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Kristensen SS, Jörntell H. Local field potential sharp waves with diversified impact on cortical neuronal encoding of haptic input. Sci Rep 2024; 14:15243. [PMID: 38956102 PMCID: PMC11219916 DOI: 10.1038/s41598-024-65200-3] [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: 02/24/2024] [Accepted: 06/18/2024] [Indexed: 07/04/2024] Open
Abstract
Cortical sensory processing is greatly impacted by internally generated activity. But controlling for that activity is difficult since the thalamocortical network is a high-dimensional system with rapid state changes. Therefore, to unwind the cortical computational architecture there is a need for physiological 'landmarks' that can be used as frames of reference for computational state. Here we use a waveshape transform method to identify conspicuous local field potential sharp waves (LFP-SPWs) in the somatosensory cortex (S1). LFP-SPW events triggered short-lasting but massive neuronal activation in all recorded neurons with a subset of neurons initiating their activation up to 20 ms before the LFP-SPW onset. In contrast, LFP-SPWs differentially impacted the neuronal spike responses to ensuing tactile inputs, depressing the tactile responses in some neurons and enhancing them in others. When LFP-SPWs coactivated with more distant cortical surface (ECoG)-SPWs, suggesting an involvement of these SPWs in global cortical signaling, the impact of the LFP-SPW on the neuronal tactile response could change substantially, including inverting its impact to the opposite. These cortical SPWs shared many signal fingerprint characteristics as reported for hippocampal SPWs and may be a biomarker for a particular type of state change that is possibly shared byboth hippocampus and neocortex.
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Affiliation(s)
- Sofie S Kristensen
- Department of Experimental Medical Science, Neural Basis of Sensorimotor Control, Lund University, Lund, Sweden
| | - Henrik Jörntell
- Department of Experimental Medical Science, Neural Basis of Sensorimotor Control, Lund University, Lund, Sweden.
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2
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Bayman E, Chee K, Mendlen M, Denman DJ, Tien RN, Ojemann S, Kramer DR, Thompson JA. Subthalamic nucleus synchronization between beta band local field potential and single-unit activity in Parkinson's disease. Physiol Rep 2024; 12:e16001. [PMID: 38697943 PMCID: PMC11065686 DOI: 10.14814/phy2.16001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2023] [Revised: 12/24/2023] [Accepted: 03/26/2024] [Indexed: 05/05/2024] Open
Abstract
Local field potential (LFP) oscillations in the beta band (13-30 Hz) in the subthalamic nucleus (STN) of Parkinson's disease patients have been implicated in disease severity and treatment response. The relationship between single-neuron activity in the STN and regional beta power changes remains unclear. We used spike-triggered average (STA) to assess beta synchronization in STN. Beta power and STA magnitude at the beta frequency range were compared in three conditions: STN versus other subcortical structures, dorsal versus ventral STN, and high versus low beta power STN recordings. Magnitude of STA-LFP was greater within the STN compared to extra-STN structures along the trajectory path, despite no difference in percentage of the total power. Within the STN, there was a higher percent beta power in dorsal compared to ventral STN but no difference in STA-LFP magnitude. Further refining the comparison to high versus low beta peak power recordings inside the STN to evaluate if single-unit activity synchronized more strongly with beta band activity in areas of high beta power resulted in a significantly higher STA magnitude for areas of high beta power. Overall, these results suggest that STN single units strongly synchronize to beta activity, particularly units in areas of high beta power.
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Affiliation(s)
- Eric Bayman
- Department of NeurosurgeryUniversity of Colorado Anschutz Medical CampusAuroraColoradoUSA
| | - Keanu Chee
- Department of NeurosurgeryUniversity of Colorado Anschutz Medical CampusAuroraColoradoUSA
| | - Madelyn Mendlen
- Department of NeurosurgeryUniversity of Colorado Anschutz Medical CampusAuroraColoradoUSA
| | - Daniel J. Denman
- Department of Neurophysiology and BiophysicsUniversity of Colorado Anschutz Medical CampusAuroraColoradoUSA
| | - Rex N. Tien
- Department of NeurosurgeryUniversity of Colorado Anschutz Medical CampusAuroraColoradoUSA
| | - Steven Ojemann
- Department of NeurosurgeryUniversity of Colorado Anschutz Medical CampusAuroraColoradoUSA
| | - Daniel R. Kramer
- Department of NeurosurgeryUniversity of Colorado Anschutz Medical CampusAuroraColoradoUSA
| | - John A. Thompson
- Department of NeurosurgeryUniversity of Colorado Anschutz Medical CampusAuroraColoradoUSA
- Department of NeurologyUniversity of Colorado Anschutz Medical CampusAuroraColoradoUSA
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3
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Kim B, Erickson BA, Fernandez-Nunez G, Rich R, Mentzelopoulos G, Vitale F, Medaglia JD. EEG Phase Can Be Predicted with Similar Accuracy across Cognitive States after Accounting for Power and Signal-to-Noise Ratio. eNeuro 2023; 10:ENEURO.0050-23.2023. [PMID: 37558464 PMCID: PMC10481640 DOI: 10.1523/eneuro.0050-23.2023] [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: 02/13/2023] [Revised: 05/25/2023] [Accepted: 06/15/2023] [Indexed: 08/11/2023] Open
Abstract
EEG phase is increasingly used in cognitive neuroscience, brain-computer interfaces, and closed-loop stimulation devices. However, it is unknown how accurate EEG phase prediction is across cognitive states. We determined the EEG phase prediction accuracy of parieto-occipital alpha waves across rest and task states in 484 participants over 11 public datasets. We were able to track EEG phase accurately across various cognitive conditions and datasets, especially during periods of high instantaneous alpha power and signal-to-noise ratio (SNR). Although resting states generally have higher accuracies than task states, absolute accuracy differences were small, with most of these differences attributable to EEG power and SNR. These results suggest that experiments and technologies using EEG phase should focus more on minimizing external noise and waiting for periods of high power rather than inducing a particular cognitive state.
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Affiliation(s)
- Brian Kim
- Department of Psychological and Brain Sciences, Drexel University, Philadelphia, Pennsylvania 19104
| | - Brian A Erickson
- Department of Psychological and Brain Sciences, Drexel University, Philadelphia, Pennsylvania 19104
| | | | - Ryan Rich
- Department of Psychological and Brain Sciences, Drexel University, Philadelphia, Pennsylvania 19104
| | - Georgios Mentzelopoulos
- Department of Bioengineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104
- Center for Neuroengineering and Therapeutics, University of Pennsylvania, Philadelphia, Pennsylvania 19104
- Center for Neurotrauma, Neurodegeneration, and Restoration, Corporal Michael J. Crescenz Veterans Affairs Medical Center, Philadelphia, Pennsylvania 19104
| | - Flavia Vitale
- Department of Bioengineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104
- Center for Neuroengineering and Therapeutics, University of Pennsylvania, Philadelphia, Pennsylvania 19104
- Center for Neurotrauma, Neurodegeneration, and Restoration, Corporal Michael J. Crescenz Veterans Affairs Medical Center, Philadelphia, Pennsylvania 19104
- Departments of Neurology, University of Pennsylvania, Philadelphia, Pennsylvania 19104
- Physical Medicine and Rehabilitation, University of Pennsylvania, Philadelphia, Pennsylvania 19146
| | - John D Medaglia
- Department of Psychological and Brain Sciences, Drexel University, Philadelphia, Pennsylvania 19104
- Departments of Neurology, University of Pennsylvania, Philadelphia, Pennsylvania 19104
- Department of Neurology, Drexel University, Philadelphia, Pennsylvania 19104
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Westerberg JA, Schall MS, Maier A, Woodman GF, Schall JD. Laminar microcircuitry of visual cortex producing attention-associated electric fields. eLife 2022; 11:72139. [PMID: 35089128 PMCID: PMC8846592 DOI: 10.7554/elife.72139] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2021] [Accepted: 01/25/2022] [Indexed: 11/24/2022] Open
Abstract
Cognitive operations are widely studied by measuring electric fields through EEG and ECoG. However, despite their widespread use, the neural circuitry giving rise to these signals remains unknown because the functional architecture of cortical columns producing attention-associated electric fields has not been explored. Here, we detail the laminar cortical circuitry underlying an attention-associated electric field measured over posterior regions of the brain in humans and monkeys. First, we identified visual cortical area V4 as one plausible contributor to this attention-associated electric field through inverse modeling of cranial EEG in macaque monkeys performing a visual attention task. Next, we performed laminar neurophysiological recordings on the prelunate gyrus and identified the electric-field-producing dipoles as synaptic activity in distinct cortical layers of area V4. Specifically, activation in the extragranular layers of cortex resulted in the generation of the attention-associated dipole. Feature selectivity of a given cortical column determined the overall contribution to this electric field. Columns selective for the attended feature contributed more to the electric field than columns selective for a different feature. Last, the laminar profile of synaptic activity generated by V4 was sufficient to produce an attention-associated signal measurable outside of the column. These findings suggest that the top-down recipient cortical layers produce an attention-associated electric field that can be measured extracortically with the relative contribution of each column depending upon the underlying functional architecture.
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Affiliation(s)
- Jacob A Westerberg
- Department of Psychology, Vanderbilt University, Nashville, United States
| | - Michelle S Schall
- Department of Psychology, Vanderbilt University, Nashville, United States
| | - Alexander Maier
- Department of Psychology, Vanderbilt University, Nashville, United States
| | - Geoffrey F Woodman
- Department of Psychology, Vanderbilt University, Nashville, United States
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Characteristic changes in EEG spectral powers of patients with opioid-use disorder as compared with those with methamphetamine- and alcohol-use disorders. PLoS One 2021; 16:e0248794. [PMID: 34506492 PMCID: PMC8432824 DOI: 10.1371/journal.pone.0248794] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2021] [Accepted: 08/26/2021] [Indexed: 11/30/2022] Open
Abstract
Electroencephalography (EEG) likely reflects activity of cortical neurocircuits, making it an insightful estimation for mental health in patients with substance use disorder (SUD). EEG signals are recorded as sinusoidal waves, containing spectral amplitudes across several frequency bands with high spatio-temporal resolution. Prior work on EEG signal analysis has been made mainly at individual electrodes. These signals can be evaluated from advanced aspects, including sub-regional and hemispheric analyses. Due to limitation of computational techniques, few studies in earlier work could conduct data analyses from these aspects. Therefore, EEG in patients with SUD is not fully understood. In the present retrospective study, spectral powers from a data house containing opioid (OUD), methamphetamine/stimulants (MUD), and alcohol use disorder (AUD) were extracted, and then converted into five distinct topographic data (i.e., electrode-based, cortical subregion-based, left-right hemispheric, anterior-posterior based, and total cortex-based analyses). We found that data conversion and reorganization in the topographic way had an impact on EEG spectral powers in patients with OUD significantly different from those with MUD or AUD. Differential changes were observed from multiple perspectives, including individual electrodes, subregions, hemispheres, anterior-posterior cortices, and across the cortex as a whole. Understanding the differential changes in EEG signals may be useful for future work with machine learning and artificial intelligence (AI), not only for diagnostic but also for prognostic purposes in patients with SUD.
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Issar D, Williamson RC, Khanna SB, Smith MA. A neural network for online spike classification that improves decoding accuracy. J Neurophysiol 2020; 123:1472-1485. [PMID: 32101491 PMCID: PMC7191521 DOI: 10.1152/jn.00641.2019] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2019] [Revised: 02/26/2020] [Accepted: 02/26/2020] [Indexed: 11/22/2022] Open
Abstract
Separating neural signals from noise can improve brain-computer interface performance and stability. However, most algorithms for separating neural action potentials from noise are not suitable for use in real time and have shown mixed effects on decoding performance. With the goal of removing noise that impedes online decoding, we sought to automate the intuition of human spike-sorters to operate in real time with an easily tunable parameter governing the stringency with which spike waveforms are classified. We trained an artificial neural network with one hidden layer on neural waveforms that were hand-labeled as either spikes or noise. The network output was a likelihood metric for each waveform it classified, and we tuned the network's stringency by varying the minimum likelihood value for a waveform to be considered a spike. Using the network's labels to exclude noise waveforms, we decoded remembered target location during a memory-guided saccade task from electrode arrays implanted in prefrontal cortex of rhesus macaque monkeys. The network classified waveforms in real time, and its classifications were qualitatively similar to those of a human spike-sorter. Compared with decoding with threshold crossings, in most sessions we improved decoding performance by removing waveforms with low spike likelihood values. Furthermore, decoding with our network's classifications became more beneficial as time since array implantation increased. Our classifier serves as a feasible preprocessing step, with little risk of harm, that could be applied to both off-line neural data analyses and online decoding.NEW & NOTEWORTHY Although there are many spike-sorting methods that isolate well-defined single units, these methods typically involve human intervention and have inconsistent effects on decoding. We used human classified neural waveforms as training data to create an artificial neural network that could be tuned to separate spikes from noise that impaired decoding. We found that this network operated in real time and was suitable for both off-line data processing and online decoding.
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Affiliation(s)
- Deepa Issar
- Department of Bioengineering, University of Pittsburgh, Pittsburgh, Pennsylvania
- University of Pittsburgh School of Medicine, University of Pittsburgh, Pittsburgh, Pennsylvania
| | - Ryan C Williamson
- University of Pittsburgh School of Medicine, University of Pittsburgh, Pittsburgh, Pennsylvania
- Department of Machine Learning, Carnegie Mellon University, Pittsburgh, Pennsylvania
- Carnegie Mellon Neuroscience Institute, Pittsburgh, Pennsylvania
| | - Sanjeev B Khanna
- Department of Bioengineering, University of Pittsburgh, Pittsburgh, Pennsylvania
| | - Matthew A Smith
- Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania
- Carnegie Mellon Neuroscience Institute, Pittsburgh, Pennsylvania
- Department of Ophthalmology, University of Pittsburgh School of Medicine, University of Pittsburgh, Pittsburgh, Pennsylvania
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7
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Salelkar S, Ray S. Interaction between steady-state visually evoked potentials at nearby flicker frequencies. Sci Rep 2020; 10:5344. [PMID: 32210321 PMCID: PMC7093459 DOI: 10.1038/s41598-020-62180-y] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/26/2019] [Accepted: 03/11/2020] [Indexed: 01/20/2023] Open
Abstract
Steady-state visually evoked potential (SSVEP) studies routinely employ simultaneous presentation of two temporally modulated stimuli, with SSVEP amplitude modulations serving to index top-down cognitive processes. However, the nature of SSVEP amplitude modulations as a function of competing temporal frequency (TF) has not been systematically studied, especially in relation to the normalization framework which has been extensively used to explain visual responses to multiple stimuli. We recorded spikes and local field potential (LFP) from the primary visual cortex (V1) as well as EEG from two awake macaque monkeys while they passively fixated plaid stimuli with components counterphasing at different TFs. We observed asymmetric SSVEP response suppression by competing TFs (greater suppression for lower TFs), which further depended on the relative orientations of plaid components. A tuned normalization model, adapted to SSVEP responses, provided a good account of the suppression. Our results provide new insights into processing of temporally modulated visual stimuli.
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Affiliation(s)
- Siddhesh Salelkar
- IISc Mathematics Initiative, Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India
| | - Supratim Ray
- IISc Mathematics Initiative, Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India.
- Centre for Neuroscience, Indian Institute of Science, Bangalore, 560012, India.
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Snyder AC, Issar D, Smith MA. What does scalp electroencephalogram coherence tell us about long-range cortical networks? Eur J Neurosci 2018; 48:2466-2481. [PMID: 29363843 PMCID: PMC6497452 DOI: 10.1111/ejn.13840] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2017] [Revised: 12/20/2017] [Accepted: 01/17/2018] [Indexed: 01/01/2023]
Abstract
Long-range interactions between cortical areas are undoubtedly a key to the computational power of the brain. For healthy human subjects, the premier method for measuring brain activity on fast timescales is electroencephalography (EEG), and coherence between EEG signals is often used to assay functional connectivity between different brain regions. However, the nature of the underlying brain activity that is reflected in EEG coherence is currently the realm of speculation, because seldom have EEG signals been recorded simultaneously with intracranial recordings near cell bodies in multiple brain areas. Here, we take the early steps towards narrowing this gap in our understanding of EEG coherence by measuring local field potentials with microelectrode arrays in two brain areas (extrastriate visual area V4 and dorsolateral prefrontal cortex) simultaneously with EEG at the nearby scalp in rhesus macaque monkeys. Although we found inter-area coherence at both scales of measurement, we did not find that scalp-level coherence was reliably related to coherence between brain areas measured intracranially on a trial-to-trial basis, despite that scalp-level EEG was related to other important features of neural oscillations, such as trial-to-trial variability in overall amplitudes. This suggests that caution must be exercised when interpreting EEG coherence effects, and new theories devised about what aspects of neural activity long-range coherence in the EEG reflects.
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Affiliation(s)
- Adam C. Snyder
- Dept. of Electrical and Computer Engineering, Carnegie Mellon Univ., Pittsburgh, PA, USA,Dept. of Ophthalmology, Univ. of Pittsburgh, Pittsburgh, PA, USA,Center for the Neural Basis of Cognition, Univ. of Pittsburgh, Pittsburgh, PA, USA
| | - Deepa Issar
- Dept. of Bioengineering, Univ. of Pittsburgh, Pittsburgh, PA, USA
| | - Matthew A. Smith
- Dept. of Ophthalmology, Univ. of Pittsburgh, Pittsburgh, PA, USA,Center for the Neural Basis of Cognition, Univ. of Pittsburgh, Pittsburgh, PA, USA,Dept. of Bioengineering, Univ. of Pittsburgh, Pittsburgh, PA, USA,Fox Center for Vision Restoration, Univ. of Pittsburgh, Pittsburgh, PA, USA,Address correspondence to: Matthew A. Smith, Department of Ophthalmology, University of Pittsburgh, Eye and Ear Institute, 203 Lothrop St., 9 Fl., Pittsburgh, PA, 15213, Tel: (412) 647-2313,
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Abstract
PURPOSE OF REVIEW The computational power of the brain arises from the complex interactions between neurons. One straightforward method to quantify the strength of neuronal interactions is by measuring correlation and coherence. Efforts to measure correlation have been advancing rapidly of late, spurred by the development of advanced recording technologies enabling recording from many neurons and brain areas simultaneously. This review highlights recent results that provide clues into the principles of neural coordination, connections to cognitive and neurological phenomena, and key directions for future research. RECENT FINDINGS The correlation structure of neural activity in the brain has important consequences for the encoding properties of neural populations. Recent studies have shown that this correlation structure is not fixed, but adapts in a variety of contexts in ways that appear beneficial to task performance. By studying these changes in biological neural networks and computational models, researchers have improved our understanding of the principles guiding neural communication. SUMMARY Correlation and coherence are highly informative metrics for studying coding and communication in the brain. Recent findings have emphasized how the brain modifies correlation structure dynamically in order to improve information-processing in a goal-directed fashion. One key direction for future research concerns how to leverage these dynamic changes for therapeutic purposes.
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Affiliation(s)
- Adam C. Snyder
- Dept. of Electrical and Computer Engineering, Carnegie Mellon Univ., Pittsburgh, PA, USA
- Dept. of Ophthalmology, Univ. of Pittsburgh, Pittsburgh, PA, USA
- Center for the Neural Basis of Cognition, Univ. of Pittsburgh, Pittsburgh, PA, USA
| | - Matthew A. Smith
- Dept. of Ophthalmology, Univ. of Pittsburgh, Pittsburgh, PA, USA
- Center for the Neural Basis of Cognition, Univ. of Pittsburgh, Pittsburgh, PA, USA
- Dept. of Bioengineering, Univ. of Pittsburgh, Pittsburgh, PA, USA
- Fox Center for Vision Restoration, Univ. of Pittsburgh, Pittsburgh, PA, USA
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Zhou P, Burton SD, Snyder AC, Smith MA, Urban NN, Kass RE. Establishing a Statistical Link between Network Oscillations and Neural Synchrony. PLoS Comput Biol 2015; 11:e1004549. [PMID: 26465621 PMCID: PMC4605746 DOI: 10.1371/journal.pcbi.1004549] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2015] [Accepted: 09/04/2015] [Indexed: 01/01/2023] Open
Abstract
Pairs of active neurons frequently fire action potentials or "spikes" nearly synchronously (i.e., within 5 ms of each other). This spike synchrony may occur by chance, based solely on the neurons' fluctuating firing patterns, or it may occur too frequently to be explicable by chance alone. When spike synchrony above chances levels is present, it may subserve computation for a specific cognitive process, or it could be an irrelevant byproduct of such computation. Either way, spike synchrony is a feature of neural data that should be explained. A point process regression framework has been developed previously for this purpose, using generalized linear models (GLMs). In this framework, the observed number of synchronous spikes is compared to the number predicted by chance under varying assumptions about the factors that affect each of the individual neuron's firing-rate functions. An important possible source of spike synchrony is network-wide oscillations, which may provide an essential mechanism of network information flow. To establish the statistical link between spike synchrony and network-wide oscillations, we have integrated oscillatory field potentials into our point process regression framework. We first extended a previously-published model of spike-field association and showed that we could recover phase relationships between oscillatory field potentials and firing rates. We then used this new framework to demonstrate the statistical relationship between oscillatory field potentials and spike synchrony in: 1) simulated neurons, 2) in vitro recordings of hippocampal CA1 pyramidal cells, and 3) in vivo recordings of neocortical V4 neurons. Our results provide a rigorous method for establishing a statistical link between network oscillations and neural synchrony.
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Affiliation(s)
- Pengcheng Zhou
- Program for Neural Computation, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
- Center for the Neural Basis of Cognition, Pittsburgh, Pennsylvania, United States of America
| | - Shawn D. Burton
- Center for the Neural Basis of Cognition, Pittsburgh, Pennsylvania, United States of America
- Department of Biological Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
| | - Adam C. Snyder
- Center for the Neural Basis of Cognition, Pittsburgh, Pennsylvania, United States of America
- Department of Ophthalmology, University of Pittsburgh, Pittsburgh, Pennsylvania, United States of America
| | - Matthew A. Smith
- Center for the Neural Basis of Cognition, Pittsburgh, Pennsylvania, United States of America
- Department of Ophthalmology, University of Pittsburgh, Pittsburgh, Pennsylvania, United States of America
| | - Nathaniel N. Urban
- Center for the Neural Basis of Cognition, Pittsburgh, Pennsylvania, United States of America
- Department of Biological Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
- Department of Neurobiology, University of Pittsburgh, Pittsburgh, Pennsylvania, United States of America
| | - Robert E. Kass
- Center for the Neural Basis of Cognition, Pittsburgh, Pennsylvania, United States of America
- Department of Statistics, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
- Department of Machine Learning, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
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