Infragranular layers lead information flow during slow oscillations according to information directionality indicators

Differentiating patients with obstructive sleep apnea from healthy controls based on heart rate-blood pressure coupling quantified by entropy-based indices

We introduce an entropy-based classification method for pairs of sequences (ECPS) for quantifying mutual dependencies in heart rate and beat-to-beat blood pressure recordings. The purpose of the method is to build a classifier for data in which each item consists of two intertwined data series taken for each subject. The method is based on ordinal patterns and uses entropy-like indices. Machine learning is used to select a subset of indices most suitable for our classification problem in order to build an optimal yet simple model for distinguishing between patients suffering from obstructive sleep apnea and a control group.

Attractor competition enriches cortical dynamics during awakening from anesthesia

Slow oscillations (≲ 1 Hz), a hallmark of slow-wave sleep and deep anesthesia across species, arise from spatiotemporal patterns of activity whose complexity increases as wakefulness is approached and cognitive functions emerge. The arousal process constitutes an open window to the unknown mechanisms underlying the emergence of such dynamical richness in awake cortical networks. Here, we investigate the changes in network dynamics as anesthesia fades out in the rat visual cortex. Starting from deep anesthesia, slow oscillations gradually increase their frequency, eventually expressing maximum regularity. This stage is followed by the abrupt onset of an infra-slow (~0.2 Hz) alternation between sleep-like oscillations and activated states. A population rate model reproduces this transition driven by an increased excitability that brings it to periodically cross a critical point. Based on our model, dynamical richness emerges as a competition between two metastable attractor states, a conclusion strongly supported by the data.

Slow Waves in Cortical Slices: How Spontaneous Activity is Shaped by Laminar Structure

Cortical slow oscillations (SO) of neural activity spontaneously emerge and propagate during deep sleep and anesthesia and are also expressed in isolated brain slices and cortical slabs. We lack full understanding of how SO integrate the different structural levels underlying local excitability of cell assemblies and their mutual interaction. Here, we focus on ongoing slow waves (SWs) in cortical slices reconstructed from a 16-electrode array designed to probe the neuronal activity at multiple spatial scales. In spite of the variable propagation patterns observed, we reproducibly found a smooth strip of loci leading the SW fronts, overlapping cortical layers 4 and 5, along which Up states were the longest and displayed the highest firing rate. Propagation modes were uncorrelated in time, signaling a memoryless generation of SWs. All these features could be modeled by a multimodular large-scale network of spiking neurons with a specific balance between local and intermodular connectivity. Modules work as relaxation oscillators with a weakly stable Down state and a peak of local excitability to model layers 4 and 5. These conditions allow for both optimal sensitivity to the network structure and richness of propagation modes, both of which are potential substrates for dynamic flexibility in more general contexts.

Bistability, Causality, and Complexity in Cortical Networks: An In Vitro Perturbational Study

Measuring the spatiotemporal complexity of cortical responses to direct perturbations provides a reliable index of the brain's capacity for consciousness in humans under both physiological and pathological conditions. Upon loss of consciousness, the complex pattern of causal interactions observed during wakefulness collapses into a stereotypical slow wave, suggesting that cortical bistability may play a role. Bistability is mainly expressed in the form of slow oscillations, a default pattern of activity that emerges from cortical networks in conditions of functional or anatomical disconnection. Here, we employ an in vitro model to understand the relationship between bistability and complexity in cortical circuits. We adapted the perturbational complexity index applied in humans to electrically stimulated cortical slices under different neuromodulatory conditions. At this microscale level, we demonstrate that perturbational complexity can be effectively modulated by pharmacological reduction of bistability and, albeit to a lesser extent, by enhancement of excitability, providing mechanistic insights into the macroscale measurements performed in humans.

Assessing functional connectivity across 3D tissue engineered axonal tracts using calcium fluorescence imaging

OBJECTIVE

Micro-tissue engineered neural networks (micro-TENNs) are anatomically-inspired constructs designed to structurally and functionally emulate white matter pathways in the brain. These 3D neural networks feature long axonal tracts spanning discrete neuronal populations contained within a tubular hydrogel, and are being developed to reconstruct damaged axonal pathways in the brain as well as to serve as physiologically-relevant in vitro experimental platforms. The goal of the current study was to characterize the functional properties of these neuronal and axonal networks.

APPROACH

Bidirectional micro-TENNs were transduced to express genetically-encoded calcium indicators, and spontaneous fluorescence activity was recorded using real-time microscopy at 20 Hz from specific regions-of-interest in the neuronal populations. Network activity patterns and functional connectivity across the axonal tracts were then assessed using various techniques from statistics and information theory including Pearson cross-correlation, phase synchronization matrices, power spectral analysis, directed transfer function, and transfer entropy.

MAIN RESULTS

Pearson cross-correlation, phase synchronization matrices, and power spectral analysis revealed high values of correlation and synchronicity between the spatially segregated neuronal clusters connected by axonal tracts. Specifically, phase synchronization revealed high synchronicity of  >0.8 between micro-TENN regions of interest. Normalized directed transfer function and transfer entropy matrices suggested robust information flow between the neuronal populations. Time varying power spectrum analysis revealed the strength of information propagation at various frequencies. Signal power strength was visible at elevated peak levels for dominant delta (1-4 Hz) and theta (4-8 Hz) frequency bands and progressively weakened at higher frequencies. These signal power strength results closely matched normalized directed transfer function analysis where near synchronous information flow was detected between frequencies of 2-5 Hz.

SIGNIFICANCE

To our knowledge, this is the first report using directed transfer function and transfer entropy methods based on fluorescent calcium activity to estimate functional connectivity of distinct neuronal populations via long-projecting, 3D axonal tracts in vitro. These functional data will further improve the design and optimization of implantable neural networks that could ultimately be deployed to reconstruct the nervous system to treat neurological disease and injury.

Detecting directional couplings from multivariate flows by the joint distance distribution

The identification of directional couplings (or drive-response relationships) in the analysis of interacting nonlinear systems is an important piece of information to understand their dynamics. This task is especially challenging when the analyst's knowledge of the systems reduces virtually to time series of observations. Spurred by the success of Granger causality in econometrics, the study of cause-effect relationships (not to be confounded with statistical correlations) was extended to other fields, thus favoring the introduction of further tools such as transfer entropy. Currently, the research on old and new causality tools along with their pitfalls and applications in ever more general situations is going through a time of much activity. In this paper, we re-examine the method of the joint distance distribution to detect directional couplings between two multivariate flows. This method is based on the forced Takens theorem, and, more specifically, it exploits the existence of a continuous mapping from the reconstructed attractor of the response system to the reconstructed attractor of the driving system, an approach that is increasingly drawing the attention of the data analysts. The numerical results with Lorenz and Rössler oscillators in three different interaction networks (including hidden common drivers) are quite satisfactory, except when phase synchronization sets in. They also show that the method of the joint distance distribution outperforms the lowest dimensional transfer entropy in the cases considered. The robustness of the results to the sampling interval, time series length, observational noise, and metric is analyzed too.

Causation and information flow with respect to relative entropy

Recently, a rigorous formalism has been established for information flow and causality within dynamical systems with respect to Shannon entropy. In this study, we re-establish the formalism with respect to relative entropy, or Kullback-Leiber divergence, a well-accepted measure of predictability because of its appealing properties such as invariance upon nonlinear transformation and consistency with the second law of thermodynamics. Different from previous studies (which yield consistent results only for 2D systems), the resulting information flow, say T, is precisely the same as that with respect to Shannon entropy for systems of arbitrary dimensionality, except for a minus sign (reflecting the opposite notion of predictability vs. uncertainty). As before, T possesses a property called principle of nil causality, a fact that classical formalisms fail to verify in many situation. Besides, it proves to be invariant upon nonlinear transformation, indicating that the so-obtained information flow should be an intrinsic physical property. This formalism has been validated with the stochastic gradient system, a nonlinear system that admits an analytical equilibrium solution of the Boltzmann type.

Systematic population spike delays across cortical layers within and between primary sensory areas

The coordinated propagation of activity across cortical layers enables simultaneous local computation and inter-areal interactions. A pattern of upward propagation from deeper to more superficial layers, which has been repeatedly demonstrated in spontaneous activity, would allow these functions to occur in parallel. But it remains unclear whether upward propagation also occurs for stimulus evoked activity, and how it relates to activity in other cortical areas. Here we used a new method to analyze relative delays between spikes obtained from simultaneous laminar recordings in primary sensory cortex (S1) of both hemispheres. The results identified systematic spike delays across cortical layers that showed a general upward propagation of activity in evoked and spontaneous activity. Systematic spike delays were also observed between hemispheres. After spikes in one S1 the delays in the other S1 were shortest at infragranular layers and increased in the upward direction. Model comparisons furthermore showed that upward propagation was better explained as a step-wise progression over cortical layers than as a traveling wave. The results are in line with the notion that upward propagation functionally integrates activity into local processing at superficial layers, while efficiently allowing for simultaneous inter-areal interactions.

Computing algebraic transfer entropy and coupling directions via transcripts

Most random processes studied in nonlinear time series analysis take values on sets endowed with a group structure, e.g., the real and rational numbers, and the integers. This fact allows to associate with each pair of group elements a third element, called their transcript, which is defined as the product of the second element in the pair times the first one. The transfer entropy of two such processes is called algebraic transfer entropy. It measures the information transferred between two coupled processes whose values belong to a group. In this paper, we show that, subject to one constraint, the algebraic transfer entropy matches the (in general, conditional) mutual information of certain transcripts with one variable less. This property has interesting practical applications, especially to the analysis of short time series. We also derive weak conditions for the 3-dimensional algebraic transfer entropy to yield the same coupling direction as the corresponding mutual information of transcripts. A related issue concerns the use of mutual information of transcripts to determine coupling directions in cases where the conditions just mentioned are not fulfilled. We checked the latter possibility in the lowest dimensional case with numerical simulations and cardiovascular data, and obtained positive results.