Pitfalls in the dipolar model for the neocortical EEG sources

Cortical dynamics of neural-connectivity fields

Macroscopic studies of cortical tissue reveal a prevalence of oscillatory activity, that reflect a fine tuning of neural interactions. This research extends neural field theories by incorporating generalized oscillatory dynamics into previous work on conservative or semi-conservative neural field dynamics. Prior studies have largely assumed isotropic connections among neural units; however, this study demonstrates that a broad range of anisotropic and fluctuating connections can still sustain oscillations. Using Lagrangian field methods, we examine different types of connectivity, their dynamics, and potential interactions with neural fields. From this theoretical foundation, we derive a framework that incorporates Hebbian and non-Hebbian learning - i.e., plasticity - into the study of neural fields via the concept of a connectivity field.

Brains are Probabilistic, Electrophysiologically Intricate and Triune: A Biased- Random Walk Perspective on Computational Neuroscience

The pursuit of a unified theory that captures the intricacies of the brain and mind continues to be a significant challenge in theoretical neuroscience. This paper presents a novel, triune framework that utilizes the concept of collective biased random walk (cBRW). Our approach strives to transcend biological specifics, offering a high-level abstraction that remains general and applicable across various neural phenomena. Despite the solid traditional foundation of computational neuroscience, the intricate delicacy of neural processes calls for a renewed probabilistic approach. We aim to utilize the intuitive nature of probability concepts -such as the probability of localization and state, and uniform probability distribution- to study the stochastic organization of electric charges and signals in the brain. This electrophysiological intricacy emerges from the seemingly paradoxical reality that tiny electric events, while random, collectively give rise to predictable, long-range oscillations. These oscillations manifest in three groups of activation states. Our framework categorizes the brain as a triune system, accommodating classical, semiclassical, and non-classical interpretations of both probabilistic phenomena and cBRW models, alongside three groups of states. We conclude that by appreciating, rather than overlooking, the tiny random walks of electric charges and signals in the brain, we can gain a triune mathematical foundation for theoretical brain science, the powerful capabilities of this organ, and the electromagnetic interfaces we can develop.

kCSD-python, reliable current source density estimation with quality control

Interpretation of extracellular recordings can be challenging due to the long range of electric field. This challenge can be mitigated by estimating the current source density (CSD). Here we introduce kCSD-python, an open Python package implementing Kernel Current Source Density (kCSD) method and related tools to facilitate CSD analysis of experimental data and the interpretation of results. We show how to counter the limitations imposed by noise and assumptions in the method itself. kCSD-python allows CSD estimation for an arbitrary distribution of electrodes in 1D, 2D, and 3D, assuming distributions of sources in tissue, a slice, or in a single cell, and includes a range of diagnostic aids. We demonstrate its features in a Jupyter Notebook tutorial which illustrates a typical analytical workflow and main functionalities useful in validating analysis results.

How to assess the accuracy of volume conduction models? A validation study with stereotactic EEG data

Introduction

Volume conduction models of the human head are used in various neuroscience fields, such as for source reconstruction in EEG and MEG, and for modeling the effects of brain stimulation. Numerous studies have quantified the accuracy and sensitivity of volume conduction models by analyzing the effects of the geometrical and electrical features of the head model, the sensor model, the source model, and the numerical method. Most studies are based on simulations as it is hard to obtain sufficiently detailed measurements to compare to models. The recording of stereotactic EEG during electric stimulation mapping provides an opportunity for such empirical validation.

Methods

In the study presented here, we used the potential distribution of volume-conducted artifacts that are due to cortical stimulation to evaluate the accuracy of finite element method (FEM) volume conduction models. We adopted a widely used strategy for numerical comparison, i.e., we fixed the geometrical description of the head model and the mathematical method to perform simulations, and we gradually altered the head models, by increasing the level of detail of the conductivity profile. We compared the simulated potentials at different levels of refinement with the measured potentials in three epilepsy patients.

Results

Our results show that increasing the level of detail of the volume conduction head model only marginally improves the accuracy of the simulated potentials when compared to in-vivo sEEG measurements. The mismatch between measured and simulated potentials is, throughout all patients and models, maximally 40 microvolts (i.e., 10% relative error) in 80% of the stimulation-recording combination pairs and it is modulated by the distance between recording and stimulating electrodes.

Discussion

Our study suggests that commonly used strategies used to validate volume conduction models based solely on simulations might give an overly optimistic idea about volume conduction model accuracy. We recommend more empirical validations to be performed to identify those factors in volume conduction models that have the highest impact on the accuracy of simulated potentials. We share the dataset to allow researchers to further investigate the mismatch between measurements and FEM models and to contribute to improving volume conduction models.

Exploring Convolutional Neural Network Architectures for EEG Feature Extraction

The main purpose of this paper is to provide information on how to create a convolutional neural network (CNN) for extracting features from EEG signals. Our task was to understand the primary aspects of creating and fine-tuning CNNs for various application scenarios. We considered the characteristics of EEG signals, coupled with an exploration of various signal processing and data preparation techniques. These techniques include noise reduction, filtering, encoding, decoding, and dimension reduction, among others. In addition, we conduct an in-depth analysis of well-known CNN architectures, categorizing them into four distinct groups: standard implementation, recurrent convolutional, decoder architecture, and combined architecture. This paper further offers a comprehensive evaluation of these architectures, covering accuracy metrics, hyperparameters, and an appendix that contains a table outlining the parameters of commonly used CNN architectures for feature extraction from EEG signals.

Cortical origin of theta error signals

A multi-scale approach elucidated the origin of the error-related-negativity (ERN), with its associated theta-rhythm, and the post-error-positivity (Pe) in macaque supplementary eye field (SEF). Using biophysical modeling, synaptic inputs to a subpopulation of layer-3 (L3) and layer-5 (L5) pyramidal cells (PCs) were optimized to reproduce error-related spiking modulation and inter-spike intervals. The intrinsic dynamics of dendrites in L5 but not L3 error PCs generate theta rhythmicity with random phases. Saccades synchronized the phases of the theta-rhythm, which was magnified on errors. Contributions from error PCs to the laminar current source density (CSD) observed in SEF were negligible and could not explain the observed association between error-related spiking modulation in L3 PCs and scalp-EEG. CSD from recorded laminar field potentials in SEF was comprised of multipolar components, with monopoles indicating strong electro-diffusion, dendritic/axonal electrotonic current leakage outside SEF, or violations of the model assumptions. Our results also demonstrate the involvement of secondary cortical regions, in addition to SEF, particularly for the later Pe component. The dipolar component from the observed CSD paralleled the ERN dynamics, while the quadrupolar component paralleled the Pe. These results provide the most advanced explanation to date of the cellular mechanisms generating the ERN.

Spike-phase coupling patterns reveal laminar identity in primate cortex

The cortical column is one of the fundamental computational circuits in the brain. In order to understand the role neurons in different layers of this circuit play in cortical function it is necessary to identify the boundaries that separate the laminar compartments. While histological approaches can reveal ground truth they are not a practical means of identifying cortical layers in vivo. The gold standard for identifying laminar compartments in electrophysiological recordings is current-source density (CSD) analysis. However, laminar CSD analysis requires averaging across reliably evoked responses that target the input layer in cortex, which may be difficult to generate in less well-studied cortical regions. Further, the analysis can be susceptible to noise on individual channels resulting in errors in assigning laminar boundaries. Here, we have analyzed linear array recordings in multiple cortical areas in both the common marmoset and the rhesus macaque. We describe a pattern of laminar spike-field phase relationships that reliably identifies the transition between input and deep layers in cortical recordings from multiple cortical areas in two different non-human primate species. This measure corresponds well to estimates of the location of the input layer using CSDs, but does not require averaging or specific evoked activity. Laminar identity can be estimated rapidly with as little as a minute of ongoing data and is invariant to many experimental parameters. This method may serve to validate CSD measurements that might otherwise be unreliable or to estimate laminar boundaries when other methods are not practical.

Sampling effects and measurement overlap can bias the inference of neuronal avalanches

To date, it is still impossible to sample the entire mammalian brain with single-neuron precision. This forces one to either use spikes (focusing on few neurons) or to use coarse-sampled activity (averaging over many neurons, e.g. LFP). Naturally, the sampling technique impacts inference about collective properties. Here, we emulate both sampling techniques on a simple spiking model to quantify how they alter observed correlations and signatures of criticality. We describe a general effect: when the inter-electrode distance is small, electrodes sample overlapping regions in space, which increases the correlation between the signals. For coarse-sampled activity, this can produce power-law distributions even for non-critical systems. In contrast, spike recordings do not suffer this particular bias and underlying dynamics can be identified. This may resolve why coarse measures and spikes have produced contradicting results in the past.

Resolving the mesoscopic missing link: Biophysical modeling of EEG from cortical columns in primates

Event-related potentials (ERP) are among the most widely measured indices for studying human cognition. While their timing and magnitude provide valuable insights, their usefulness is limited by our understanding of their neural generators at the circuit level. Inverse source localization offers insights into such generators, but their solutions are not unique. To address this problem, scientists have assumed the source space generating such signals comprises a set of discrete equivalent current dipoles, representing the activity of small cortical regions. Based on this notion, theoretical studies have employed forward modeling of scalp potentials to understand how changes in circuit-level dynamics translate into macroscopic ERPs. However, experimental validation is lacking because it requires in vivo measurements of intracranial brain sources. Laminar local field potentials (LFP) offer a mechanism for estimating intracranial current sources. Yet, a theoretical link between LFPs and intracranial brain sources is missing. Here, we present a forward modeling approach for estimating mesoscopic intracranial brain sources from LFPs and predict their contribution to macroscopic ERPs. We evaluate the accuracy of this LFP-based representation of brain sources utilizing synthetic laminar neurophysiological measurements and then demonstrate the power of the approach in vivo to clarify the source of a representative cognitive ERP component. To that end, LFP was measured across the cortical layers of visual area V4 in macaque monkeys performing an attention demanding task. We show that area V4 generates dipoles through layer-specific transsynaptic currents that biophysically recapitulate the ERP component through the detailed forward modeling. The constraints imposed on EEG production by this method also revealed an important dissociation between computational and biophysical contributors. As such, this approach represents an important bridge between laminar microcircuitry, through the mesoscopic activity of cortical columns to the patterns of EEG we measure at the scalp.

A visual encoding model links magnetoencephalography signals to neural synchrony in human cortex

Synchronization of neuronal responses over large distances is hypothesized to be important for many cortical functions. However, no straightforward methods exist to estimate synchrony non-invasively in the living human brain. MEG and EEG measure the whole brain, but the sensors pool over large, overlapping cortical regions, obscuring the underlying neural synchrony. Here, we developed a model from stimulus to cortex to MEG sensors to disentangle neural synchrony from spatial pooling of the instrument. We find that synchrony across cortex has a surprisingly large and systematic effect on predicted MEG spatial topography. We then conducted visual MEG experiments and separated responses into stimulus-locked and broadband components. The stimulus-locked topography was similar to model predictions assuming synchronous neural sources, whereas the broadband topography was similar to model predictions assuming asynchronous sources. We infer that visual stimulation elicits two distinct types of neural responses, one highly synchronous and one largely asynchronous across cortex.

Monkey V1 epidural field potentials provide detailed information about stimulus location, size, shape, and color

Brain signal recordings with epidural microarrays constitute a low-invasive approach for recording distributed neuronal signals. Epidural field potentials (EFPs) may serve as a safe and highly beneficial signal source for a variety of research questions arising from both basic and applied neuroscience. A wider use of these signals, however, is constrained by a lack of data on their specific information content. Here, we make use of the high spatial resolution and the columnar organization of macaque primary visual cortex (V1) to investigate whether and to what extent EFP signals preserve information about various visual stimulus features. Two monkeys were presented with different feature combinations of location, size, shape, and color, yielding a total of 375 stimulus conditions. Visual features were chosen to access different spatial levels of functional organization. We found that, besides being highly specific for locational information, EFPs were significantly modulated by small differences in size, shape, and color, allowing for high stimulus classification rates even at the single-trial level. The results support the notion that EFPs constitute a low-invasive, highly beneficial signal source for longer-term recordings for medical and basic research by showing that they convey detailed and reliable information about constituent features of activating stimuli.

A model integrating multiple processes of synchronization and coherence for information instantiation within a cortical area

What is the form of dynamic, e.g., sensory, information in the mammalian cortex? Information in the cortex is modeled as a coherence map of a mixed chimera state of synchronous, phasic, and disordered minicolumns. The theoretical model is built on neurophysiological evidence. Complex spatiotemporal information is instantiated through a system of interacting biological processes that generate a synchronized cortical area, a coherent aperture. Minicolumn elements are grouped in macrocolumns in an array analogous to a phased-array radar, modeled as an aperture, a "hole through which radiant energy flows." Coherence maps in a cortical area transform inputs from multiple sources into outputs to multiple targets, while reducing complexity and entropy. Coherent apertures can assume extremely large numbers of different information states as coherence maps, which can be communicated among apertures with corresponding very large bandwidths. The coherent aperture model incorporates considerable reported research, integrating five conceptually and mathematically independent processes: 1) a damped Kuramoto network model, 2) a pumped area field potential, 3) the gating of nearly coincident spikes, 4) the coherence of activity across cortical lamina, and 5) complex information formed through functions in macrocolumns. Biological processes and their interactions are described in equations and a functional circuit such that the mathematical pieces can be assembled the same way the neurophysiological ones are. The model can be conceptually convolved over the specifics of local cortical areas within and across species. A coherent aperture becomes a node in a graph of cortical areas with a corresponding distribution of information.

Electrical Source Imaging in Freely Moving Rats: Evaluation of a 12-Electrode Cortical Electroencephalography System

This work presents and evaluates a 12-electrode intracranial electroencephalography system developed at the National Institute of Mental Health (Klecany, Czech Republic) in terms of an electrical source imaging (ESI) technique in rats. The electrode system was originally designed for translational research purposes. This study demonstrates that it is also possible to use this well-established system for ESI, and estimates its precision, accuracy, and limitations. Furthermore, this paper sets a methodological basis for future implants. Source localization quality is evaluated using three approaches based on surrogate data, physical phantom measurements, and in vivo experiments. The forward model for source localization is obtained from the FieldTrip-SimBio pipeline using the finite-element method. Rat brain tissue extracted from a magnetic resonance imaging template is approximated by a single-compartment homogeneous tetrahedral head model. Four inverse solvers were tested: standardized low-resolution brain electromagnetic tomography, exact low-resolution brain electromagnetic tomography (eLORETA), linear constrained minimum variance (LCMV), and dynamic imaging of coherent sources. Based on surrogate data, this paper evaluates the accuracy and precision of all solvers within the brain volume using error distance and reliability maps. The mean error distance over the whole brain was found to be the lowest in the eLORETA solution through signal to noise ratios (SNRs) (0.2 mm for 25 dB SNR). The LCMV outperformed eLORETA under higher SNR conditions, and exhibiting higher spatial precision. Both of these inverse solvers provided accurate results in a phantom experiment (1.6 mm mean error distance across shallow and 2.6 mm across subcortical testing dipoles). Utilizing the developed technique in freely moving rats, an auditory steady-state response experiment provided results in line with previously reported findings. The obtained results support the idea of utilizing a 12-electrode system for ESI and using it as a solid basis for the development of future ESI dedicated implants.

A Minimal Biophysical Model of Neocortical Pyramidal Cells: Implications for Frontal Cortex Microcircuitry and Field Potential Generation

Ca²⁺ spikes initiated in the distal trunk of layer 5 pyramidal cells (PCs) underlie nonlinear dynamic changes in the gain of cellular response, critical for top-down control of cortical processing. Detailed models with many compartments and dozens of ionic channels can account for this Ca²⁺ spike-dependent gain and associated critical frequency. However, current models do not account for all known Ca²⁺-dependent features. Previous attempts to include more features have required increasing complexity, limiting their interpretability and utility for studying large population dynamics. We overcome these limitations in a minimal two-compartment biophysical model. In our model, a basal-dendrites/somatic compartment included fast-inactivating Na⁺ and delayed-rectifier K⁺ conductances, while an apical-dendrites/trunk compartment included persistent Na⁺, hyperpolarization-activated cation (I _h ), slow-inactivating K⁺, muscarinic K⁺, and Ca²⁺ L-type. The model replicated the Ca²⁺ spike morphology and its critical frequency plus three other defining features of layer 5 PC synaptic integration: linear frequency-current relationships, back-propagation-activated Ca²⁺ spike firing, and a shift in the critical frequency by blocking I _h Simulating 1000 synchronized layer 5 PCs, we reproduced the current source density patterns evoked by Ca²⁺ spikes and describe resulting medial-frontal EEG on a male macaque monkey. We reproduced changes in the current source density when I _h was blocked. Thus, a two-compartment model with five crucial ionic currents in the apical dendrites reproduces all features of these neurons. We discuss the utility of this minimal model to study the microcircuitry of agranular areas of the frontal lobe involved in cognitive control and responsible for event-related potentials, such as the error-related negativity.SIGNIFICANCE STATEMENT A minimal model of layer 5 pyramidal cells replicates all known features crucial for distal synaptic integration in these neurons. By redistributing voltage-gated and returning transmembrane currents in the model, we establish a theoretical framework for the investigation of cortical microcircuit contribution to intracranial local field potentials and EEG. This tractable model will enable biophysical evaluation of multiscale electrophysiological signatures and computational investigation of cortical processing.

Direct Activation of Cortical Neurons in the Primary Somatosensory Cortex of the Rat in Vivo Using Focused Ultrasound

We address the recent controversy over whether focused ultrasound (FUS) activates cortical neurons directly or indirectly by initially activating auditory pathways. We obtained two types of evidence that FUS can directly activate cortical neurons. The depth profile of the local field potential (LFP) in the barrel cortex of the rat in vivo indicated a generator was located within the cortical gray matter. The onset and peak latencies of the initial component p1 were 3.2 ± 0.25 ms (mean ± standard error of the mean) and 7.6 ± 0.12 ms, respectively, for the direct cortical response (DCR), 6.8 ± 0.40 and 14.3 ± 0.54 ms for the FUS-evoked LFP (4 MHz, 3.2 MPa, 50 or 300 µs/pulse, 1-20 pulses at 1 kHz) and 6.9 ± 0.51 and 15.8 ± 0.94 ms for the LFP evoked by 1-ms deflection of the C2 whisker projecting to the same area. The peak latency of the FUS p1 was statistically (t-test) longer than the DCR, but shorter than the whisker p1 at p < 0.005.

Impact of Brain Surface Boundary Conditions on Electrophysiology and Implications for Electrocorticography

Volume conduction of electrical potentials in the brain is highly influenced by the material properties and geometry of the tissue and recording devices implanted into the tissue. These effects are very large in EEG due to the volume conduction through the skull and scalp but are often neglected in intracranial electrophysiology. When considering penetrating electrodes deep in the brain, the assumption of an infinite and homogenous medium can be used when the sources are far enough from the brain surface and the electrodes to minimize the boundary effect. When the electrodes are recording from the brain's surface the effect of the boundary cannot be neglected, and the large surface area and commonly used insulating materials in surface electrode arrays may further increase the effect by altering the nature of the boundary in the immediate vicinity of the electrodes. This gives the experimenter some control over the spatial profiles of the potentials by appropriate design of the electrode arrays. We construct a simple three-layer model to describe the effect of material properties and geometry above the brain surface on the electric potentials and conduct empirical experiments to validate this model. A laminar electrode array is used to measure the effect of insulating and relatively conducting layers above the cortical surface by recording evoked potentials alternating between a dried surface and saline covering layer, respectively. Empirically, we find that an insulating boundary amplifies the potentials relative to conductive saline by about a factor of 4, and that the effect is not constrained to potentials that originate near the surface. The model is applied to predict the influence of array design and implantation procedure on the recording amplitude and spatial selectivity of the surface electrode arrays.

The multipole approach for EEG forward modeling using the finite element method

For accurate EEG forward solutions, it is necessary to apply numerical methods that allow to take into account the realistic geometry of the subject's head. A commonly used method to solve this task is the finite element method (FEM). Different approaches have been developed to obtain EEG forward solutions for dipolar sources with the FEM. The St. Venant approach is frequently applied, since its high numerical accuracy and stability as well as its computational efficiency was demonstrated in multiple comparison studies. In this manuscript, we propose a variation of the St. Venant approach, the multipole approach, to improve the numerical accuracy of the St. Venant approach even further and to allow for the simulation of additional source scenarios, such as quadrupolar sources. Exploiting the multipole expansion of electric fields, we demonstrate that the newly proposed multipole approach achieves even higher numerical accuracies than the St. Venant approach in both multi-layer sphere and realistic head models. Additionally, we exemplarily show that the multipole approach allows to not only simulate dipolar but also quadrupolar sources.

Validating Non-invasive EEG Source Imaging Using Optimal Electrode Configurations on a Representative Rat Head Model

The curtain of technical limitations impeding rat multichannel non-invasive electroencephalography (EEG) has risen. Given the importance of this preclinical model, development and validation of EEG source imaging (ESI) is essential. We investigate the validity of well-known human ESI methodologies in rats which individual tissue geometries have been approximated by those extracted from an MRI template, leading also to imprecision in electrode localizations. With the half and fifth sensitivity volumes we determine both the theoretical minimum electrode separation for non-redundant scalp EEG measurements and the electrode sensitivity resolution, which vary over the scalp because of the head geometry. According to our results, electrodes should be at least ~3 to 3.5 mm apart for an optimal configuration. The sensitivity resolution is generally worse for electrodes at the boundaries of the scalp measured region, though, by analogy with human montages, concentrates the sensitivity enough to localize sources. Cramér-Rao lower bounds of source localization errors indicate it is theoretically possible to achieve ESI accuracy at the level of anatomical structures, such as the stimulus-specific somatosensory areas, using the template. More validation for this approximation is provided through the comparison between the template and the individual lead field matrices, for several rats. Finally, using well-accepted inverse methods, we demonstrate that somatosensory ESI is not only expected but also allows exploring unknown phenomena related to global sensory integration. Inheriting the advantages and pitfalls of human ESI, rat ESI will boost the understanding of brain pathophysiological mechanisms and the evaluation of ESI methodologies, new pharmacological treatments and ESI-based biomarkers.

Simulating human sleep spindle MEG and EEG from ion channel and circuit level dynamics

BACKGROUND

Although they form a unitary phenomenon, the relationship between extracranial M/EEG and transmembrane ion flows is understood only as a general principle rather than as a well-articulated and quantified causal chain.

METHOD

We present an integrated multiscale model, consisting of a neural simulation of thalamus and cortex during stage N2 sleep and a biophysical model projecting cortical current densities to M/EEG fields. Sleep spindles were generated through the interactions of local and distant network connections and intrinsic currents within thalamocortical circuits. 32,652 cortical neurons were mapped onto the cortical surface reconstructed from subjects' MRI, interconnected based on geodesic distances, and scaled-up to current dipole densities based on laminar recordings in humans. MRIs were used to generate a quasi-static electromagnetic model enabling simulated cortical activity to be projected to the M/EEG sensors.

RESULTS

The simulated M/EEG spindles were similar in amplitude and topography to empirical examples in the same subjects. Simulated spindles with more core-dominant activity were more MEG weighted.

COMPARISON WITH EXISTING METHODS

Previous models lacked either spindle-generating thalamic neural dynamics or whole head biophysical modeling; the framework presented here is the first to simultaneously capture these disparate scales.

CONCLUSIONS

This multiscale model provides a platform for the principled quantitative integration of existing information relevant to the generation of sleep spindles, and allows the implications of future findings to be explored. It provides a proof of principle for a methodological framework allowing large-scale integrative brain oscillations to be understood in terms of their underlying channels and synapses.

Multi-Scale Neural Sources of EEG: Genuine, Equivalent, and Representative. A Tutorial Review

A biophysical framework needed to interpret electrophysiological data recorded at multiple spatial scales of brain tissue is developed. Micro current sources at membrane surfaces produce local field potentials, electrocorticography, and electroencephalography (EEG). We categorize multi-scale sources as genuine, equivalent, or representative. Genuine sources occur at the micro scale of cell surfaces. Equivalent sources provide identical experimental outcomes over a range of scales and applications. In contrast, each representative source distribution is just one of many possible source distributions that yield similar experimental outcomes. Macro sources ("dipoles") may be defined at the macrocolumn (mm) scale and depend on several features of the micro sources-magnitudes, micro synchrony within columns, and distribution through the cortical depths. These micro source properties are determined by brain dynamics and the columnar structure of cortical tissue. The number of representative sources underlying EEG data depends on the spatial scale of neural tissue under study. EEG inverse solutions (e.g. dipole localization) and high resolution estimates (e.g. Laplacian, dura imaging) have both strengths and limitations that depend on experimental conditions. The proposed theoretical framework informs studies of EEG source localization, source characterization, and low pass filtering. It also facilitates interpretations of brain dynamics and cognition, including measures of synchrony, functional connections between cortical locations, and other aspects of brain complexity.

Cortical microcircuitry of performance monitoring

Medial frontal cortex enables performance monitoring, indexed by the error-related negativity (ERN) and manifest by performance adaptations. In monkeys performing a saccade countermanding (stop signal) task, we recorded EEG over and neural spiking across all layers of the supplementary eye field (SEF), an agranular cortical area. Neurons signaling error production, feedback predicting reward gain or loss, and delivery of fluid reward had different spike widths and were concentrated differently across layers. Neurons signaling error or loss of reward were more common in layers 2 and 3 (L2/3), while neurons signaling gain of reward were more common in layers 5 and 6 (L5/6). Variation of error- and reinforcement-related spike rates in L2/3 but not L5/6 predicted response time adaptation. Variation in error-related spike rate in L2/3 but not L5/6 predicted ERN magnitude. These findings reveal novel features of cortical microcircuitry supporting performance monitoring and confirm one cortical source of the ERN.

A Finite Element Solution of the Forward Problem in EEG for Multipolar Sources

Multipolar source models have been presented in the context of electro/magnetoencephalography (E/MEG) to compensate for the limitations of the classical equivalent current dipole to represent realistic generators of brain activity. Although there exist several reports accounting for the advantages of multipolar components over single dipoles, there is still no available numerical implementation in fully personalized scenarios. In this paper, we present, for the first time, a finite element framework for simulating EEG signals generated by multipolar current sources in individualized, heterogeneous, and anisotropic head models. This formulation is based on the subtraction approach, guaranteeing the existence and uniqueness of the solution. In particular, we analyze the cases of monopolar, dipolar, and quadrupolar source components, for which we study their performance in idealized and realistic head models. Numerical solutions are compared with analytical formulas in multi-layered spherical models. Such formulas are available in the case of monopolar and dipolar sources, and here derived for the quadrupolar components. We finally illustrate their advantages in the description of extended current generators using a realistic head model. The framework presented here enables further analysis towards the estimation of biophysically principled source parameters from standard E/MEG experiments.

waveCSD: A method for estimating transmembrane currents originated from propagating neuronal activity in the neocortex: Application to study cortical spreading depression

BACKGROUND

Recent years have witnessed an upsurge in the development of methods for estimating current source densities (CSDs) in the neocortical tissue from their recorded local field potential (LFP) reflections using microelectrode arrays. Among these, methods utilizing linear arrays work under the assumption that CSDs vary as a function of cortical depth; whereas they are constant in the tangential direction, infinitely or in a confined cylinder. This assumption is violated in the analysis of neuronal activity propagating along the neocortical sheet, e.g. propagation of alpha waves or cortical spreading depression.

NEW METHOD

Here, we developed a novel mathematical method (waveCSD) for CSD analysis of LFPs associated with a planar wave of neocortical neuronal activity propagating at a constant velocity towards a linear probe.

RESULTS

Results show that the algorithm is robust to the presence of noise in LFP data and uncertainties in knowledge of propagation velocity. Also, results show high level of accuracy of the method in a wide range of electrode resolutions. Using in vivo experimental recordings from the rat neocortex, we employed waveCSD to characterize transmembrane currents associated with cortical spreading depressions.

COMPARISON WITH EXISTING METHOD(S)

Simulation results indicate that waveCSD has a significantly higher reconstruction accuracy compared to the widely-used inverse CSD method (iCSD), and the regularized kernel CSD method (kCSD), in the analysis of CSDs originating from propagating neuronal activity.

CONCLUSIONS

The waveCSD method provides a theoretical platform for estimation of transmembrane currents from their LFPs in experimental paradigms involving wave propagation.

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.

Neural Mechanisms of High-Level Vision

The last three decades have seen major strides in our understanding of neural mechanisms of high-level vision, or visual cognition of the world around us. Vision has also served as a model system for the study of brain function. Several broad insights, as yet incomplete, have recently emerged. First, visual perception is best understood not as an end unto itself, but as a sensory process that subserves the animal's behavioral goal at hand. Visual perception is likely to be simply a side effect that reflects the readout of visual information processing that leads to behavior. Second, the brain is essentially a probabilistic computational system that produces behaviors by collectively evaluating, not necessarily consciously or always optimally, the available information about the outside world received from the senses, the behavioral goals, prior knowledge about the world, and possible risks and benefits of a given behavior. Vision plays a prominent role in the overall functioning of the brain providing the lion's share of information about the outside world. Third, the visual system does not function in isolation, but rather interacts actively and reciprocally with other brain systems, including other sensory faculties. Finally, various regions of the visual system process information not in a strict hierarchical manner, but as parts of various dynamic brain-wide networks, collectively referred to as the "connectome." Thus, a full understanding of vision will ultimately entail understanding, in granular, quantitative detail, various aspects of dynamic brain networks that use visual sensory information to produce behavior under real-world conditions. © 2017 American Physiological Society. Compr Physiol 8:903-953, 2018.

Electrophysiological Source Imaging: A Noninvasive Window to Brain Dynamics

Brain activity and connectivity are distributed in the three-dimensional space and evolve in time. It is important to image brain dynamics with high spatial and temporal resolution. Electroencephalography (EEG) and magnetoencephalography (MEG) are noninvasive measurements associated with complex neural activations and interactions that encode brain functions. Electrophysiological source imaging estimates the underlying brain electrical sources from EEG and MEG measurements. It offers increasingly improved spatial resolution and intrinsically high temporal resolution for imaging large-scale brain activity and connectivity on a wide range of timescales. Integration of electrophysiological source imaging and functional magnetic resonance imaging could further enhance spatiotemporal resolution and specificity to an extent that is not attainable with either technique alone. We review methodological developments in electrophysiological source imaging over the past three decades and envision its future advancement into a powerful functional neuroimaging technology for basic and clinical neuroscience applications.

Heterogeneous Origins of Human Sleep Spindles in Different Cortical Layers

Sleep spindles are a cardinal feature in human NREM sleep and may be important for memory consolidation. We studied the intracortical organization of spindles in men and women by recording spontaneous sleep spindles from different cortical layers using linear microelectrode arrays. Two patterns of spindle generation were identified using visual inspection, and confirmed with factor analysis. Spindles (10-16 Hz) were largest and most common in upper and middle channels, with limited involvement of deep channels. Many spindles were observed in only upper or only middle channels, but approximately half occurred in both. In spindles involving both middle and upper channels, the spindle envelope onset in middle channels led upper by ∼25-50 ms on average. The phase relationship between spindle waves in upper and middle channels varied dynamically within spindle epochs, and across individuals. Current source density analysis demonstrated that upper and middle channel spindles were both generated by an excitatory supragranular current sink while an additional deep source was present for middle channel spindles only. Only middle channel spindles were accompanied by deep low (25-50 Hz) and high (70-170 Hz) gamma activity. These results suggest that upper channel spindles are generated by supragranular pyramids, and middle channel by infragranular. Possibly, middle channel spindles are generated by core thalamocortical afferents, and upper channel by matrix. The concurrence of these patterns could reflect engagement of cortical circuits in the integration of more focal (core) and distributed (matrix) aspects of memory. These results demonstrate that at least two distinct intracortical systems generate human sleep spindles.SIGNIFICANCE STATEMENT Bursts of ∼14 Hz oscillations, lasting ∼1 s, have been recognized for over 80 years as cardinal features of mammalian sleep. Recent findings suggest that they play a key role in organizing cortical activity during memory consolidation. We used linear microelectrode arrays to study their intracortical organization in humans. We found that spindles could be divided into two types. One mainly engages upper layers of the cortex, which are considered to be specialized for associative activity. The other engages both upper and middle layers, including those devoted to sensory input. The interaction of these two spindle types may help organize the interaction of sensory and associative aspects of memory consolidation.

Linear distributed source modeling of local field potentials recorded with intra-cortical electrode arrays

Planar intra-cortical electrode (Utah) arrays provide a unique window into the spatial organization of cortical activity. Reconstruction of the current source density (CSD) underlying such recordings, however, requires “inverting” Poisson’s equation. For inter-laminar recordings, this is commonly done by the CSD method, which consists in taking the second-order spatial derivative of the recorded local field potentials (LFPs). Although the CSD method has been tremendously successful in mapping the current generators underlying inter-laminar LFPs, its application to planar recordings is more challenging. While for inter-laminar recordings the CSD method seems reasonably robust against violations of its assumptions, is it unclear as to what extent this holds for planar recordings. One of the objectives of this study is to characterize the conditions under which the CSD method can be successfully applied to Utah array data. Using forward modeling, we find that for spatially coherent CSDs, the CSD method yields inaccurate reconstructions due to volume-conducted contamination from currents in deeper cortical layers. An alternative approach is to “invert” a constructed forward model. The advantage of this approach is that any a priori knowledge about the geometrical and electrical properties of the tissue can be taken into account. Although several inverse methods have been proposed for LFP data, the applicability of existing electroencephalographic (EEG) and magnetoencephalographic (MEG) inverse methods to LFP data is largely unexplored. Another objective of our study therefore, is to assess the applicability of the most commonly used EEG/MEG inverse methods to Utah array data. Our main conclusion is that these inverse methods provide more accurate CSD reconstructions than the CSD method. We illustrate the inverse methods using event-related potentials recorded from primary visual cortex of a macaque monkey during a motion discrimination task.

EEG microstates as a tool for studying the temporal dynamics of whole-brain neuronal networks: A review

The present review discusses a well-established method for characterizing resting-state activity of the human brain using multichannel electroencephalography (EEG). This method involves the examination of electrical microstates in the brain, which are defined as successive short time periods during which the configuration of the scalp potential field remains semi-stable, suggesting quasi-simultaneity of activity among the nodes of large-scale networks. A few prototypic microstates, which occur in a repetitive sequence across time, can be reliably identified across participants. Researchers have proposed that these microstates represent the basic building blocks of the chain of spontaneous conscious mental processes, and that their occurrence and temporal dynamics determine the quality of mentation. Several studies have further demonstrated that disturbances of mental processes associated with neurological and psychiatric conditions manifest as changes in the temporal dynamics of specific microstates. Combined EEG-fMRI studies and EEG source imaging studies have indicated that EEG microstates are closely associated with resting-state networks as identified using fMRI. The scale-free properties of the time series of EEG microstates explain why similar networks can be observed at such different time scales. The present review will provide an overview of these EEG microstates, available methods for analysis, the functional interpretations of findings regarding these microstates, and their behavioral and clinical correlates.

Concurrent Recording of Co-localized Electroencephalography and Local Field Potential in Rodent

Although electroencephalography (EEG) is widely used as a non-invasive technique for recording neural activities of the brain, our understanding of the neurogenesis of EEG is still very limited. Local field potentials (LFPs) recorded via a multi-laminar microelectrode can provide a more detailed account of simultaneous neural activity across different cortical layers in the neocortex, but the technique is invasive. Combining EEG and LFP measurements in a pre-clinical model can greatly enhance understanding of the neural mechanisms involved in the generation of EEG signals, and facilitate the derivation of a more realistic and biologically accurate mathematical model of EEG. A simple procedure for acquiring concurrent and co-localized EEG and multi-laminar LFP signals in the anesthetized rodent is presented here. We also investigated whether EEG signals were significantly affected by a burr hole drilled in the skull for the insertion of a microelectrode. Our results suggest that the burr hole has a negligible impact on EEG recordings.

Dendritic calcium spikes are clearly detectable at the cortical surface

Cortical surface recording techniques such as EEG and ECoG are widely used for measuring brain activity. The prevailing assumption is that surface potentials primarily reflect synaptic activity, although non-synaptic events may also contribute. Here we show that dendritic calcium spikes occurring in pyramidal neurons (that we showed previously are cognitively relevant) are clearly detectable in cortical surface potentials. To show this we developed an optogenetic, non-synaptic approach to evoke dendritic calcium spikes in vivo. We found that optogenetically evoked calcium spikes were easily detectable and had an unexpected waveform near the cortical surface. Sensory-evoked dendritic calcium spikes were also clearly detectable with amplitudes that matched the contribution of synaptic input. These results reveal how dendritic calcium spikes appear at the cortical surface and their significant impact on surface potentials, suggesting that long-standing surface recording data may contain information about dendritic activity that is relevant to behavior and cognitive function.

Surface EEG recordings are thought to primarily detect synaptic activity. Here the authors devise an optogenetic method to evoke dendritic calcium spikes in layer 5 pyramidal cells of the rat somatosensory cortex, and report that optogenetically evoked, as well as sensory-evoked dendritic calcium spikes make a significant contribution to surface EEG recordings.

Analysis and Modeling of Subthreshold Neural Multi-Electrode Array Data by Statistical Field Theory

Multi-electrode arrays (MEA) are increasingly used to investigate spontaneous neuronal network activity. The recorded signals comprise several distinct components: Apart from artifacts without biological significance, one can distinguish between spikes (action potentials) and subthreshold fluctuations (local fields potentials). Here we aim to develop a theoretical model that allows for a compact and robust characterization of subthreshold fluctuations in terms of a Gaussian statistical field theory in two spatial and one temporal dimension. What is usually referred to as the driving noise in the context of statistical physics is here interpreted as a representation of the neural activity. Spatial and temporal correlations of this activity give valuable information about the connectivity in the neural tissue. We apply our methods on a dataset obtained from MEA-measurements in an acute hippocampal brain slice from a rat. Our main finding is that the empirical correlation functions indeed obey the logarithmic behavior that is a general feature of theoretical models of this kind. We also find a clear correlation between the activity and the occurrence of spikes. Another important insight is the importance of correctly separating out certain artifacts from the data before proceeding with the analysis.

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.

Ion diffusion may introduce spurious current sources in current-source density (CSD) analysis

Standard CSD analysis does not account for ionic diffusion. Using biophysically realistic computer simulations, we show that unaccounted-for diffusive currents can lead to the prediction of spurious current sources. This finding may be of strong interest for in vivo electrophysiologists doing extracellular recordings in general, and CSD analysis in particular.

Current-source density (CSD) analysis is a well-established method for analyzing recorded local field potentials (LFPs), that is, the low-frequency part of extracellular potentials. Standard CSD theory is based on the assumption that all extracellular currents are purely ohmic, and thus neglects the possible impact from ionic diffusion on recorded potentials. However, it has previously been shown that in physiological conditions with large ion-concentration gradients, diffusive currents can evoke slow shifts in extracellular potentials. Using computer simulations, we here show that diffusion-evoked potential shifts can introduce errors in standard CSD analysis, and can lead to prediction of spurious current sources. Further, we here show that the diffusion-evoked prediction errors can be removed by using an improved CSD estimator which accounts for concentration-dependent effects.

NEW & NOTEWORTHY Standard CSD analysis does not account for ionic diffusion. Using biophysically realistic computer simulations, we show that unaccounted-for diffusive currents can lead to the prediction of spurious current sources. This finding may be of strong interest for in vivo electrophysiologists doing extracellular recordings in general, and CSD analysis in particular.

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.

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).

Discrepancies between Multi-Electrode LFP and CSD Phase-Patterns: A Forward Modeling Study

Multi-electrode recordings of local field potentials (LFPs) provide the opportunity to investigate the spatiotemporal organization of neural activity on the scale of several millimeters. In particular, the phases of oscillatory LFPs allow studying the coordination of neural oscillations in time and space and to tie it to cognitive processing. Given the computational roles of LFP phases, it is important to know how they relate to the phases of the underlying current source densities (CSDs) that generate them. Although CSDs and LFPs are distinct physical quantities, they are often (implicitly) identified when interpreting experimental observations. That this identification is problematic is clear from the fact that LFP phases change when switching to different electrode montages, while the underlying CSD phases remain unchanged. In this study we use a volume-conductor model to characterize discrepancies between LFP and CSD phase-patterns, to identify the contributing factors, and to assess the effect of different electrode montages. Although we focus on cortical LFPs recorded with two-dimensional (Utah) arrays, our findings are also relevant for other electrode configurations. We found that the main factors that determine the discrepancy between CSD and LFP phase-patterns are the frequency of the neural oscillations and the extent to which the laminar CSD profile is balanced. Furthermore, the presence of laminar phase-differences in cortical oscillations, as commonly observed in experiments, precludes identifying LFP phases with those of the CSD oscillations at a given cortical depth. This observation potentially complicates the interpretation of spike-LFP coherence and spike-triggered LFP averages. With respect to reference strategies, we found that the average-reference montage leads to larger discrepancies between LFP and CSD phases as compared with the referential montage, while the Laplacian montage reduces these discrepancies. We therefore advice to conduct analysis of two-dimensional LFP recordings using the Laplacian montage.

1D Current Source Density (CSD) Estimation in Inverse Theory: A Unified Framework for Higher-Order Spectral Regularization of Quadrature and Expansion-Type CSD Methods

Estimation of current source density (CSD) from the low-frequency part of extracellular electric potential recordings is an unstable linear inverse problem. To make the estimation possible in an experimental setting where recordings are contaminated with noise, it is necessary to stabilize the inversion. Here we present a unified framework for zero- and higher-order singular-value-decomposition (SVD)-based spectral regularization of 1D (linear) CSD estimation from local field potentials. The framework is based on two general approaches commonly employed for solving inverse problems: quadrature and basis function expansion. We first show that both inverse CSD (iCSD) and kernel CSD (kCSD) fall into the category of basis function expansion methods. We then use these general categories to introduce two new estimation methods, quadrature CSD (qCSD), based on discretizing the CSD integral equation with a chosen quadrature rule, and representer CSD (rCSD), an even-determined basis function expansion method that uses the problem's data kernels (representers) as basis functions. To determine the best candidate methods to use in the analysis of experimental data, we compared the different methods on simulations under three regularization schemes (Tikhonov, tSVD, and dSVD), three regularization parameter selection methods (NCP, L-curve, and GCV), and seven different a priori spatial smoothness constraints on the CSD distribution. This resulted in a comparison of 531 estimation schemes. We evaluated the estimation schemes according to their source reconstruction accuracy by testing them using different simulated noise levels, lateral source diameters, and CSD depth profiles. We found that ranking schemes according to the average error over all tested conditions results in a reproducible ranking, where the top schemes are found to perform well in the majority of tested conditions. However, there is no single best estimation scheme that outperforms all others under all tested conditions. The unified framework we propose expands the set of available estimation methods, provides increased flexibility for 1D CSD estimation in noisy experimental conditions, and allows for a meaningful comparison between estimation schemes.

Cortical Thinning in Healthy Aging Correlates with Larger Motor-Evoked EEG Desynchronization

Although electroencephalography (EEG) is a valuable tool to investigate neural activity in patients and controls, exactly how local anatomy impacts the measured signal remains unclear. Better characterizing this relationship is important to improve the understanding of how inter-subject differences in the EEG signal are related to neural activity. We hypothesized that cortical structure might affect event-related desynchronization (ERD) in EEG. Since aging is a well-documented cause of cortical thinning, we investigated the effects of cortical thickness (CT) and cortical depth (CD - the skull-to-cortex distance) on ERD using anatomical MRI and motor-evoked EEG in 17 healthy young adults and 20 healthy older persons. Results showed a significant negative correlation between ERD and CT, but no consistent relationship between ERD and CD. A thinner cortex was associated with a larger ERD in the α/β band and correcting for CT removed most of the inter-group difference in ERD. This indicates that differences in neural activity might not be the primary cause for the observed aging-related differences in ERD, at least in the motor cortex. Further, it emphasizes the importance of considering conditions affecting the EEG signal, such as cortical anatomical changes due to aging, when interpreting differences between healthy controls and/or patients.

Insertion of linear 8.4 μm diameter 16 channel carbon fiber electrode arrays for single unit recordings

OBJECTIVE

Single carbon fiber electrodes (d = 8.4 μm) insulated with parylene-c and functionalized with

PEDOT

pTS have been shown to record single unit activity but manual implantation of these devices with forceps can be difficult. Without an improvement in the insertion method any increase in the channel count by fabricating carbon fiber arrays would be impractical. In this study, we utilize a water soluble coating and structural backbones that allow us to create, implant, and record from fully functionalized arrays of carbon fibers with ∼150 μm pitch.

APPROACH

Two approaches were tested for the insertion of carbon fiber arrays. The first method used a poly(ethylene glycol) (PEG) coating that temporarily stiffened the fibers while leaving a small portion at the tip exposed. The small exposed portion (500 μm-1 mm) readily penetrated the brain allowing for an insertion that did not require the handling of each fiber by forceps. The second method involved the fabrication of silicon support structures with individual shanks spaced 150 μm apart. Each shank consisted of a small groove that held an individual carbon fiber.

MAIN RESULTS

Our results showed that the PEG coating allowed for the chronic implantation of carbon fiber arrays in five rats with unit activity detected at 31 days post-implant. The silicon support structures recorded single unit activity in three acute rat surgeries. In one of those surgeries a stacked device with three layers of silicon support structures and carbon fibers was built and shown to readily insert into the brain with unit activity on select sites.

SIGNIFICANCE

From these studies we have found that carbon fibers spaced at ∼150 μm readily insert into the brain. This greatly increases the recording density of chronic neural probes and paves the way for even higher density devices that have a minimal scarring response.

Tools for probing local circuits: high-density silicon probes combined with optogenetics

To understand how function arises from the interactions between neurons, it is necessary to use methods that allow the monitoring of brain activity at the single-neuron, single-spike level and the targeted manipulation of the diverse neuron types selectively in a closed-loop manner. Large-scale recordings of neuronal spiking combined with optogenetic perturbation of identified individual neurons has emerged as a suitable method for such tasks in behaving animals. To fully exploit the potential power of these methods, multiple steps of technical innovation are needed. We highlight the current state of the art in electrophysiological recording methods, combined with optogenetics, and discuss directions for progress. In addition, we point to areas where rapid development is in progress and discuss topics where near-term improvements are possible and needed.

Brain Source Imaging in Preclinical Rat Models of Focal Epilepsy using High-Resolution EEG Recordings

Electroencephalogram (EEG) has been traditionally used to determine which brain regions are the most likely candidates for resection in patients with focal epilepsy. This methodology relies on the assumption that seizures originate from the same regions of the brain from which interictal epileptiform discharges (IEDs) emerge. Preclinical models are very useful to find correlates between IED locations and the actual regions underlying seizure initiation in focal epilepsy. Rats have been commonly used in preclinical studies of epilepsy; hence, there exist a large variety of models for focal epilepsy in this particular species. However, it is challenging to record multichannel EEG and to perform brain source imaging in such a small animal. To overcome this issue, we combine a patented-technology to obtain 32-channel EEG recordings from rodents and an MRI probabilistic atlas for brain anatomical structures in Wistar rats to perform brain source imaging. In this video, we introduce the procedures to acquire multichannel EEG from Wistar rats with focal cortical dysplasia, and describe the steps both to define the volume conductor model from the MRI atlas and to uniquely determine the IEDs. Finally, we validate the whole methodology by obtaining brain source images of IEDs and compare them with those obtained at different time frames during the seizure onset.

Magnetoencephalography in the presurgical evaluation of epilepsy

Magnetoencephalography (MEG) is an important tool in the presurgical evaluation of patients with medically refractory epilepsy. The appropriate utilization and interpretation of MEG studies can increase the proportion of patients who may be able to further pursue surgical evaluation, refine surgical planning, and potentially increase the probability of seizure freedom after surgery. The aim of this paper is to provide the reader with a comprehensive but accessible guide to MEG, with particular emphasis on acquiring a working knowledge of MEG analysis, identifying patient groups that are most likely to benefit, and clarifying the limitations of this technology.

Invariance in current dipole moment density across brain structures and species: physiological constraint for neuroimaging

Although anatomical constraints have been shown to be effective for MEG and EEG inverse solutions, there are still no effective physiological constraints. Strength of the current generator is normally described by the moment of an equivalent current dipole Q. This value is quite variable since it depends on size of active tissue. In contrast, the current dipole moment density q, defined as Q per surface area of active cortex, is independent of size of active tissue. Here we studied whether the value of q has a maximum in physiological conditions across brain structures and species. We determined the value due to the primary neuronal current (q primary) alone, correcting for distortions due to measurement conditions and secondary current sources at boundaries separating regions of differing electrical conductivities. The values were in the same range for turtle cerebellum (0.56-1.48 nAm/mm(2)), guinea pig hippocampus (0.30-1.34 nAm/mm(2)), and swine neocortex (0.18-1.63 nAm/mm(2)), rat neocortex (~2.2 nAm/mm(2)), monkey neocortex (~0.40 nAm/mm(2)) and human neocortex (0.16-0.77 nAm/mm(2)). Thus, there appears to be a maximum value across the brain structures and species (1-2 nAm/mm(2)). The empirical values closely matched the theoretical values obtained with our independently validated neural network model (1.6-2.8 nAm/mm(2) for initial spike and 0.7-3.1 nAm/mm(2) for burst), indicating that the apparent invariance is not coincidental. Our model study shows that a single maximum value may exist across a wide range of brain structures and species, varying in neuron density, due to fundamental electrical properties of neurons. The maximum value of q primary may serve as an effective physiological constraint for MEG/EEG inverse solutions.

Maximally reliable spatial filtering of steady state visual evoked potentials

Due to their high signal-to-noise ratio (SNR) and robustness to artifacts, steady state visual evoked potentials (SSVEPs) are a popular technique for studying neural processing in the human visual system. SSVEPs are conventionally analyzed at individual electrodes or linear combinations of electrodes which maximize some variant of the SNR. Here we exploit the fundamental assumption of evoked responses--reproducibility across trials--to develop a technique that extracts a small number of high SNR, maximally reliable SSVEP components. This novel spatial filtering method operates on an array of Fourier coefficients and projects the data into a low-dimensional space in which the trial-to-trial spectral covariance is maximized. When applied to two sample data sets, the resulting technique recovers physiologically plausible components (i.e., the recovered topographies match the lead fields of the underlying sources) while drastically reducing the dimensionality of the data (i.e., more than 90% of the trial-to-trial reliability is captured in the first four components). Moreover, the proposed technique achieves a higher SNR than that of the single-best electrode or the Principal Components. We provide a freely-available MATLAB implementation of the proposed technique, herein termed "Reliable Components Analysis".

Generalized cable formalism to calculate the magnetic field of single neurons and neuronal populations

Neurons generate magnetic fields which can be recorded with macroscopic techniques such as magnetoencephalography. The theory that accounts for the genesis of neuronal magnetic fields involves dendritic cable structures in homogeneous resistive extracellular media. Here we generalize this model by considering dendritic cables in extracellular media with arbitrarily complex electric properties. This method is based on a multiscale mean-field theory where the neuron is considered in interaction with a "mean" extracellular medium (characterized by a specific impedance). We first show that, as expected, the generalized cable equation and the standard cable generate magnetic fields that mostly depend on the axial current in the cable, with a moderate contribution of extracellular currents. Less expected, we also show that the nature of the extracellular and intracellular media influence the axial current, and thus also influence neuronal magnetic fields. We illustrate these properties by numerical simulations and suggest experiments to test these findings.