021] [Indexed: 06/14/2023]
Abstract
A large-scale computational model of the basal ganglia network and thalamus is proposed to describe movement disorders and treatment effects of deep brain stimulation (DBS). The model of this complex network considers three areas of the basal ganglia region: the subthalamic nucleus (STN) as target area of DBS, the globus pallidus, both pars externa and pars interna (GPe-GPi), and the thalamus. Parkinsonian conditions are simulated by assuming reduced dopaminergic input and corresponding pronounced inhibitory or disinhibited projections to GPe and GPi. Macroscopic quantities are derived which correlate closely to thalamic responses and hence motor programme fidelity. It can be demonstrated that depending on different levels of striatal projections to the GPe and GPi, the dynamics of these macroscopic quantities (synchronisation index, mean synaptic activity and response efficacy) switch from normal to Parkinsonian conditions. Simulating DBS of the STN affects the dynamics of the entire network, increasing the thalamic activity to levels close to normal, while differing from both normal and Parkinsonian dynamics. Using the mentioned macroscopic quantities, the model proposes optimal DBS frequency ranges above 130 Hz.
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Affiliation(s)
| | - Jens Starke
- Institute of Mathematics, University of Rostock, 18057 Rostock, Germany
| | - Denise Franz
- Oscar-Langendorff-Institute of Physiology, Rostock University Medical Center, Rostock, Germany
| | - Angelika Richter
- Institute of Pharmacology, Pharmacy and Toxicology, Faculty of Veterinary Medicine, University of Leipzig, Leipzig, Germany
| | - Rüdiger Köhling
- Oscar-Langendorff-Institute of Physiology, Rostock University Medical Center, Rostock, Germany
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7
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Manos T, Diaz-Pier S, Tass PA. Long-Term Desynchronization by Coordinated Reset Stimulation in a Neural Network Model With Synaptic and Structural Plasticity. Front Physiol 2021; 12:716556. [PMID: 34566681 PMCID: PMC8455881 DOI: 10.3389/fphys.2021.716556] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2021] [Accepted: 08/16/2021] [Indexed: 11/16/2022] Open
Abstract
Several brain disorders are characterized by abnormal neuronal synchronization. To specifically counteract abnormal neuronal synchrony and, hence, related symptoms, coordinated reset (CR) stimulation was computationally developed. In principle, successive epochs of synchronizing and desynchronizing stimulation may reversibly move neural networks with plastic synapses back and forth between stable regimes with synchronized and desynchronized firing. Computationally derived predictions have been verified in pre-clinical and clinical studies, paving the way for novel therapies. However, as yet, computational models were not able to reproduce the clinically observed increase of desynchronizing effects of regularly administered CR stimulation intermingled by long stimulation-free epochs. We show that this clinically important phenomenon can be computationally reproduced by taking into account structural plasticity (SP), a mechanism that deletes or generates synapses in order to homeostatically adapt the firing rates of neurons to a set point-like target firing rate in the course of days to months. If we assume that CR stimulation favorably reduces the target firing rate of SP, the desynchronizing effects of CR stimulation increase after long stimulation-free epochs, in accordance with clinically observed phenomena. Our study highlights the pivotal role of stimulation- and dosing-induced modulation of homeostatic set points in therapeutic processes.
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Affiliation(s)
- Thanos Manos
- Institute of Neuroscience and Medicine, Brain and Behaviour (INM-7), Research Centre Jülich, Jülich, Germany.,Medical Faculty, Institute of Systems Neuroscience, Heinrich Heine University Düsseldorf, Düsseldorf, Germany.,Laboratoire de Physique Théorique et Modélisation, CNRS, UMR 8089, CY Cergy Paris Université, Cergy-Pontoise Cedex, France
| | - Sandra Diaz-Pier
- Simulation & Data Lab Neuroscience, Institute for Advanced Simulation, Jülich Supercomputing Centre (JSC), Forschungszentrum Jülich GmbH, JARA, Jülich, Germany
| | - Peter A Tass
- Department of Neurosurgery, Stanford University School of Medicine, Stanford, CA, United States
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8
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Burdakov D, Karnani MM. Ultra-sparse Connectivity within the Lateral Hypothalamus. Curr Biol 2020; 30:4063-4070.e2. [PMID: 32822604 PMCID: PMC7575142 DOI: 10.1016/j.cub.2020.07.061] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2020] [Revised: 06/22/2020] [Accepted: 07/17/2020] [Indexed: 01/08/2023]
Abstract
The lateral hypothalamic area (LH) is a vital controller of arousal, feeding, and metabolism [1, 2], which integrates external and internal sensory information. Whereas sensory and whole-body output properties of LH cell populations have received much interest, their intrinsic synaptic organization has remained largely unstudied. Local inhibitory and excitatory connections could help integrate and filter sensory information and mutually inhibitory connections [3] could allow coordinating activity between LH cell types, some of which have mutually exclusive behavioral effects, such as LH VGLUT2 and VGAT neurons [4-7] and orexin- (ORX) and melanin-concentrating hormone (MCH) neurons [8-10]. However, classical Golgi staining studies did not find interneurons with locally ramifying axons in the LH [11, 12], and nearby subthalamic and thalamic areas lack local synaptic connectivity [13, 14]. Studies with optogenetic circuit mapping within the LH have demonstrated only a minority of connections when a large pool of presynaptic neurons was activated [15-19]. Because multiple patch clamp has not been used to study LH connectivity, aside from a limited dataset of MCH neurons where no connections were discovered [15], we used quadruple whole-cell recordings to screen connectivity within the LH with standard methodology we previously used in the neocortex [20-22]. Finding a lack of local connectivity, we used optogenetic circuit mapping to study the strength of LH optogenetic responses and network oscillations, which were consistent with ultra-sparse intrinsic connectivity within the LH. These results suggest that input from other brain structures is decisive for selecting active populations in the LH.
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Affiliation(s)
- Denis Burdakov
- Laboratory of Neurobehavioral Dynamics, Institute for Neuroscience, Department of Health Sciences and Technology, ETH Zürich, Zürich 8603, Switzerland; The Francis Crick Institute, London NW1 1AT, UK; Institute of Psychiatry, Psychology & Neuroscience, King's College London, London SE5 8AF, UK; Neuroscience Center Zürich (ZNZ), ETH Zürich and University of Zürich, Zürich 8057, Switzerland
| | - Mahesh M Karnani
- Laboratory of Neurobehavioral Dynamics, Institute for Neuroscience, Department of Health Sciences and Technology, ETH Zürich, Zürich 8603, Switzerland; The Francis Crick Institute, London NW1 1AT, UK; Institute of Psychiatry, Psychology & Neuroscience, King's College London, London SE5 8AF, UK; Université de Paris, Saints-Pères Paris Institute for the Neurosciences (SPPIN), CNRS, Paris 75006, France.
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9
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Vissani M, Isaias IU, Mazzoni A. Deep brain stimulation: a review of the open neural engineering challenges. J Neural Eng 2020; 17:051002. [PMID: 33052884 DOI: 10.1088/1741-2552/abb581] [Citation(s) in RCA: 32] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
OBJECTIVE Deep brain stimulation (DBS) is an established and valid therapy for a variety of pathological conditions ranging from motor to cognitive disorders. Still, much of the DBS-related mechanism of action is far from being understood, and there are several side effects of DBS whose origin is unclear. In the last years DBS limitations have been tackled by a variety of approaches, including adaptive deep brain stimulation (aDBS), a technique that relies on using chronically implanted electrodes on 'sensing mode' to detect the neural markers of specific motor symptoms and to deliver on-demand or modulate the stimulation parameters accordingly. Here we will review the state of the art of the several approaches to improve DBS and summarize the main challenges toward the development of an effective aDBS therapy. APPROACH We discuss models of basal ganglia disorders pathogenesis, hardware and software improvements for conventional DBS, and candidate neural and non-neural features and related control strategies for aDBS. MAIN RESULTS We identify then the main operative challenges toward optimal DBS such as (i) accurate target localization, (ii) increased spatial resolution of stimulation, (iii) development of in silico tests for DBS, (iv) identification of specific motor symptoms biomarkers, in particular (v) assessing how LFP oscillations relate to behavioral disfunctions, and (vi) clarify how stimulation affects the cortico-basal-ganglia-thalamic network to (vii) design optimal stimulation patterns. SIGNIFICANCE This roadmap will lead neural engineers novel to the field toward the most relevant open issues of DBS, while the in-depth readers might find a careful comparison of advantages and drawbacks of the most recent attempts to improve DBS-related neuromodulatory strategies.
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Affiliation(s)
- Matteo Vissani
- The BioRobotics Institute, Scuola Superiore Sant'Anna, 56025 Pisa, Italy. Department of Excellence in Robotics and AI, Scuola Superiore Sant'Anna, 56025 Pisa, Italy
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10
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Sabourin S, Khazen O, DiMarzio M, Staudt MD, Williams L, Gillogly M, Durphy J, Hanspal EK, Adam OR, Pilitsis JG. Effect of Directional Deep Brain Stimulation on Sensory Thresholds in Parkinson's Disease. Front Hum Neurosci 2020; 14:217. [PMID: 32581755 PMCID: PMC7296062 DOI: 10.3389/fnhum.2020.00217] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2019] [Accepted: 05/14/2020] [Indexed: 11/17/2022] Open
Abstract
Objective Previous studies showed that deep brain stimulation (DBS) relieves pain symptoms in Parkinson disease (PD) patients when programmed for motor-symptom relief. One factor involved in pain processing is sensory perception of stimuli. With the advent of directional leads, we explore whether directional DBS affects quantitative sensory testing (QST) metrics acutely. Methods PD patients with subthalamic (STN) DBS and directional leads were tested in 5 settings (DBS-OFF, DBS-ON with omnidirectional stimulation, and DBS-ON) for each of three directional segments of contact used for clinical programming. The Unified Parkinson’s Disease Rating Scale (UPDRS-III) assessed patient’s motor skills at time of study visit at clinical contact and at contact which produced optimal sensory threshold (defined by the greatest tolerance to mechanical stimuli). Correlation analyses were performed between stimulation parameters [amplitude, frequency, pulse width (PW), total electrical energy delivered (TEED)] and outcome metrics. Results Sensory thresholds were obtained in nine patients. Directional stimulation did not significantly alter patient perceptions of sensory stimulus [cold pain (p = 0.69), warm pain (p = 0.99), Von frey fibers (p = 0.09), pin-prick (p = 0.88), vibration (p = 0.40), pressure (p = 0.98)]. With correlation analysis, increasing PW at the posterior contact increased pin prick and vibration sensitivity (p < 0.001). Additionally, an increase in TEED caused a decrease in sensitivity to warm detection when using the anterior (p = 0.04), lateral (p = 0.02), and medial contacts (p = 0.03), and also caused a decrease in sensitivity to cold detection when using the medial contact (p = 0.03). UPDRS-III remained stable during testing. Conclusion Motor benefit can be acutely maintained at directional contacts, whereas directional stimulation can modulate thermal and mechanical sensitivity. Further investigation will determine whether these changes are maintained chronically or can be improved with optimized programming.
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Affiliation(s)
- Shelby Sabourin
- Department of Neuroscience and Experimental Therapeutics, Albany Medical College, Albany, NY, United States
| | - Olga Khazen
- Department of Neuroscience and Experimental Therapeutics, Albany Medical College, Albany, NY, United States
| | - Marisa DiMarzio
- Department of Neuroscience and Experimental Therapeutics, Albany Medical College, Albany, NY, United States
| | - Michael D Staudt
- Department of Neurosurgery, Albany Medical College, Albany, NY, United States
| | - Lucian Williams
- Department of Neuroscience and Experimental Therapeutics, Albany Medical College, Albany, NY, United States
| | - Michael Gillogly
- Department of Neurosurgery, Albany Medical College, Albany, NY, United States
| | - Jennifer Durphy
- Department of Neurology, Albany Medical College, Albany, NY, United States
| | - Era K Hanspal
- Department of Neurology, Albany Medical College, Albany, NY, United States
| | - Octavian R Adam
- Department of Neurology, Albany Medical College, Albany, NY, United States
| | - Julie G Pilitsis
- Department of Neuroscience and Experimental Therapeutics, Albany Medical College, Albany, NY, United States.,Department of Neurosurgery, Albany Medical College, Albany, NY, United States
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11
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Schaefer LV, Bittmann FN. Parkinson patients without tremor show changed patterns of mechanical muscle oscillations during a specific bilateral motor task compared to controls. Sci Rep 2020; 10:1168. [PMID: 31980683 PMCID: PMC6981166 DOI: 10.1038/s41598-020-57766-5] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2019] [Accepted: 01/06/2020] [Indexed: 02/07/2023] Open
Abstract
The pathophysiology of Parkinson's disease (PD) is still not understood. There are investigations which show a changed oscillatory behaviour of brain circuits or changes in variability of, e.g., gait parameters in PD. The aim of this study was to investigate whether or not the motor output differs between PD patients and healthy controls. Thereby, patients without tremor are investigated in the medication off state performing a special bilateral isometric motor task. The force and accelerations (ACC) were recorded as well as the Mechanomyography (MMG) of the biceps brachii, the brachioradialis and of the pectoralis major muscles using piezoelectric-sensors during the bilateral motor task at 60% of the maximal isometric contraction. The frequency, a specific power ratio, the amplitude variation and the slope of amplitudes were analysed. The results indicate that the oscillatory behaviour of motor output in PD patients without tremor deviates from controls: thereby, the 95%-confidence-intervals of power ratio and of amplitude variation of all signals are disjoint between PD and controls and show significant differences in group comparisons (power ratio: p = 0.000-0.004, r = 0.441-0.579; amplitude variation: p = 0.000-0.001, r = 0.37-0.67). The mean frequency shows a significant difference for ACC (p = 0.009, r = 0.43), but not for MMG. It remains open, whether this muscular output reflects changes of brain circuits and whether the results are reproducible and specific for PD.
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Affiliation(s)
- Laura V Schaefer
- Regulative Physiology and Prevention, Department Sports and Health Sciences, University of Potsdam, Potsdam, Germany.
| | - Frank N Bittmann
- Regulative Physiology and Prevention, Department Sports and Health Sciences, University of Potsdam, Potsdam, Germany
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12
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Multistable properties of human subthalamic nucleus neurons in Parkinson's disease. Proc Natl Acad Sci U S A 2019; 116:24326-24333. [PMID: 31712414 PMCID: PMC6883794 DOI: 10.1073/pnas.1912128116] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
Behaviors are realized through concerted activity in neural circuits. This activity results from a combination of neural connectivity and the properties of the involved neurons. By studying the activity of neurons in the human subthalamic nucleus during surgery for Parkinson’s disease, we report that these neurons have multiple stable states, and that brief electrical stimuli can lead to transitions between states. We thus suggest that these neurons function as finite state machines. The different states could influence the function of key motor circuits of the basal ganglia, and thus knowledge of these states in disease or in response to treatment could help to define new treatment strategies for people with movement disorders. To understand the function and dysfunction of neural circuits, it is necessary to understand the properties of the neurons participating in the behavior, the connectivity between these neurons, and the neuromodulatory status of the circuits at the time they are producing the behavior. Such knowledge of human neural circuits is difficult, at best, to obtain. Here, we study firing properties of human subthalamic neurons, using microelectrode recordings and microstimulation during awake surgery for Parkinson’s disease. We demonstrate that low-amplitude, brief trains of microstimulation can lead to persistent changes in neuronal firing behavior including switching between firing rates, entering silent periods, or firing several bursts then entering a silent period. We suggest that these multistable states reflect properties of finite state machines and could have implications for the function of circuits involving the subthalamic nucleus. Furthermore, understanding these states could lead to therapeutic strategies aimed at regulating the transitions between states.
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13
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Peng Y, Mittermaier FX, Planert H, Schneider UC, Alle H, Geiger JRP. High-throughput microcircuit analysis of individual human brains through next-generation multineuron patch-clamp. eLife 2019; 8:48178. [PMID: 31742558 PMCID: PMC6894931 DOI: 10.7554/elife.48178] [Citation(s) in RCA: 31] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2019] [Accepted: 11/18/2019] [Indexed: 12/18/2022] Open
Abstract
Comparing neuronal microcircuits across different brain regions, species and individuals can reveal common and divergent principles of network computation. Simultaneous patch-clamp recordings from multiple neurons offer the highest temporal and subthreshold resolution to analyse local synaptic connectivity. However, its establishment is technically complex and the experimental performance is limited by high failure rates, long experimental times and small sample sizes. We introduce an in vitro multipatch setup with an automated pipette pressure and cleaning system facilitating recordings of up to 10 neurons simultaneously and sequential patching of additional neurons. We present hardware and software solutions that increase the usability, speed and data throughput of multipatch experiments which allowed probing of 150 synaptic connections between 17 neurons in one human cortical slice and screening of over 600 connections in tissue from a single patient. This method will facilitate the systematic analysis of microcircuits and allow unprecedented assessment of inter-individual variability.
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Affiliation(s)
- Yangfan Peng
- Institute of Neurophysiology, Charité - Universitätsmedizin Berlin, Berlin, Germany.,Department of Neurology, Charité - Universitätsmedizin Berlin, Berlin, Germany
| | | | - Henrike Planert
- Institute of Neurophysiology, Charité - Universitätsmedizin Berlin, Berlin, Germany
| | | | - Henrik Alle
- Institute of Neurophysiology, Charité - Universitätsmedizin Berlin, Berlin, Germany
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14
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Koelman LA, Lowery MM. Beta-Band Resonance and Intrinsic Oscillations in a Biophysically Detailed Model of the Subthalamic Nucleus-Globus Pallidus Network. Front Comput Neurosci 2019; 13:77. [PMID: 31749692 PMCID: PMC6848887 DOI: 10.3389/fncom.2019.00077] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2019] [Accepted: 10/17/2019] [Indexed: 12/29/2022] Open
Abstract
Increased beta-band oscillatory activity in the basal ganglia network is associated with Parkinsonian motor symptoms and is suppressed with medication and deep brain stimulation (DBS). The origins of the beta-band oscillations, however, remains unclear with both intrinsic oscillations arising within the subthalamic nucleus (STN)-external globus pallidus (GPe) network and exogenous beta-activity, originating outside the network, proposed as potential sources of the pathological activity. The aim of this study was to explore the relative contribution of autonomous oscillations and exogenous oscillatory inputs in the generation of pathological oscillatory activity in a biophysically detailed model of the parkinsonian STN-GPe network. The network model accounts for the integration of synaptic currents and their interaction with intrinsic membrane currents in dendritic structures within the STN and GPe. The model was used to investigate the development of beta-band synchrony and bursting within the STN-GPe network by changing the balance of excitation and inhibition in both nuclei, and by adding exogenous oscillatory inputs with varying phase relationships through the hyperdirect cortico-subthalamic and indirect striato-pallidal pathways. The model showed an intrinsic susceptibility to beta-band oscillations that was manifest in weak autonomously generated oscillations within the STN-GPe network and in selective amplification of exogenous beta-band synaptic inputs near the network's endogenous oscillation frequency. The frequency at which this resonance peak occurred was determined by the net level of excitatory drive to the network. Intrinsic or endogenously generated oscillations were too weak to support a pacemaker role for the STN-GPe network, however, they were considerably amplified by sparse cortical beta inputs and were further amplified by striatal beta inputs that promoted anti-phase firing of the cortex and GPe, resulting in maximum transient inhibition of STN neurons. The model elucidates a mechanism of cortical patterning of the STN-GPe network through feedback inhibition whereby intrinsic susceptibility to beta-band oscillations can lead to phase locked spiking under parkinsonian conditions. These results point to resonance of endogenous oscillations with exogenous patterning of the STN-GPe network as a mechanism of pathological synchronization, and a role for the pallido-striatal feedback loop in amplifying beta oscillations.
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Affiliation(s)
- Lucas A. Koelman
- Neuromuscular Systems Laboratory, School of Electrical and Electronic Engineering, University College Dublin, Dublin, Ireland
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15
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Milosevic L, Kalia SK, Hodaie M, Lozano A, Popovic MR, Hutchison W. Subthalamic suppression defines therapeutic threshold of deep brain stimulation in Parkinson's disease. J Neurol Neurosurg Psychiatry 2019; 90:1105-1108. [PMID: 31422369 DOI: 10.1136/jnnp-2019-321140] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 05/06/2019] [Revised: 08/08/2019] [Accepted: 08/08/2019] [Indexed: 11/04/2022]
Abstract
INTRODUCTION Subthalamic deep brain stimulation (DBS) is beneficial when delivered at a high frequency. However, the effects of current amplitude and pulse width on subthalamic neuronal activity during high-frequency stimulation have not been investigated. METHODS In 20 patients with Parkinson's disease each undergoing subthalamic DBS, we recorded single-unit subthalamic activity using one microelectrode, while a separate microelectrode was used to deliver 5-10 s trains of stimulation at 100 Hz using varying current amplitudes and pulse widths (44 neurons investigated). RESULTS Analysis of variance tests confirmed significant (p<0.001) main effects of both current amplitude and pulse width on subthalamic neuronal firing during stimulation and on poststimulus inhibitory silent periods. Prolonged silent periods were often followed by postinhibitory rebound burst excitations. Additionally, a significant (p<0.0001) correlation was found between neuronal firing and total electrical energy delivered (TEED). With TEED values≤31.2 µJ/s (associated with DBS parameters of ≤2.0 mA, 130 Hz stimulation frequency and 60 µs pulse width, assuming 1 kΩ impedance), neuronal firing was sustained at a rate of 32.4%±3.3% (mean±SE), while with values>31.2 µJ/s, neurons fired at only 4.3%±1.2%. CONCLUSIONS Neuronal suppression is likely an important mechanism of action of therapeutically beneficial subthalamic DBS, which may underlie clinically relevant behavioural changes.
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Affiliation(s)
- Luka Milosevic
- Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto, Ontario, Canada
| | - Suneil K Kalia
- Division of Neurosurgery, Toronto Western Hospital, Toronto, Ontario, Canada.,Department of Surgery, University of Toronto, Toronto, Ontario, Canada.,Krembil Research Institute, Toronto, Ontario, Canada
| | - Mojgan Hodaie
- Division of Neurosurgery, Toronto Western Hospital, Toronto, Ontario, Canada.,Department of Surgery, University of Toronto, Toronto, Ontario, Canada.,Krembil Research Institute, Toronto, Ontario, Canada
| | - Andres Lozano
- Division of Neurosurgery, Toronto Western Hospital, Toronto, Ontario, Canada.,Department of Surgery, University of Toronto, Toronto, Ontario, Canada.,Krembil Research Institute, Toronto, Ontario, Canada
| | - Milos R Popovic
- Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto, Ontario, Canada.,KITE, Toronto Rehabilitation Institute, Toronto, Ontario, Canada
| | - William Hutchison
- Krembil Research Institute, Toronto, Ontario, Canada.,Department of Physiology, University of Toronto, Toronto, Ontario, Canada
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16
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Dunovan K, Vich C, Clapp M, Verstynen T, Rubin J. Reward-driven changes in striatal pathway competition shape evidence evaluation in decision-making. PLoS Comput Biol 2019; 15:e1006998. [PMID: 31060045 PMCID: PMC6534331 DOI: 10.1371/journal.pcbi.1006998] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2018] [Revised: 05/24/2019] [Accepted: 04/01/2019] [Indexed: 01/25/2023] Open
Abstract
Cortico-basal-ganglia-thalamic (CBGT) networks are critical for adaptive decision-making, yet how changes to circuit-level properties impact cognitive algorithms remains unclear. Here we explore how dopaminergic plasticity at corticostriatal synapses alters competition between striatal pathways, impacting the evidence accumulation process during decision-making. Spike-timing dependent plasticity simulations showed that dopaminergic feedback based on rewards modified the ratio of direct and indirect corticostriatal weights within opposing action channels. Using the learned weight ratios in a full spiking CBGT network model, we simulated neural dynamics and decision outcomes in a reward-driven decision task and fit them with a drift diffusion model. Fits revealed that the rate of evidence accumulation varied with inter-channel differences in direct pathway activity while boundary height varied with overall indirect pathway activity. This multi-level modeling approach demonstrates how complementary learning and decision computations can emerge from corticostriatal plasticity. Cognitive process models such as reinforcement learning (RL) and the drift diffusion model (DDM) have helped to elucidate the basic algorithms underlying error-corrective learning and the evaluation of accumulating decision evidence leading up to a choice. While these relatively abstract models help to guide experimental and theoretical probes into associated phenomena, they remain uninformative about the actual physical mechanics by which learning and decision algorithms are carried out in a neurobiological substrate during adaptive choice behavior. Here we present an “upwards mapping” approach to bridging neural and cognitive models of value-based decision-making, showing how dopaminergic feedback alters the network-level dynamics of cortico-basal-ganglia-thalamic (CBGT) pathways during learning to bias behavioral choice towards more rewarding actions. By mapping “up” the levels of analysis, this approach yields specific predictions about aspects of neuronal activity that map to the quantities appearing in the cognitive decision-making framework.
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Affiliation(s)
- Kyle Dunovan
- Dept. of Psychology, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
- Center for the Neural Basis of Cognition, Pittsburgh, Pennsylvania, United States of America
| | - Catalina Vich
- Dept. de Matemàtiques i Informàtica, Universitat de les Illes Balears, Palma, Illes Balears, Spain
- Institute of Applied Computing and Community Code, Palma, Illes Balears, Spain
| | - Matthew Clapp
- Dept. of Biomedical Engineering, University of South Carolina, Columbia, South Carolina, United States of America
| | - Timothy Verstynen
- Dept. of Psychology, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
- Center for the Neural Basis of Cognition, Pittsburgh, Pennsylvania, United States of America
- * E-mail: (TV); (JR)
| | - Jonathan Rubin
- Center for the Neural Basis of Cognition, Pittsburgh, Pennsylvania, United States of America
- Dept. of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania, United States of America
- * E-mail: (TV); (JR)
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