A framework to reconcile frequency scaling measurements, from intracellular recordings, local-field potentials, up to EEG and MEG signals

Extracellular and intracellular components of the impedance of neural tissue

Electric phenomena in brain tissue can be measured using extracellular potentials, such as the local field potential, or the electro-encephalogram. The interpretation of these signals depends on the electric structure and properties of extracellular media, but the measurements of these electric properties are still debated. Some measurements point to a model in which the extracellular medium is purely resistive, and thus parameters such as electric conductivity and permittivity should be independent of frequency. Other measurements point to a pronounced frequency dependence of these parameters, with scaling laws that are consistent with capacitive or diffusive effects. However, these experiments correspond to different preparations, and it is unclear how to correctly compare them. Here, we provide for the first time, impedance measurements (in the 1-10 kHz frequency range) using the same setup in various preparations, from primary cell cultures to acute brain slices, and a comparison with similar measurements performed in artificial cerebrospinal fluid with no biological material. The measurements show that when the current flows across a cell membrane, the frequency dependence of the macroscopic impedance between intracellular and extracellular electrodes is significant, and cannot be captured by a model with resistive media. Fitting a mean-field model to the data shows that this frequency dependence could be explained by the ionic diffusion mainly associated with Debye layers surrounding the membranes. We conclude that neuronal membranes and their ionic environment induce strong deviations to resistivity that should be taken into account to correctly interpret extracellular potentials generated by neurons.

Standard multiscale entropy reflects neural dynamics at mismatched temporal scales: What's signal irregularity got to do with it?

Multiscale Entropy (MSE) is used to characterize the temporal irregularity of neural time series patterns. Due to its' presumed sensitivity to non-linear signal characteristics, MSE is typically considered a complementary measure of brain dynamics to signal variance and spectral power. However, the divergence between these measures is often unclear in application. Furthermore, it is commonly assumed (yet sparingly verified) that entropy estimated at specific time scales reflects signal irregularity at those precise time scales of brain function. We argue that such assumptions are not tenable. Using simulated and empirical electroencephalogram (EEG) data from 47 younger and 52 older adults, we indicate strong and previously underappreciated associations between MSE and spectral power, and highlight how these links preclude traditional interpretations of MSE time scales. Specifically, we show that the typical definition of temporal patterns via "similarity bounds" biases coarse MSE scales-that are thought to reflect slow dynamics-by high-frequency dynamics. Moreover, we demonstrate that entropy at fine time scales-presumed to indicate fast dynamics-is highly sensitive to broadband spectral power, a measure dominated by low-frequency contributions. Jointly, these issues produce counterintuitive reflections of frequency-specific content on MSE time scales. We emphasize the resulting inferential problems in a conceptual replication of cross-sectional age differences at rest, in which scale-specific entropy age effects could be explained by spectral power differences at mismatched temporal scales. Furthermore, we demonstrate how such problems may be alleviated, resulting in the indication of scale-specific age differences in rhythmic irregularity. By controlling for narrowband contributions, we indicate that spontaneous alpha rhythms during eyes open rest transiently reduce broadband signal irregularity. Finally, we recommend best practices that may better permit a valid estimation and interpretation of neural signal irregularity at time scales of interest.

The Impact of Frequency Scale on the Response Sensitivity and Reliability of Cortical Neurons to 1/fβ Input Signals

What type of principle features intrinsic inside of the fluctuated input signals could drive neurons with the maximal excitations is one of the crucial neural coding issues. In this article, we examined both experimentally and theoretically the cortical neuronal responsivity (including firing rate and spike timing reliability) to input signals with different intrinsic correlational statistics (e.g., white-type noise, showed 1/f0 power spectrum, pink noise 1/f, and brown noises 1/f2) and different frequency ranges. Our results revealed that the response sensitivity and reliability of cortical neurons is much higher in response to 1/f noise stimuli with long-term correlations than 1/f0 with short-term correlations for a broad frequency range, and also higher than 1/f2 for all frequency ranges. In addition, we found that neuronal sensitivity diverges to opposite directions for 1/f noise comparing with 1/f0 white noise as a function of cutoff frequency of input signal. As the cutoff frequency is progressively increased from 50 to 1,000 Hz, the neuronal responsiveness increased gradually for 1/f noise, while decreased exponentially for white noise. Computational simulations of a general cortical model revealed that, neuronal sensitivity and reliability to input signal statistics was majorly dominated by fast sodium inactivation, potassium activation, and membrane time constants.

Analysis of Claims that the Brain Extracellular Impedance Is High and Non-resistive

Numerous measurements in the brain of the impedance between two extracellular electrodes have shown that it is approximately resistive in the range of biological interest, <10 kHz, and has a value close to that expected from the conductivity of physiological saline and the extracellular volume fraction in brain tissue. Recent work from Gomes et al. has claimed that the impedance of the extracellular space is some three orders of magnitude greater than these values and also displays a 1/f frequency dependence (above a low-frequency corner frequency). Their measurements were performed between an intracellular electrode and an extracellular electrode. It is argued that they incorrectly extracted the extracellular impedance because of an inaccurate representation of the large confounding impedance of the neuronal membrane. In conclusion, no compelling evidence has been provided to undermine the well-established and physically plausible consensus that the brain extracellular impedance is low and approximately resistive.

Is the Extracellular Impedance High and Non-resistive in Cerebral Cortex?

A recent commentary to Biophysical Journal criticized a previous study published in the same journal by Gomes et al. in 2016, and an alternative interpretation of the measurements was proposed. We reply here to these criticisms and provide some additional clarification, in particular, about a possible misinterpretation of the electrical circuit corresponding to these experiments. We suggest that, indeed, the extracellular impedance in cerebral cortex could be high and non-resistive, and we propose further experiments to settle this issue.

EEG Frequency Bands in Psychiatric Disorders: A Review of Resting State Studies

A significant proportion of the electroencephalography (EEG) literature focuses on differences in historically pre-defined frequency bands in the power spectrum that are typically referred to as alpha, beta, gamma, theta and delta waves. Here, we review 184 EEG studies that report differences in frequency bands in the resting state condition (eyes open and closed) across a spectrum of psychiatric disorders including depression, attention deficit-hyperactivity disorder (ADHD), autism, addiction, bipolar disorder, anxiety, panic disorder, post-traumatic stress disorder (PTSD), obsessive compulsive disorder (OCD) and schizophrenia to determine patterns across disorders. Aggregating across all reported results we demonstrate that characteristic patterns of power change within specific frequency bands are not necessarily unique to any one disorder but show substantial overlap across disorders as well as variability within disorders. In particular, we show that the most dominant pattern of change, across several disorder types including ADHD, schizophrenia and OCD, is power increases across lower frequencies (delta and theta) and decreases across higher frequencies (alpha, beta and gamma). However, a considerable number of disorders, such as PTSD, addiction and autism show no dominant trend for spectral change in any direction. We report consistency and validation scores across the disorders and conditions showing that the dominant result across all disorders is typically only 2.2 times as likely to occur in the literature as alternate results, and typically with less than 250 study participants when summed across all studies reporting this result. Furthermore, the magnitudes of the results were infrequently reported and were typically small at between 20% and 30% and correlated weakly with symptom severity scores. Finally, we discuss the many methodological challenges and limitations relating to such frequency band analysis across the literature. These results caution any interpretation of results from studies that consider only one disorder in isolation, and for the overall potential of this approach for delivering valuable insights in the field of mental health.

Bridging Neural and Computational Viewpoints on Perceptual Decision-Making

Sequential sampling models have provided a dominant theoretical framework guiding computational and neurophysiological investigations of perceptual decision-making. While these models share the basic principle that decisions are formed by accumulating sensory evidence to a bound, they come in many forms that can make similar predictions of choice behaviour despite invoking fundamentally different mechanisms. The identification of neural signals that reflect some of the core computations underpinning decision formation offers new avenues for empirically testing and refining key model assumptions. Here, we highlight recent efforts to explore these avenues and, in so doing, consider the conceptual and methodological challenges that arise when seeking to infer decision computations from complex neural data.

Cortical travelling waves: mechanisms and computational principles

Multichannel recording technologies have revealed travelling waves of neural activity in multiple sensory, motor and cognitive systems. These waves can be spontaneously generated by recurrent circuits or evoked by external stimuli. They travel along brain networks at multiple scales, transiently modulating spiking and excitability as they pass. Here, we review recent experimental findings that have found evidence for travelling waves at single-area (mesoscopic) and whole-brain (macroscopic) scales. We place these findings in the context of the current theoretical understanding of wave generation and propagation in recurrent networks. During the large low-frequency rhythms of sleep or the relatively desynchronized state of the awake cortex, travelling waves may serve a variety of functions, from long-term memory consolidation to processing of dynamic visual stimuli. We explore new avenues for experimental and computational understanding of the role of spatiotemporal activity patterns in the cortex.