Intrinsic dendritic filtering gives low-pass power spectra of local field potentials

Focal inputs are a potential origin of local field potential (LFP) in the brain regions without laminar structure

Current sinks and sources spatially separated between the apical and basal dendrites have been believed to be essential in generating local field potentials (LFPs). According to this theory, LFPs would not be large enough to be observed in the regions without laminar structures, such as striatum and thalamus. However, LFPs are experimentally recorded in these regions. We hypothesized that focal excitatory input induces a concentric current sink and source generating LFPs in these regions. In this study, we tested this hypothesis by the numerical simulations of multicompartment neuron models and the analysis of simplified models. Both confirmed that focal excitatory input can generate LFPs on the order of 0.1 mV in a region without laminar structures. The present results suggest that LFPs in subcortical nuclei indicate localized excitatory input.

Neural correlates of the DMT experience assessed with multivariate EEG

Studying transitions in and out of the altered state of consciousness caused by intravenous (IV) N,N-Dimethyltryptamine (DMT - a fast-acting tryptamine psychedelic) offers a safe and powerful means of advancing knowledge on the neurobiology of conscious states. Here we sought to investigate the effects of IV DMT on the power spectrum and signal diversity of human brain activity (6 female, 7 male) recorded via multivariate EEG, and plot relationships between subjective experience, brain activity and drug plasma concentrations across time. Compared with placebo, DMT markedly reduced oscillatory power in the alpha and beta bands and robustly increased spontaneous signal diversity. Time-referenced and neurophenomenological analyses revealed close relationships between changes in various aspects of subjective experience and changes in brain activity. Importantly, the emergence of oscillatory activity within the delta and theta frequency bands was found to correlate with the peak of the experience - particularly its eyes-closed visual component. These findings highlight marked changes in oscillatory activity and signal diversity with DMT that parallel broad and specific components of the subjective experience, thus advancing our understanding of the neurobiological underpinnings of immersive states of consciousness.

Random Recurrent Networks Near Criticality Capture the Broadband Power Distribution of Human ECoG Dynamics

Brain electric field potentials are dominated by an arrhythmic broadband signal, but the underlying mechanism is poorly understood. Here we propose that broadband power spectra characterize recurrent neural networks of nodes (neurons or clusters of neurons), endowed with an effective balance between excitation and inhibition tuned to keep the network on the edge of dynamical instability. These networks show a fast mode reflecting local dynamics and a slow mode emerging from distributed recurrent connections. Together, the 2 modes produce power spectra similar to those observed in human intracranial EEG (i.e., electrocorticography, ECoG) recordings. Moreover, such networks convert spatial input correlations across nodes into temporal autocorrelation of network activity. Consequently, increased independence between nodes reduces low-frequency power, which may explain changes observed during behavioral tasks. Lastly, varying network coupling causes activity changes that resemble those observed in human ECoG across different arousal states. The model links macroscopic features of empirical ECoG power to a parsimonious underlying network structure, and suggests mechanisms for changes observed across behavioral and arousal states. This work provides a computational framework to generate and test hypotheses about cellular and network mechanisms underlying whole brain electrical dynamics, their variations across states, and potential alterations in brain diseases.

Bayesian Modelling of Induced Responses and Neuronal Rhythms

Neural rhythms or oscillations are ubiquitous in neuroimaging data. These spectral responses have been linked to several cognitive processes; including working memory, attention, perceptual binding and neuronal coordination. In this paper, we show how Bayesian methods can be used to finesse the ill-posed problem of reconstructing-and explaining-oscillatory responses. We offer an overview of recent developments in this field, focusing on (i) the use of MEG data and Empirical Bayes to build hierarchical models for group analyses-and the identification of important sources of inter-subject variability and (ii) the construction of novel dynamic causal models of intralaminar recordings to explain layer-specific activity. We hope to show that electrophysiological measurements contain much more spatial information than is often thought: on the one hand, the dynamic causal modelling of non-invasive (low spatial resolution) electrophysiology can afford sub-millimetre (hyper-acute) resolution that is limited only by the (spatial) complexity of the underlying (dynamic causal) forward model. On the other hand, invasive microelectrode recordings (that penetrate different cortical layers) can reveal laminar-specific responses and elucidate hierarchical message passing and information processing within and between cortical regions at a macroscopic scale. In short, the careful and biophysically grounded modelling of sparse data enables one to characterise the neuronal architectures generating oscillations in a remarkable detail.

ELFENN: A Generalized Platform for Modeling Ephaptic Coupling in Spiking Neuron Models

The transmembrane ionic currents that underlie changes in a cell's membrane potential give rise to electric fields in the extracellular space. In the context of brain activity, these electric fields form the basis for extracellularly recorded signals, such as multiunit activity, local field potentials and electroencephalograms. Understanding the underlying neuronal dynamics and localizing current sources using these signals is often challenging, and therefore effective computational modeling approaches are critical. Typically, the electric fields from neural activity are modeled in a post-hoc form, i.e., a traditional neuronal model is used to first generate the membrane currents, which in turn are then used to calculate the electric fields. When the conductivity of the extracellular space is high, the electric fields are weak, and therefore treating membrane currents and electric fields separately is justified. However, in brain regions of lower conductivity, extracellular fields can feed back and significantly influence the underlying transmembrane currents and dynamics of nearby neurons—this is often referred to as ephaptic coupling. The closed-loop nature of ephaptic coupling cannot be modeled using the post-hoc approaches implemented by existing software tools; instead, electric fields and neuronal dynamics must be solved simultaneously. To this end, we have developed a generalized modeling toolbox for studying ephaptic coupling in compartmental neuron models: E_LFENN (E_Lectric Field Effects in Neural Networks). In open loop conditions, we validate the separate components of E_LFENN for modeling membrane dynamics and associated field potentials against standard approaches (NEURON and LFPy). Unlike standard approaches however, E_LFENN enables the closed-loop condition to be modeled as well, in that the field potentials can feed back and influence membrane dynamics. As an example closed-loop case, we use E_LFENN to study phase-locking of action potentials generated by a population of axons running parallel in a bundle. Being able to efficiently explore ephaptic coupling from a computational perspective using tools, such as E_LFENN will allow us to better understand the physical basis of electric fields in the brain, as well as the conditions in which these fields may influence neuronal dynamics in general.

Linking demyelination to compound action potential dispersion with a spike-diffuse-spike approach

To establish and exploit novel biomarkers of demyelinating diseases requires a mechanistic understanding of axonal propagation. Here, we present a novel computational framework called the stochastic spike-diffuse-spike (SSDS) model for assessing the effects of demyelination on axonal transmission. It models transmission through nodal and internodal compartments with two types of operations: a stochastic integrate-and-fire operation captures nodal excitability and a linear filtering operation describes internodal propagation. The effects of demyelinated segments on the probability of transmission, transmission delay and spike time jitter are explored. We argue that demyelination-induced impedance mismatch prevents propagation mostly when the action potential leaves a demyelinated region, not when it enters a demyelinated region. In addition, we model sodium channel remodeling as a homeostatic control of nodal excitability. We find that the effects of mild demyelination on transmission probability and delay can be largely counterbalanced by an increase in excitability at the nodes surrounding the demyelination. The spike timing jitter, however, reflects the level of demyelination whether excitability is fixed or is allowed to change in compensation. This jitter can accumulate over long axons and leads to a broadening of the compound action potential, linking microscopic defects to a mesoscopic observable. Our findings articulate why action potential jitter and compound action potential dispersion can serve as potential markers of weak and sporadic demyelination.

Cortical Electrocorticogram (ECoG) Is a Local Signal

Electrocorticogram (ECoG), obtained by low-pass filtering the brain signal recorded from a macroelectrode placed on the cortex, is extensively used to find the seizure focus in drug-resistant epilepsy and is of growing importance in cognitive and brain-machine-interfacing studies. To accurately estimate the epileptogenic cortex or to make inferences about cognitive processes, it is important to determine the "spatial spread" of ECoG (i.e., the extent of cortical tissue that contributes to its activity). However, the ECoG spread is currently unknown; even the spread of local field potential (LFP) obtained from microelectrodes is debated, with estimates ranging from a few hundred micrometers to several millimeters. Spatial spread can be estimated by measuring the receptive field (RF) and multiplying by the cortical magnification factor, but this method overestimates the spread because RF size gets inflated due to several factors. This issue can be partially addressed using a model that compares the RFs of two measures, such as LFP and multi-unit activity (MUA). To use this approach for ECoG, we designed a customized array containing both microelectrodes and ECoG electrodes to simultaneously map MUA, LFP, and ECoG RFs from the primary visual cortex of awake monkeys (three female Macaca radiata). The spatial spread of ECoG was surprisingly local (diameter ∼3 mm), only 3 times that of the LFP. Similar results were obtained using a model to simulate ECoG as a sum of LFPs of varying electrode sizes. Our results further validate the use of ECoG in clinical and basic cognitive research.SIGNIFICANCE STATEMENT Brains signals capture different attributes of the neural network depending on the size and location of the recording electrode. Electrocorticogram (ECoG), obtained by placing macroelectrodes (typically 2-3 mm diameter) on the exposed surface of the cortex, is widely used by neurosurgeons to identify the source of seizures in drug-resistant epileptic patients. The brain area responsible for seizures is subsequently surgically removed. Accurate estimation of the epileptogenic cortex and its removal requires the estimation of spatial spread of ECoG. Here, we estimated the spatial spread of ECoG in five behaving monkeys using two different approaches. Our results suggest that ECoG is a local signal (diameter of ∼3 mm), which can provide a useful tool for clinical, cognitive neuroscience, and brain-machine-interfacing applications.

Alterations in Schizophrenia-Associated Genes Can Lead to Increased Power in Delta Oscillations

Genome-wide association studies have implicated many ion channels in schizophrenia pathophysiology. Although the functions of these channels are relatively well characterized by single-cell studies, the contributions of common variation in these channels to neurophysiological biomarkers and symptoms of schizophrenia remain elusive. Here, using computational modeling, we show that a common biomarker of schizophrenia, namely, an increase in delta-oscillation power, may be a direct consequence of altered expression or kinetics of voltage-gated ion channels or calcium transporters. Our model of a circuit of layer V pyramidal cells highlights multiple types of schizophrenia-related variants that contribute to altered dynamics in the delta-frequency band. Moreover, our model predicts that the same membrane mechanisms that increase the layer V pyramidal cell network gain and response to delta-frequency oscillations may also cause a deficit in a single-cell correlate of the prepulse inhibition, which is a behavioral biomarker highly associated with schizophrenia.

Lateral Inhibition Organizes Beta Attentional Modulation in the Primary Visual Cortex

We have previously shown that during top-down attentional modulation (stimulus expectation) correlations of the beta signals across the primary visual cortex were uniform, while during bottom-up attentional processing (visual stimulation) their values were heterogeneous. These different patterns of attentional beta modulation may be caused by feed-forward lateral inhibitory interactions in the visual cortex, activated solely during stimulus processing. To test this hypothesis, we developed a large-scale computational model of the cortical network. We first identified the parameter range needed to support beta rhythm generation, and next, simulated the different activity states corresponding to experimental paradigms. The model matched our experimental data in terms of spatial organization of beta correlations during different attentional states and provided a computational confirmation of the hypothesis that the paradigm-specific beta activation spatial maps depend on the lateral inhibitory mechanism. The model also generated testable predictions that cross-correlation values depend on the distance between the activated columns and on their spatial position with respect to the location of the sensory inputs from the thalamus.

Differential recordings of local field potential: A genuine tool to quantify functional connectivity

Local field potential (LFP) recording is a very useful electrophysiological method to study brain processes. However, this method is criticized for recording low frequency activity in a large area of extracellular space potentially contaminated by distal activity. Here, we theoretically and experimentally compare ground-referenced (RR) with differential recordings (DR). We analyze electrical activity in the rat cortex with these two methods. Compared with RR, DR reveals the importance of local phasic oscillatory activities and their coherence between cortical areas. Finally, we show that DR provides a more faithful assessment of functional connectivity caused by an increase in the signal to noise ratio, and of the delay in the propagation of information between two cortical structures.

Multimodal Modeling of Neural Network Activity: Computing LFP, ECoG, EEG, and MEG Signals With LFPy 2.0

Recordings of extracellular electrical, and later also magnetic, brain signals have been the dominant technique for measuring brain activity for decades. The interpretation of such signals is however nontrivial, as the measured signals result from both local and distant neuronal activity. In volume-conductor theory the extracellular potentials can be calculated from a distance-weighted sum of contributions from transmembrane currents of neurons. Given the same transmembrane currents, the contributions to the magnetic field recorded both inside and outside the brain can also be computed. This allows for the development of computational tools implementing forward models grounded in the biophysics underlying electrical and magnetic measurement modalities. LFPy (LFPy.readthedocs.io) incorporated a well-established scheme for predicting extracellular potentials of individual neurons with arbitrary levels of biological detail. It relies on NEURON (neuron.yale.edu) to compute transmembrane currents of multicompartment neurons which is then used in combination with an electrostatic forward model. Its functionality is now extended to allow for modeling of networks of multicompartment neurons with concurrent calculations of extracellular potentials and current dipole moments. The current dipole moments are then, in combination with suitable volume-conductor head models, used to compute non-invasive measures of neuronal activity, like scalp potentials (electroencephalographic recordings; EEG) and magnetic fields outside the head (magnetoencephalographic recordings; MEG). One such built-in head model is the four-sphere head model incorporating the different electric conductivities of brain, cerebrospinal fluid, skull and scalp. We demonstrate the new functionality of the software by constructing a network of biophysically detailed multicompartment neuron models from the Neocortical Microcircuit Collaboration (NMC) Portal (bbp.epfl.ch/nmc-portal) with corresponding statistics of connections and synapses, and compute in vivo-like extracellular potentials (local field potentials, LFP; electrocorticographical signals, ECoG) and corresponding current dipole moments. From the current dipole moments we estimate corresponding EEG and MEG signals using the four-sphere head model. We also show strong scaling performance of LFPy with different numbers of message-passing interface (MPI) processes, and for different network sizes with different density of connections. The open-source software LFPy is equally suitable for execution on laptops and in parallel on high-performance computing (HPC) facilities and is publicly available on GitHub.com.

Dynamics of large-scale electrophysiological networks: A technical review

For several years it has been argued that neural synchronisation is crucial for cognition. The idea that synchronised temporal patterns between different neural groups carries information above and beyond the isolated activity of these groups has inspired a shift in focus in the field of functional neuroimaging. Specifically, investigation into the activation elicited within certain regions by some stimulus or task has, in part, given way to analysis of patterns of co-activation or functional connectivity between distal regions. Recently, the functional connectivity community has been looking beyond the assumptions of stationarity that earlier work was based on, and has introduced methods to incorporate temporal dynamics into the analysis of connectivity. In particular, non-invasive electrophysiological data (magnetoencephalography/electroencephalography (MEG/EEG)), which provides direct measurement of whole-brain activity and rich temporal information, offers an exceptional window into such (potentially fast) brain dynamics. In this review, we discuss challenges, solutions, and a collection of analysis tools that have been developed in recent years to facilitate the investigation of dynamic functional connectivity using these imaging modalities. Further, we discuss the applications of these approaches in the study of cognition and neuropsychiatric disorders. Finally, we review some existing developments that, by using realistic computational models, pursue a deeper understanding of the underlying causes of non-stationary connectivity.

Negative effects of interictal spikes on theta rhythm in human temporal lobe epilepsy

Interictal spike is a biomarker of epilepsy that can occur frequently between seizures. Its potential effects on brain oscillations, especially on theta rhythm (4-8 Hz) that is related to a variety of cognitive processes, remain controversial. Using local field potentials recorded from patients with temporal lobe epilepsy (TLE), we investigated here the impact of spikes on theta rhythm immediately after spikes and during the prolonged periods (lasting 4-36 s) between adjacent spikes. Local field potentials (LFPs) were recorded in different epileptogenic areas including the anterior hippocampus (aH) and the entorhinal cortex (EC) as well as in the extended propagation pathway. We found that interictal spikes had a significant inhibitory effect on theta rhythm. Power of theta rhythm was reduced immediately after spikes, and the inhibitory effect on theta rhythm might sustain during the prolonged between-spike periods. The inhibitory effect was more severe when the epileptogenic areas involved both the aH and EC compared to that involved only a single structure. These observations suggest that interictal spikes have a significant negative impact on theta rhythm and may thus play a role in theta-related cognition changes in patients with TLE.

Deciphering the Contribution of Oriens-Lacunosum/Moleculare (OLM) Cells to Intrinsic θ Rhythms Using Biophysical Local Field Potential (LFP) Models

Oscillations in local field potentials (LFPs) are prevalent and contribute to brain function. An understanding of the cellular correlates and pathways affecting LFPs is needed, but many overlapping pathways in vivo make this difficult to achieve. A prevalent LFP rhythm in the hippocampus associated with memory processing and spatial navigation is the θ (3–12 Hz) oscillation. θ rhythms emerge intrinsically in an in vitro whole hippocampus preparation and this reduced preparation makes it possible to assess the contribution of different cell types to LFP generation. We focus on oriens-lacunosum/moleculare (OLM) cells as a major class of interneurons in the hippocampus. OLM cells can influence pyramidal (PYR) cells through two distinct pathways: by direct inhibition of PYR cell distal dendrites, and by indirect disinhibition of PYR cell proximal dendrites. We use previous inhibitory network models and build biophysical LFP models using volume conductor theory. We examine the effect of OLM cells to ongoing intrinsic LFP θ rhythms by directly comparing our model LFP features with experiment. We find that OLM cell inputs regulate the robustness of LFP responses without affecting their average power and that this robust response depends on coactivation of distal inhibition and basal excitation. We use our models to estimate the spatial extent of the region generating LFP θ rhythms, leading us to predict that about 22,000 PYR cells participate in intrinsic θ generation. Besides obtaining an understanding of OLM cell contributions to intrinsic LFP θ rhythms, our work can help decipher cellular correlates of in vivo LFPs.

Effect of Stimulation Waveform on the Non-linear Entrainment of Cortical Alpha Oscillations

In the past decade, there has been a surge of interest in using patterned brain stimulation to manipulate cortical oscillations, in both experimental and clinical settings. But the relationship between stimulation waveform and its impact on ongoing oscillations remains poorly understood and severely restrains the development of new paradigms. To address some aspects of this intricate problem, we combine computational and mathematical approaches, providing new insights into the influence of waveform of both low and high-frequency stimuli on synchronous neural activity. Using a cellular-based cortical microcircuit network model, we performed numerical simulations to test the influence of different waveforms on ongoing alpha oscillations, and derived a mean-field description of stimulation-driven dynamics to better understand the observed responses. Our analysis shows that high-frequency periodic stimulation translates into an effective transformation of the neurons' response function, leading to waveform-dependent changes in oscillatory dynamics and resting state activity. Moreover, we found that randomly fluctuating stimulation linearizes the neuron response function while constant input moves its activation threshold. Taken together, our findings establish a new theoretical framework in which stimulation waveforms impact neural systems at the population-scale through non-linear interactions.

1/f electrophysiological spectra in resting and drug-induced states can be explained by the dynamics of multiple oscillatory relaxation processes

Neurophysiological recordings are dominated by arhythmical activity whose spectra can be characterised by power-law functions, and on this basis are often referred to as reflecting scale-free brain dynamics (1/f^β). Relatively little is known regarding the neural generators and temporal dynamics of this arhythmical behaviour compared to rhythmical behaviour. Here we used Irregularly Resampled AutoSpectral Analysis (IRASA) to quantify β, in both the high (5-100 Hz, β_hf) and low frequency bands (0.1-2.5 Hz, β_lf) in MEG/EEG/ECoG recordings and to separate arhythmical from rhythmical modes of activity, such as, alpha rhythms. In MEG/EEG/ECoG data, we demonstrate that oscillatory alpha power dynamically correlates over time with β_hf and similarly, participants with higher rhythmical alpha power have higher β_hf. In a series of pharmaco-MEG investigations using the GABA reuptake inhibitor tiagabine, the glutamatergic AMPA receptor antagonist perampanel, the NMDA receptor antagonist ketamine and the mixed partial serotonergic agonist LSD, a variety of effects on both β_hf and β_lf were observed. Additionally, strong modulations of β_hf were seen in monkey ECoG data during general anaesthesia using propofol and ketamine. We develop and test a unifying model which can explain, the 1/f nature of electrophysiological spectra, their dynamic interaction with oscillatory rhythms as well as the sensitivity of 1/f activity to drug interventions by considering electrophysiological spectra as being generated by a collection of stochastically perturbed damped oscillators having a distribution of relaxation rates.

Investigating large-scale brain dynamics using field potential recordings: analysis and interpretation

New technologies to record electrical activity from the brain on a massive scale offer tremendous opportunities for discovery. Electrical measurements of large-scale brain dynamics, termed field potentials, are especially important to understanding and treating the human brain. Here, our goal is to provide best practices on how field potential recordings (electroencephalograms, magnetoencephalograms, electrocorticograms and local field potentials) can be analyzed to identify large-scale brain dynamics, and to highlight critical issues and limitations of interpretation in current work. We focus our discussion of analyses around the broad themes of activation, correlation, communication and coding. We provide recommendations for interpreting the data using forward and inverse models. The forward model describes how field potentials are generated by the activity of populations of neurons. The inverse model describes how to infer the activity of populations of neurons from field potential recordings. A recurring theme is the challenge of understanding how field potentials reflect neuronal population activity given the complexity of the underlying brain systems.

Contribution of the Axon Initial Segment to Action Potentials Recorded Extracellularly

Action potentials (APs) are electric phenomena that are recorded both intracellularly and extracellularly. APs are usually initiated in the short segment of the axon called the axon initial segment (AIS). It was recently proposed that at the onset of an AP the soma and the AIS form a dipole. We study the extracellular signature [the extracellular AP (EAP)] generated by such a dipole. First, we demonstrate the formation of the dipole and its extracellular signature in detailed morphological models of a reconstructed pyramidal neuron. Then, we study the EAP waveform and its spatial dependence in models with axonal AP initiation and contrast it with the EAP obtained in models with somatic AP initiation. We show that in the models with axonal AP initiation the dipole forms between somatodendritic compartments and the AIS, and not between soma and dendrites as in the classical models. The soma-dendrites dipole is present only in models with somatic AP initiation. Our study has consequences for interpreting extracellular recordings of single-neuron activity and determining electrophysiological neuron types, but also for better understanding the origins of the high-frequency macroscopic extracellular potentials recorded in the brain.

h-Type Membrane Current Shapes the Local Field Potential from Populations of Pyramidal Neurons

In cortex, the local field potential (LFP) is thought to mainly stem from correlated synaptic input to populations of geometrically aligned neurons. Computer models of single cortical pyramidal neurons showed that subthreshold voltage-dependent membrane conductances can also shape the LFP signal, in particular the hyperpolarization-activated cation current (I_h; h-type). This ion channel is prominent in various types of pyramidal neurons, typically showing an increasing density gradient along the apical dendrites. Here, we investigate how I_h affects the LFP generated by a model of a population of cortical pyramidal neurons. We find that the LFP from populations of neurons that receive uncorrelated synaptic input can be well predicted by the LFP from single neurons. In this case, when input impinges on the distal dendrites, where most h-type channels are located, a strong resonance in the LFP was measured near the soma, whereas the opposite configuration does not reveal an I_h contribution to the LFP. Introducing correlations in the synaptic inputs to the pyramidal cells strongly amplifies the LFP, while maintaining the differential effects of I_h for distal dendritic versus perisomatic input. Previous theoretical work showed that input correlations do not amplify LFP power when neurons receive synaptic input uniformly across the cell. We find that this crucially depends on the membrane conductance distribution: the asymmetric distribution of I_h results in a strong amplification of the LFP when synaptic inputs to the cell population are correlated. In conclusion, we find that the h-type current is particularly suited to shape the LFP signal in cortical populations.SIGNIFICANCE STATEMENT The local field potential (LFP), the low-frequency part of extracellular potentials recorded in neural tissue, is often used for probing neural circuit activity. While the cortical LFP is thought to mainly reflect synaptic inputs onto pyramidal neurons, little is known about the role of subthreshold active conductances in shaping the LFP. By means of biophysical modeling we obtain a comprehensive, qualitative understanding of how LFPs generated by populations of cortical pyramidal neurons depend on active subthreshold currents, and identify the key importance of the h-type channel. Our results show that LFPs can give information about the active properties of neurons and that preferred frequencies in the LFP can result from those cellular properties instead of, for example, network dynamics.

Non-uniform weighting of local motion inputs underlies dendritic computation in the fly visual system

The fly visual system offers a unique opportunity to explore computations performed by single neurons. Two previous studies characterized, in vivo, the receptive field (RF) of the vertical system (VS) cells of the blowfly (calliphora vicina), both intracellularly in the axon, and, independently using Ca²⁺ imaging, in hundreds of distal dendritic branchlets. We integrated this information into detailed passive cable and compartmental models of 3D reconstructed VS cells. Within a given VS cell type, the transfer resistance (TR) from different branchlets to the axon differs substantially, suggesting that they contribute unequally to the shaping of the axonal RF. Weighting the local RFs of all dendritic branchlets by their respective TR yielded a faithful reproduction of the axonal RF. The model also predicted that the various dendritic branchlets are electrically decoupled from each other, thus acting as independent local functional subunits. The study suggests that single neurons in the fly visual system filter dendritic noise and compute the weighted average of their inputs.

An Interneuron Circuit Reproducing Essential Spectral Features of Field Potentials

Recent advances in engineering and signal processing have renewed the interest in invasive and surface brain recordings, yet many features of cortical field potentials remain incompletely understood. In the computational study that follows, we show that a model circuit of interneurons, coupled via both GABA_A receptor synapses and electrical synapses, reproduces many essential features of the power spectrum of local field potential (LFP) recordings, such as 1/ f power scaling at low frequency (below 10 Hz), power accumulation in the γ-frequency band (30-100 Hz), and a robust α rhythm in the absence of stimulation. The low-frequency 1/ f power scaling depends on strong reciprocal inhibition, whereas the α rhythm is generated by electrical coupling of intrinsically active neurons. As in previous studies, the γ power arises through the amplification of single-neuron spectral properties, owing to the refractory period, by parameters that favor neuronal synchrony, such as delayed inhibition. This study also confirms that both synaptic and voltage-gated membrane currents contribute substantially to the LFP and that high-frequency signals such as action potentials quickly taper off with distance. Given the ubiquity of electrically coupled interneuron circuits in the mammalian brain, they may be major determinants of the recorded potentials.

Superficial Slow Rhythms Integrate Cortical Processing in Humans

The neocortex is composed of six anatomically and physiologically specialized layers. It has been proposed that integration of activity across cortical areas is mediated anatomically by associative connections terminating in superficial layers, and physiologically by slow cortical rhythms. However, the means through which neocortical anatomy and physiology interact to coordinate neural activity remains obscure. Using laminar microelectrode arrays in 19 human participants, we found that most EEG activity is below 10-Hz (delta/theta) and generated by superficial cortical layers during both wakefulness and sleep. Cortical surface grid, grid-laminar, and dual-laminar recordings demonstrate that these slow rhythms are synchronous within upper layers across broad cortical areas. The phase of this superficial slow activity is reset by infrequent stimuli and coupled to the amplitude of faster oscillations and neuronal firing across all layers. These findings support a primary role of superficial slow rhythms in generating the EEG and integrating cortical activity.

Stochastic resonance mediates the state-dependent effect of periodic stimulation on cortical alpha oscillations

Brain stimulation can be used to engage and modulate rhythmic activity in brain networks. However, the outcomes of brain stimulation are shaped by behavioral states and endogenous fluctuations in brain activity. To better understand how this intrinsic oscillatory activity controls the susceptibility of the brain to stimulation, we analyzed a computational model of the thalamo-cortical system in two distinct states (rest and task-engaged) to identify the mechanisms by which endogenous alpha oscillations (8Hz–12Hz) are modulated by periodic stimulation. Our analysis shows that the different responses to stimulation observed experimentally in these brain states can be explained by a passage through a bifurcation combined with stochastic resonance — a mechanism by which irregular fluctuations amplify the response of a nonlinear system to weak periodic signals. Indeed, our findings suggest that modulation of brain oscillations is best achieved in states of low endogenous rhythmic activity, and that irregular state-dependent fluctuations in thalamic inputs shape the susceptibility of cortical population to periodic stimulation.

Contribution of action potentials to the extracellular field potential in the nucleus laminaris of barn owl

Extracellular field potentials (EFP) are widely used to evaluate in vivo neural activity, but identification of multiple sources and their relative contributions is often ambiguous, making the interpretation of the EFP difficult. We have therefore analyzed a model EFP from a simple brainstem circuit with separable pre- and postsynaptic components to determine whether we could isolate its sources. Our previous papers had shown that the barn owl neurophonic largely originates with spikes from input axons and synapses that terminate on the neurons in the nucleus laminaris (NL) (Kuokkanen PT, Wagner H, Ashida G, Carr CE, Kempter R. J Neurophysiol 104: 2274-2290, 2010; Kuokkanen PT, Ashida G, Carr CE, Wagner H, Kempter R. J Neurophysiol 110: 117-130, 2013; McColgan T, Liu J, Kuokkanen PT, Carr CE, Wagner H, Kempter R. eLife 6: e26106, 2017). To determine how much the postsynaptic NL neurons contributed to the neurophonic, we recorded EFP responses in NL in vivo. Power spectral analyses showed that a small spectral component of the evoked response, between 200 and 700 Hz, could be attributed to the NL neurons' spikes, while nucleus magnocellularis (NM) spikes dominate the EFP at frequencies ≳1 kHz. Thus, spikes of NL neurons and NM axons contribute to the EFP in NL in distinct frequency bands. We conclude that if the spectral components of source types are different and if their activities can be selectively modulated, the identification of EFP sources is possible. NEW & NOTEWORTHY Extracellular field potentials (EFPs) generate clinically important signals, but their sources are incompletely understood. As a model, we have analyzed the auditory neurophonic in the barn owl's nucleus laminaris. There the EFP originates predominantly from spiking in the afferent axons, with spectral power ≳1 kHz, while postsynaptic laminaris neurons contribute little. In conclusion, the identification of EFP sources is possible if they have different spectral components and if their activities can be modulated selectively.

The roadmap for estimation of cell-type-specific neuronal activity from non-invasive measurements

The computational properties of the human brain arise from an intricate interplay between billions of neurons connected in complex networks. However, our ability to study these networks in healthy human brain is limited by the necessity to use non-invasive technologies. This is in contrast to animal models where a rich, detailed view of cellular-level brain function with cell-type-specific molecular identity has become available due to recent advances in microscopic optical imaging and genetics. Thus, a central challenge facing neuroscience today is leveraging these mechanistic insights from animal studies to accurately draw physiological inferences from non-invasive signals in humans. On the essential path towards this goal is the development of a detailed 'bottom-up' forward model bridging neuronal activity at the level of cell-type-specific populations to non-invasive imaging signals. The general idea is that specific neuronal cell types have identifiable signatures in the way they drive changes in cerebral blood flow, cerebral metabolic rate of O2 (measurable with quantitative functional Magnetic Resonance Imaging), and electrical currents/potentials (measurable with magneto/electroencephalography). This forward model would then provide the 'ground truth' for the development of new tools for tackling the inverse problem-estimation of neuronal activity from multimodal non-invasive imaging data.This article is part of the themed issue 'Interpreting BOLD: a dialogue between cognitive and cellular neuroscience'.

Revealing the distribution of transmembrane currents along the dendritic tree of a neuron from extracellular recordings

Revealing the current source distribution along the neuronal membrane is a key step on the way to understanding neural computations; however, the experimental and theoretical tools to achieve sufficient spatiotemporal resolution for the estimation remain to be established. Here, we address this problem using extracellularly recorded potentials with arbitrarily distributed electrodes for a neuron of known morphology. We use simulations of models with varying complexity to validate the proposed method and to give recommendations for experimental applications. The method is applied to in vitro data from rat hippocampus.

Shaping Intrinsic Neural Oscillations with Periodic Stimulation

Rhythmic brain activity plays an important role in neural processing and behavior. Features of these oscillations, including amplitude, phase, and spectrum, can be influenced by internal states (e.g., shifts in arousal, attention or cognitive ability) or external stimulation. Electromagnetic stimulation techniques such as transcranial magnetic stimulation, transcranial direct current stimulation, and transcranial alternating current stimulation are used increasingly in both research and clinical settings. Currently, the mechanisms whereby time-dependent external stimuli influence population-scale oscillations remain poorly understood. Here, we provide computational insights regarding the mapping between periodic pulsatile stimulation parameters such as amplitude and frequency and the response dynamics of recurrent, nonlinear spiking neural networks. Using a cortical model built of excitatory and inhibitory neurons, we explored a wide range of stimulation intensities and frequencies systematically. Our results suggest that rhythmic stimulation can form the basis of a control paradigm in which one can manipulate the intrinsic oscillatory properties of driven networks via a plurality of input-driven mechanisms. Our results show that, in addition to resonance and entrainment, nonlinear acceleration is involved in shaping the rhythmic response of our modeled network. Such nonlinear acceleration of spontaneous and synchronous oscillatory activity in a neural network occurs in regimes of intense, high-frequency rhythmic stimulation. These results open new perspectives on the manipulation of synchronous neural activity for basic and clinical research.

SIGNIFICANCE STATEMENT

Oscillatory activity is widely recognized as a core mechanism for information transmission within and between brain circuits. Noninvasive stimulation methods can shape this activity, something that is increasingly capitalized upon in basic research and clinical practice. Here, we provide computational insights on the mechanistic bases for such effects. Our results show that rhythmic stimulation forms the basis of a control paradigm in which one can manipulate the intrinsic oscillatory properties of driven networks via a plurality of input-driven mechanisms. In addition to resonance and entrainment, nonlinear acceleration is involved in shaping the rhythmic response of our modeled network, particularly in regimes of high-frequency rhythmic stimulation. These results open new perspectives on the manipulation of synchronous neural activity for basic and clinical research.

Focal Local Field Potential Signature of the Single-Axon Monosynaptic Thalamocortical Connection

A resurgence has taken place in recent years in the use of the extracellularly recorded local field potential (LFP) to investigate neural network activity. To probe monosynaptic thalamic activation of cortical postsynaptic target cells, so called spike-trigger-averaged LFP (stLFP) signatures have been measured. In these experiments, the cortical LFP is measured by multielectrodes covering several cortical lamina and averaged on spontaneous spikes of thalamocortical (TC) cells. Using a well established forward-modeling scheme, we investigated the biophysical origin of this stLFP signature with simultaneous synaptic activation of cortical layer-4 neurons, mimicking the effect of a single afferent spike from a single TC neuron. Constrained by previously measured intracellular responses of the main postsynaptic target cell types and with biologically plausible assumptions regarding the spatial distribution of thalamic synaptic inputs into layer 4, the model predicted characteristic contributions to monosynaptic stLFP signatures both for the regular-spiking (RS) excitatory neurons and the fast-spiking (FS) inhibitory interneurons. In particular, the FS cells generated stLFP signatures of shorter temporal duration than the RS cells. Added together, a sum of the stLFP signatures of these two principal synaptic targets of TC cells were observed to resemble experimentally measured stLFP signatures. Outside the volume targeted by TC afferents, the resulting postsynaptic LFP signals were found to be sharply attenuated. This implies that such stLFP signatures provide a very local measure of TC synaptic activation, and that newly developed inverse current-source density (CSD)-estimation methods are needed for precise assessment of the underlying spatiotemporal CSD profiles.SIGNIFICANCE STATEMENT Despite its long history and prevalent use, the proper interpretation of the extracellularly recorded local field potential (LFP) is still not fully established. Here we investigate by biophysical modeling the origin of the focal LFP signature of the single-axon monosynaptic thalamocortical connection as measured by spike-trigger-averaging of cortical LFPs on spontaneous spikes of thalamocortical neurons. We find that this LFP signature is well accounted for by a model assuming thalamic projections to two cortical layer-4 cell populations: one excitatory (putatively regular-spiking cells) and one inhibitory (putatively fast-spiking cells). The LFP signature is observed to decay sharply outside the cortical region receiving the thalamocortical projection, implying that it indeed provides a very local measure of thalamocortical synaptic activation.

From Maxwell's equations to the theory of current-source density analysis

Despite the widespread use of current‐source density (CSD) analysis of extracellular potential recordings in the brain, the physical mechanisms responsible for the generation of the signal are still debated. While the extracellular potential is thought to be exclusively generated by the transmembrane currents, recent studies suggest that extracellular diffusive, advective and displacement currents—traditionally neglected—may also contribute considerably toward extracellular potential recordings. Here, we first justify the application of the electro‐quasistatic approximation of Maxwell's equations to describe the electromagnetic field of physiological origin. Subsequently, we perform spatial averaging of currents in neural tissue to arrive at the notion of the CSD and derive an equation relating it to the extracellular potential. We show that, in general, the extracellular potential is determined by the CSD of membrane currents as well as the gradients of the putative extracellular diffusion current. The diffusion current can contribute significantly to the extracellular potential at frequencies less than a few Hertz; in which case it must be subtracted to obtain correct CSD estimates. We also show that the advective and displacement currents in the extracellular space are negligible for physiological frequencies while, within cellular membrane, displacement current contributes toward the CSD as a capacitive current. Taken together, these findings elucidate the relationship between electric currents and the extracellular potential in brain tissue and form the necessary foundation for the analysis of extracellular recordings.

Linking canonical microcircuits and neuronal activity: Dynamic causal modelling of laminar recordings

Neural models describe brain activity at different scales, ranging from single cells to whole brain networks. Here, we attempt to reconcile models operating at the microscopic (compartmental) and mesoscopic (neural mass) scales to analyse data from microelectrode recordings of intralaminar neural activity. Although these two classes of models operate at different scales, it is relatively straightforward to create neural mass models of ensemble activity that are equipped with priors obtained after fitting data generated by detailed microscopic models. This provides generative (forward) models of measured neuronal responses that retain construct validity in relation to compartmental models. We illustrate our approach using cross spectral responses obtained from V1 during a visual perception paradigm that involved optogenetic manipulation of the basal forebrain. We find that the resulting neural mass model can distinguish between activity in distinct cortical layers - both with and without optogenetic activation - and that cholinergic input appears to enhance (disinhibit) superficial layer activity relative to deep layers. This is particularly interesting from the perspective of predictive coding, where neuromodulators are thought to boost prediction errors that ascend the cortical hierarchy.

Local field potentials primarily reflect inhibitory neuron activity in human and monkey cortex

The local field potential (LFP) is generated by large populations of neurons, but unitary contribution of spiking neurons to LFP is not well characterised. We investigated this contribution in multi-electrode array recordings from human and monkey neocortex by examining the spike-triggered LFP average (st-LFP). The resulting st-LFPs were dominated by broad spatio-temporal components due to ongoing activity, synaptic inputs and recurrent connectivity. To reduce the spatial reach of the st-LFP and observe the local field related to a single spike we applied a spatial filter, whose weights were adapted to the covariance of ongoing LFP. The filtered st-LFPs were limited to the perimeter of 800 μm around the neuron, and propagated at axonal speed, which is consistent with their unitary nature. In addition, we discriminated between putative inhibitory and excitatory neurons and found that the inhibitory st-LFP peaked at shorter latencies, consistently with previous findings in hippocampal slices. Thus, in human and monkey neocortex, the LFP reflects primarily inhibitory neuron activity.

Dipolar extracellular potentials generated by axonal projections

Extracellular field potentials (EFPs) are an important source of information in neuroscience, but their physiological basis is in many cases still a matter of debate. Axonal sources are typically discounted in modeling and data analysis because their contributions are assumed to be negligible. Here, we established experimentally and theoretically that contributions of axons to EFPs can be significant. Modeling action potentials propagating along axons, we showed that EFPs were prominent in the presence of terminal zones where axons branch and terminate in close succession, as found in many brain regions. Our models predicted a dipolar far field and a polarity reversal at the center of the terminal zone. We confirmed these predictions using EFPs from the barn owl auditory brainstem where we recorded in nucleus laminaris using a multielectrode array. These results demonstrate that axonal terminal zones can produce EFPs with considerable amplitude and spatial reach.

Impedance Spectrum in Cortical Tissue: Implications for Propagation of LFP Signals on the Microscopic Level

Brain research investigating electrical activity within neural tissue is producing an increasing amount of physiological data including local field potentials (LFPs) obtained via extracellular in vivo and in vitro recordings. In order to correctly interpret such electrophysiological data, it is vital to adequately understand the electrical properties of neural tissue itself. An ongoing controversy in the field of neuroscience is whether such frequency-dependent effects bias LFP recordings and affect the proper interpretation of the signal. On macroscopic scales and with large injected currents, previous studies have found various grades of frequency dependence of cortical tissue, ranging from negligible to strong, within the frequency band typically considered relevant for neuroscience (less than a few thousand hertz). Here, we performed a detailed investigation of the frequency dependence of the conductivity within cortical tissue at microscopic distances using small current amplitudes within the typical (neuro)physiological micrometer and sub-nanoampere range. We investigated the propagation of LFPs, induced by extracellular electrical current injections via patch-pipettes, in acute rat brain slice preparations containing the somatosensory cortex in vitro using multielectrode arrays. Based on our data, we determined the cortical tissue conductivity over a 100-fold increase in signal frequency (5-500 Hz). Our results imply at most very weak frequency-dependent effects within the frequency range of physiological LFPs. Using biophysical modeling, we estimated the impact of different putative impedance spectra. Our results indicate that frequency dependencies of the order measured here and in most other studies have negligible impact on the typical analysis and modeling of LFP signals from extracellular brain recordings.

Assessing human brain impedance using simultaneous surface and intracerebral recordings

Most of the literature on the brain impedance proposes a frequency-independent resistive model. Recently, this conclusion was tackled by a series of papers (Bédard et al., 2006; Bédard and Destexhe, 2009; Gomes et al., 2016), based on microscopic sale modeling and measurements. Our paper aims to investigate the impedance issue using simultaneous in vivo depth and surface signals recorded during intracerebral electrical stimulation of epileptic patients, involving a priori different tissues with different impedances. Our results confirm the conclusions from Logothethis et al. (2007): there is no evidence of frequency dependence of the brain tissue impedance (more precisely, there is no difference, in terms of frequency filtering, between the brain and the skull bone), at least at a macroscopic scale. In order to conciliate findings from both microscopic and macroscopic scales, we recall different neural/synaptic current generators' models from the literature and we propose an original computational model, based on fractional dynamics.

Local Field Potentials: Myths and Misunderstandings

The intracerebral local field potential (LFP) is a measure of brain activity that reflects the highly dynamic flow of information across neural networks. This is a composite signal that receives contributions from multiple neural sources, yet interpreting its nature and significance may be hindered by several confounding factors and technical limitations. By and large, the main factor defining the amplitude of LFPs is the geometry of the current sources, over and above the degree of synchronization or the properties of the media. As such, similar levels of activity may result in potentials that differ in several orders of magnitude in different populations. The geometry of these sources has been experimentally inaccessible until intracerebral high density recordings enabled the co-activating sources to be revealed. Without this information, it has proven difficult to interpret a century's worth of recordings that used temporal cues alone, such as event or spike related potentials and frequency bands. Meanwhile, a collection of biophysically ill-founded concepts have been considered legitimate, which can now be corrected in the light of recent advances. The relationship of LFPs to their sources is often counterintuitive. For instance, most LFP activity is not local but remote, it may be larger further from rather than close to the source, the polarity does not define its excitatory or inhibitory nature, and the amplitude may increase when source's activity is reduced. As technological developments foster the use of LFPs, the time is now ripe to raise awareness of the need to take into account spatial aspects of these signals and of the errors derived from neglecting to do so.

Effect of Ionic Diffusion on Extracellular Potentials in Neural Tissue

Recorded potentials in the extracellular space (ECS) of the brain is a standard measure of population activity in neural tissue. Computational models that simulate the relationship between the ECS potential and its underlying neurophysiological processes are commonly used in the interpretation of such measurements. Standard methods, such as volume-conductor theory and current-source density theory, assume that diffusion has a negligible effect on the ECS potential, at least in the range of frequencies picked up by most recording systems. This assumption remains to be verified. We here present a hybrid simulation framework that accounts for diffusive effects on the ECS potential. The framework uses (1) the NEURON simulator to compute the activity and ionic output currents from multicompartmental neuron models, and (2) the electrodiffusive Kirchhoff-Nernst-Planck framework to simulate the resulting dynamics of the potential and ion concentrations in the ECS, accounting for the effect of electrical migration as well as diffusion. Using this framework, we explore the effect that ECS diffusion has on the electrical potential surrounding a small population of 10 pyramidal neurons. The neural model was tuned so that simulations over ∼100 seconds of biological time led to shifts in ECS concentrations by a few millimolars, similar to what has been seen in experiments. By comparing simulations where ECS diffusion was absent with simulations where ECS diffusion was included, we made the following key findings: (i) ECS diffusion shifted the local potential by up to ∼0.2 mV. (ii) The power spectral density (PSD) of the diffusion-evoked potential shifts followed a 1/f2 power law. (iii) Diffusion effects dominated the PSD of the ECS potential for frequencies up to several hertz. In scenarios with large, but physiologically realistic ECS concentration gradients, diffusion was thus found to affect the ECS potential well within the frequency range picked up in experimental recordings.

Hybrid Scheme for Modeling Local Field Potentials from Point-Neuron Networks

With rapidly advancing multi-electrode recording technology, the local field potential (LFP) has again become a popular measure of neuronal activity in both research and clinical applications. Proper understanding of the LFP requires detailed mathematical modeling incorporating the anatomical and electrophysiological features of neurons near the recording electrode, as well as synaptic inputs from the entire network. Here we propose a hybrid modeling scheme combining efficient point-neuron network models with biophysical principles underlying LFP generation by real neurons. The LFP predictions rely on populations of network-equivalent multicompartment neuron models with layer-specific synaptic connectivity, can be used with an arbitrary number of point-neuron network populations, and allows for a full separation of simulated network dynamics and LFPs. We apply the scheme to a full-scale cortical network model for a ∼1 mm² patch of primary visual cortex, predict laminar LFPs for different network states, assess the relative LFP contribution from different laminar populations, and investigate effects of input correlations and neuron density on the LFP. The generic nature of the hybrid scheme and its public implementation in hybridLFPy form the basis for LFP predictions from other and larger point-neuron network models, as well as extensions of the current application with additional biological detail.

Intracellular Impedance Measurements Reveal Non-ohmic Properties of the Extracellular Medium around Neurons

Determining the electrical properties of the extracellular space around neurons is important for understanding the genesis of extracellular potentials, as well as for localizing neuronal activity from extracellular recordings. However, the exact nature of these extracellular properties is still uncertain. Here, we introduce a method to measure the impedance of the tissue, one that preserves the intact cell-medium interface using whole-cell patch-clamp recordings in vivo and in vitro. We find that neural tissue has marked non-ohmic and frequency-filtering properties, which are not consistent with a resistive (ohmic) medium, as often assumed. The amplitude and phase profiles of the measured impedance are consistent with the contribution of ionic diffusion. We also show that the impact of such frequency-filtering properties is possibly important on the genesis of local field potentials, as well as on the cable properties of neurons. These results show non-ohmic properties of the extracellular medium around neurons, and suggest that source estimation methods, as well as the cable properties of neurons, which all assume ohmic extracellular medium, may need to be reevaluated.

The neurogenesis of P1 and N1: A concurrent EEG/LFP study

It is generally recognised that event related potentials (ERPs) of electroencephalogram (EEG) primarily reflect summed post-synaptic activity of the local pyramidal neural population(s). However, it is still not understood how the positive and negative deflections (e.g. P1, N1 etc) observed in ERP recordings are related to the underlying excitatory and inhibitory post-synaptic activity. We investigated the neurogenesis of P1 and N1 in ERPs by pharmacologically manipulating inhibitory post-synaptic activity in the somatosensory cortex of rodent, and concurrently recording EEG and local field potentials (LFPs). We found that the P1 wave in the ERP and LFP of the supragranular layers is determined solely by the excitatory post-synaptic activity of the local pyramidal neural population, as is the initial segment of the N1 wave across cortical depth. The later part of the N1 wave was modulated by inhibitory post-synaptic activity, with its peak and the pulse width increasing as inhibition was reduced. These findings suggest that the temporal delay of inhibition with respect to excitation observed in intracellular recordings is also reflected in extracellular field potentials (FPs), resulting in a temporal window during which only excitatory post-synaptic activity and leak channel activity are recorded in the ERP and evoked LFP time series. Based on these findings, we provide clarification on the interpretation of P1 and N1 in terms of the excitatory and inhibitory post-synaptic activities of the local pyramidal neural population(s).

Spatial spread of local field potential is band-pass in the primary visual cortex

Local field potential (LFP) is a valuable tool in understanding brain function and in brain machine-interfacing applications. However, there is no consensus on the spatial extent of the cortex that contributes to the LFP (its "spatial spread"), with different studies reporting values between a few hundred micrometers and several millimeters. Furthermore, the dependency of the spatial spread on frequency, which could reflect properties of the network architecture and extracellular medium, is not well studied, with theory and models predicting either "all-pass" (frequency-independent) or "low-pass" behavior. Surprisingly, we found the LFP spread to be "band-pass" in the primate primary visual cortex, with the greatest spread in the high-gamma range (60-150 Hz). This was accompanied by an increase in phase coherency across neighboring sites in the same frequency range, consistent with the findings of a recent model that reconciles previous studies by suggesting that spatial spread depends on neuronal correlations.

Estimation and modeling of EEG amplitude-temporal characteristics using a marked point process approach

We propose a novel interpretation of single channel Electroencephalogram (EEG) traces based on the transient nature of encoded processes in the brain. In particular, the proposed framework models EEG as the output of the noisy addition of temporal, reoccurring, transient patterns known as phasic events. This is not only neurophysiologically sound, but it also provides additional information that classical EEG analysis often disregards. Furthermore, by utilizing sparse decomposition techniques, it is possible to obtain amplitude and timing that is further modeled using estimation and fitting techniques. We model Brain-Computer Interfaces (BCI) competition data features as Gaussian Mixture Model (GMM) samples in order to show the potential of working in the joint space of the parameters. The results not only preserve the topographic discriminant behavior but also expand the realm of possible EEG analysis.

Active subthreshold dendritic conductances shape the local field potential

Key points

The local field potential (LFP), the low‐frequency part of extracellular potentials recorded in neural tissue, is often used for probing neural circuit activity. Interpreting the LFP signal is difficult, however.

While the cortical LFP is thought mainly to reflect synaptic inputs onto pyramidal neurons, little is known about the role of the various subthreshold active conductances in shaping the LFP.

By means of biophysical modelling we obtain a comprehensive qualitative understanding of how the LFP generated by a single pyramidal neuron depends on the type and spatial distribution of active subthreshold currents.

For pyramidal neurons, the h‐type channels probably play a key role and can cause a distinct resonance in the LFP power spectrum.

Our results show that the LFP signal can give information about the active properties of neurons and imply that preferred frequencies in the LFP can result from those cellular properties instead of, for example, network dynamics.

Abstract

The main contribution to the local field potential (LFP) is thought to stem from synaptic input to neurons and the ensuing subthreshold dendritic processing. The role of active dendritic conductances in shaping the LFP has received little attention, even though such ion channels are known to affect the subthreshold neuron dynamics. Here we used a modelling approach to investigate the effects of subthreshold dendritic conductances on the LFP. Using a biophysically detailed, experimentally constrained model of a cortical pyramidal neuron, we identified conditions under which subthreshold active conductances are a major factor in shaping the LFP. We found that, in particular, the hyperpolarization‐activated inward current, I_h, can have a sizable effect and cause a resonance in the LFP power spectral density. To get a general, qualitative understanding of how any subthreshold active dendritic conductance and its cellular distribution can affect the LFP, we next performed a systematic study with a simplified model. We found that the effect on the LFP is most pronounced when (1) the synaptic drive to the cell is asymmetrically distributed (i.e. either basal or apical), (2) the active conductances are distributed non‐uniformly with the highest channel densities near the synaptic input and (3) when the LFP is measured at the opposite pole of the cell relative to the synaptic input. In summary, we show that subthreshold active conductances can be strongly reflected in LFP signals, opening up the possibility that the LFP can be used to characterize the properties and cellular distributions of active conductances.

The local field potential (LFP), the low‐frequency part of extracellular potentials recorded in neural tissue, is often used for probing neural circuit activity. Interpreting the LFP signal is difficult, however.

While the cortical LFP is thought mainly to reflect synaptic inputs onto pyramidal neurons, little is known about the role of the various subthreshold active conductances in shaping the LFP.

By means of biophysical modelling we obtain a comprehensive qualitative understanding of how the LFP generated by a single pyramidal neuron depends on the type and spatial distribution of active subthreshold currents.

For pyramidal neurons, the h‐type channels probably play a key role and can cause a distinct resonance in the LFP power spectrum.

Our results show that the LFP signal can give information about the active properties of neurons and imply that preferred frequencies in the LFP can result from those cellular properties instead of, for example, network dynamics.

Effect of Reference Scheme on Power and Phase of the Local Field Potential

Brain signals are often analyzed in the spectral domain, where the power spectral density (PSD) and phase differences and consistency can reveal important information about the network. However, for proper interpretation, it is important to know whether these measures depend on stimulus/behavioral conditions or the reference scheme used to analyze data. We recorded local field potential (LFP) from an array of microelectrodes chronically implanted in area V1 of monkeys under different stimulus/behavioral conditions and computed PSD slopes, coherence, and phase difference between LFPs as a function of frequency and interelectrode distance while using four reference schemes: single wire, average, bipolar, and current source density. PSD slopes were dependent on reference scheme at low frequencies (below 200 Hz) but became invariant at higher frequencies. Average phase differences between sites also depended critically on referencing, switching from 0 degrees for single-wire to 180 degrees for average reference. Results were consistent across different stimulus/behavioral conditions. We were able to account for these results based on the coherence profile across sites and properties of the spectral estimator. Our results show that using different reference schemes can have drastic effects on phase differences and PSD slopes and therefore must be interpreted carefully to gain insights about network properties.

Generalized Laminar Population Analysis (gLPA) for Interpretation of Multielectrode Data from Cortex

Laminar population analysis (LPA) is a method for analysis of electrical data recorded by linear multielectrodes passing through all lamina of cortex. Like principal components analysis (PCA) and independent components analysis (ICA), LPA offers a way to decompose the data into contributions from separate cortical populations. However, instead of using purely mathematical assumptions in the decomposition, LPA is based on physiological constraints, i.e., that the observed LFP (low-frequency part of signal) is driven by action-potential firing as observed in the MUA (multi-unit activity; high-frequency part of the signal). In the presently developed generalized laminar population analysis (gLPA) the set of basis functions accounting for the LFP data is extended compared to the original LPA, thus allowing for a better fit of the model to experimental data. This enhances the risk for overfitting, however, and we therefore tested various versions of gLPA on virtual LFP data in which we knew the ground truth. These synthetic data were generated by biophysical forward-modeling of electrical signals from network activity in the comprehensive, and well-known, thalamocortical network model developed by Traub and coworkers. The results for the Traub model imply that while the laminar components extracted by the original LPA method overall are in fair agreement with the ground-truth laminar components, the results may be improved by use of gLPA method with two (gLPA-2) or even three (gLPA-3) postsynaptic LFP kernels per laminar population.

Functional Effects of Schizophrenia-Linked Genetic Variants on Intrinsic Single-Neuron Excitability: A Modeling Study

BACKGROUND

Recent genome-wide association studies have identified a large number of genetic risk factors for schizophrenia (SCZ) featuring ion channels and calcium transporters. For some of these risk factors, independent prior investigations have examined the effects of genetic alterations on the cellular electrical excitability and calcium homeostasis. In the present proof-of-concept study, we harnessed these experimental results for modeling of computational properties on layer V cortical pyramidal cells and identified possible common alterations in behavior across SCZ-related genes.

METHODS

We applied a biophysically detailed multicompartmental model to study the excitability of a layer V pyramidal cell. We reviewed the literature on functional genomics for variants of genes associated with SCZ and used changes in neuron model parameters to represent the effects of these variants.

RESULTS

We present and apply a framework for examining the effects of subtle single nucleotide polymorphisms in ion channel and calcium transporter-encoding genes on neuron excitability. Our analysis indicates that most of the considered SCZ-related genetic variants affect the spiking behavior and intracellular calcium dynamics resulting from summation of inputs across the dendritic tree.

CONCLUSIONS

Our results suggest that alteration in the ability of a single neuron to integrate the inputs and scale its excitability may constitute a fundamental mechanistic contributor to mental disease, alongside the previously proposed deficits in synaptic communication and network behavior.

Computing the Local Field Potential (LFP) from Integrate-and-Fire Network Models

Leaky integrate-and-fire (LIF) network models are commonly used to study how the spiking dynamics of neural networks changes with stimuli, tasks or dynamic network states. However, neurophysiological studies in vivo often rather measure the mass activity of neuronal microcircuits with the local field potential (LFP). Given that LFPs are generated by spatially separated currents across the neuronal membrane, they cannot be computed directly from quantities defined in models of point-like LIF neurons. Here, we explore the best approximation for predicting the LFP based on standard output from point-neuron LIF networks. To search for this best "LFP proxy", we compared LFP predictions from candidate proxies based on LIF network output (e.g, firing rates, membrane potentials, synaptic currents) with "ground-truth" LFP obtained when the LIF network synaptic input currents were injected into an analogous three-dimensional (3D) network model of multi-compartmental neurons with realistic morphology, spatial distributions of somata and synapses. We found that a specific fixed linear combination of the LIF synaptic currents provided an accurate LFP proxy, accounting for most of the variance of the LFP time course observed in the 3D network for all recording locations. This proxy performed well over a broad set of conditions, including substantial variations of the neuronal morphologies. Our results provide a simple formula for estimating the time course of the LFP from LIF network simulations in cases where a single pyramidal population dominates the LFP generation, and thereby facilitate quantitative comparison between computational models and experimental LFP recordings in vivo.