Top-down influences on local networks: basic theory with experimental implications

A tutorial on fitting joint models of M/EEG and behavior to understand cognition

We present motivation and practical steps necessary to find parameter estimates of joint models of behavior and neural electrophysiological data. This tutorial is written for researchers wishing to build joint models of human behavior and scalp and intracranial electroencephalographic (EEG) or magnetoencephalographic (MEG) data, and more specifically those researchers who seek to understand human cognition. Although these techniques could easily be applied to animal models, the focus of this tutorial is on human participants. Joint modeling of M/EEG and behavior requires some knowledge of existing computational and cognitive theories, M/EEG artifact correction, M/EEG analysis techniques, cognitive modeling, and programming for statistical modeling implementation. This paper seeks to give an introduction to these techniques as they apply to estimating parameters from neurocognitive models of M/EEG and human behavior, and to evaluate model results and compare models. Due to our research and knowledge on the subject matter, our examples in this paper will focus on testing specific hypotheses in human decision-making theory. However, most of the motivation and discussion of this paper applies across many modeling procedures and applications. We provide Python (and linked R) code examples in the tutorial and appendix. Readers are encouraged to try the exercises at the end of the document.

Biophysical Model: A Promising Method in the Study of the Mechanism of Propofol: A Narrative Review

The physiological and neuroregulatory mechanism of propofol is largely based on very limited knowledge. It is one of the important puzzling issues in anesthesiology and is of great value in both scientific and clinical fields. It is acknowledged that neural networks which are comprised of a number of neural circuits might be involved in the anesthetic mechanism. However, the mechanism of this hypothesis needs to be further elucidated. With the progress of artificial intelligence, it is more likely to solve this problem through using artificial neural networks to perform temporal waveform data analysis and to construct biophysical computational models. This review focuses on current knowledge regarding the anesthetic mechanism of propofol, an intravenous general anesthetic, by constructing biophysical computational models.

Bidirectionally Regulating Gamma Oscillations in Wilson-Cowan Model by Self-Feedback Loops: A Computational Study

The Wilson-Cowan model can emulate gamma oscillations, and thus is extensively used to research the generation of gamma oscillations closely related to cognitive functions. Previous studies have revealed that excitatory and inhibitory inputs to the model can modulate its gamma oscillations. Inhibitory and excitatory self-feedback loops are important structural features of the model, however, its functional role in the regulation of gamma oscillations in the model is still unclear. In the present study, bifurcation analysis and spectrum analysis are employed to elucidate the regulating mechanism of gamma oscillations underlined by the inhibitory and excitatory self-feedback loops, especially how the two self-feedback loops cooperate to generate the gamma oscillations and regulate the oscillation frequency. The present results reveal that, on one hand, the inhibitory self-feedback loop is not conducive to the generation of gamma oscillations, and increased inhibitory self-feedback strength facilitates the enhancement of the oscillation frequency. On the other hand, the excitatory self-feedback loop promotes the generation of gamma oscillations, and increased excitatory self-feedback strength leads to the decrease of oscillation frequency. Finally, theoretical analysis is conducted to provide explain on how the two self-feedback loops play a crucial role in the generation and regulation of neural oscillations in the model. To sum up, Inhibitory and excitatory self-feedback loops play a complementary role in generating and regulating the gamma oscillation in Wilson-Cowan model, and cooperate to bidirectionally regulate the gamma-oscillation frequency in a more flexible manner. These results might provide testable hypotheses for future experimental research.

Neural field theory of evoked response potentials in a spherical brain geometry

Evoked response potentials (ERPs) are calculated in spherical and planar geometries using neural field theory of the corticothalamic system. The ERP is modeled as an impulse response and the resulting modal effects of spherical corticothalamic dynamics are explored, showing that results for spherical and planar geometries converge in the limit of large brain size. Cortical modal effects can lead to a double-peak structure in the ERP time series. It is found that the main difference between infinite planar geometry and spherical geometry is that the ERP peak is sharper and stronger in the spherical geometry. It is also found that the magnitude of the response decreases with increasing spatial width of the stimulus at the cortex. The peak is slightly delayed at large angles from the stimulus point, corresponding to group velocities of 6-10 m s^{-1}. Strong modal effects are found in the spherical geometry, with the lowest few modes sufficing to describe the main features of ERPs, except very near to spatially narrow stimuli.

Reduced memory-related ongoing oscillatory activity in healthy older adults

Age-related impairments in episodic memory have been linked to alterations in encoding-induced neural activity. In young individuals, even prestimulus activity has been shown to influence the encoding of an upcoming stimulus, with ongoing theta and beta oscillations being predictive of subsequent recognition. The present study investigated if these memory-related ongoing oscillations are also affected by aging. In an EEG experiment, healthy older and young individuals performed an encoding task with a subsequent recognition test on picture and word stimuli. The group of younger participants showed an increased oscillatory activity in the lower frequency range (ranging from 3 to 17 Hz) in the pre- and post-stimulus period compared with the older adults. Only in young participants, ongoing beta power during encoding was related to later memory in both stimulus categories, whereas in older participants, this effect was diminished. Interestingly, there was no general age-related decrease in recognition performance. These results indicate that ongoing low beta oscillations might constitute a functional indicator of cognitive aging that reveals itself even before a strong decline in behavioral performance is noticeable, and that could be a potential target for neuromodulatory interventions.

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.

Consequences of tuning network function by tonic and phasic locus coeruleus output and stress: Regulating detection and discrimination of peripheral stimuli

Flexible and adaptive behaviors have evolved with increasing complexity and numbers of neuromodulator systems. The neuromodulatory locus coeruleus-norepinephrine (LC-NE) system is central to regulating cognitive function in a behaviorally-relevant and arousal-dependent manner. Through its nearly ubiquitous efferent projections, the LC-NE system acts to modulate neuron function on a cell-by-cell basis and exert a spectrum of actions across different brain regions to optimize target circuit function. As LC neuron activity, NE signaling, and arousal level increases, cognitive performance improves over an inverted-U shaped curve. Additionally, LC neurons burst phasically in relation to novel or salient sensory stimuli and top-down decision- or response-related processes. Together, the variety of LC activity patterns and complex actions of the LC-NE system indicate that the LC-NE system may dynamically regulate the function of target neural circuits. The manner in which neural networks encode, represent, and perform neurocomputations continue to be revealed. This has improved our ability to understand the optimization of neural circuits by NE and generation of flexible and adaptive goal-directed behaviors. In this review, the rat vibrissa somatosensory system is explored as a model neural circuit to bridge known modulatory actions of NE and changes in cognitive function. It is argued that fluid transitions between neural computational states reflect the ability of this sensory system to shift between two principal functions: detection of novel or salient sensory information and detailed descriptions of sensory information. Such flexibility in circuit function is likely critical for producing context-appropriate sensory signal processing. Nonetheless, many challenges remain including providing a causal link between NE mediated changes in sensory neural coding and perceptual changes, as well as extending these principles to higher cognitive functions including behavioral flexibility and decision making.

Cinematic Operation of the Cerebral Cortex Interpreted via Critical Transitions in Self-Organized Dynamic Systems

Measurements of local field potentials over the cortical surface and the scalp of animals and human subjects reveal intermittent bursts of beta and gamma oscillations. During the bursts, narrow-band metastable amplitude modulation (AM) patters emerge for a fraction of a second and ultimately dissolve to the broad-band random background activity. The burst process depends on previously learnt conditioned stimuli (CS), thus different AM patterns may emerge in response to different CS. This observation leads to our cinematic theory of cognition when perception happens in discrete steps manifested in the sequence of AM patterns. Our article summarizes findings in the past decades on experimental evidence of cinematic theory of cognition and relevant mathematical models. We treat cortices as dissipative systems that self-organize themselves near a critical level of activity that is a non-equilibrium metastable state. Criticality is arguably a key aspect of brains in their rapid adaptation, reconfiguration, high storage capacity, and sensitive response to external stimuli. Self-organized criticality (SOC) became an important concept to describe neural systems. We argue that transitions from one AM pattern to the other require the concept of phase transitions, extending beyond the dynamics described by SOC. We employ random graph theory (RGT) and percolation dynamics as fundamental mathematical approaches to model fluctuations in the cortical tissue. Our results indicate that perceptions are formed through a phase transition from a disorganized (high entropy) to a well-organized (low entropy) state, which explains the swiftness of the emergence of the perceptual experience in response to learned stimuli.

Cortical Resonance Frequencies Emerge from Network Size and Connectivity

Neural oscillations occur within a wide frequency range with different brain regions exhibiting resonance-like characteristics at specific points in the spectrum. At the microscopic scale, single neurons possess intrinsic oscillatory properties, such that is not yet known whether cortical resonance is consequential to neural oscillations or an emergent property of the networks that interconnect them. Using a network model of loosely-coupled Wilson-Cowan oscillators to simulate a patch of cortical sheet, we demonstrate that the size of the activated network is inversely related to its resonance frequency. Further analysis of the parameter space indicated that the number of excitatory and inhibitory connections, as well as the average transmission delay between units, determined the resonance frequency. The model predicted that if an activated network within the visual cortex increased in size, the resonance frequency of the network would decrease. We tested this prediction experimentally using the steady-state visual evoked potential where we stimulated the visual cortex with different size stimuli at a range of driving frequencies. We demonstrate that the frequency corresponding to peak steady-state response inversely correlated with the size of the network. We conclude that although individual neurons possess resonance properties, oscillatory activity at the macroscopic level is strongly influenced by network interactions, and that the steady-state response can be used to investigate functional networks.

When entrained using repetitive stimulation, sensory cortices appear to respond maximally, or resonate, at different driving frequencies: 10Hz in visual cortex; 20Hz and 40Hz in somatosensory and auditory cortices, respectively. The resonance frequencies are inversely correlated to the cortical volume of the respective regions, but it is unclear what drives this relationship. Here we used both computational and empirical data to demonstrate that resonance frequencies are emergent properties of the connectivity parameters of the underlying networks. The experimental paradigm stimulated large and small areas of visual cortex with different size objects made of flickering dots, and varied the driving frequency. Larger cortical areas exhibited maximum response at lower frequency than smaller areas, suggesting the inverse relationship between cortical size and resonance frequency holds, even within the same sensory modality. Computationally, we simulated cortical patches of different sizes and varied their connectivity parameters. We demonstrate that the size of the activated network is inversely related to its resonance frequency and that this change is due to the increased transmission delay and greater node degree within the larger network. The results are important for understanding the functional significance of oscillatory processes, and as a tool for probing changes in functional connectivity.

A study of the dynamics of seizure propagation across micro domains in the vicinity of the seizure onset zone

OBJECTIVE

The use of micro-electrode arrays to measure electrical activity from the surface of the brain is increasingly being investigated as a means to improve seizure onset zone (SOZ) localization. In this work, we used a multivariate autoregressive model to determine the evolution of seizure dynamics in the [Formula: see text] Hz high frequency band across micro-domains sampled by such micro-electrode arrays. We showed that a directed transfer function (DTF) can be used to estimate the flow of seizure activity in a set of simulated micro-electrode data with known propagation pattern.

APPROACH

We used seven complex partial seizures recorded from four patients undergoing intracranial monitoring for surgical evaluation to reconstruct the seizure propagation pattern over sliding windows using a DTF measure.

MAIN RESULTS

We showed that a DTF can be used to estimate the flow of seizure activity in a set of simulated micro-electrode data with a known propagation pattern. In general, depending on the location of the micro-electrode grid with respect to the clinical SOZ and the time from seizure onset, ictal propagation changed in directional characteristics over a 2-10 s time scale, with gross directionality limited to spatial dimensions of approximately [Formula: see text]. It was also seen that the strongest seizure patterns in the high frequency band and their sources over such micro-domains are more stable over time and across seizures bordering the clinically determined SOZ than inside.

SIGNIFICANCE

This type of propagation analysis might in future provide an additional tool to epileptologists for characterizing epileptogenic tissue. This will potentially help narrowing down resection zones without compromising essential brain functions as well as provide important information about targeting anti-epileptic stimulation devices.

Neocortical dynamics due to axon propagation delays in cortico-cortical fibers: EEG traveling and standing waves with implications for top-down influences on local networks and white matter disease

The brain is treated as a nested hierarchical complex system with substantial interactions across spatial scales. Local networks are pictured as embedded within global fields of synaptic action and action potentials. Global fields may act top-down on multiple networks, acting to bind remote networks. Because of scale-dependent properties, experimental electrophysiology requires both local and global models that match observational scales. Multiple local alpha rhythms are embedded in a global alpha rhythm. Global models are outlined in which cm-scale dynamic behaviors result largely from propagation delays in cortico-cortical axons and cortical background excitation level, controlled by neuromodulators on long time scales. The idealized global models ignore the bottom-up influences of local networks on global fields so as to employ relatively simple mathematics. The resulting models are transparently related to several EEG and steady state visually evoked potentials correlated with cognitive states, including estimates of neocortical coherence structure, traveling waves, and standing waves. The global models suggest that global oscillatory behavior of self-sustained (limit-cycle) modes lower than about 20 Hz may easily occur in neocortical/white matter systems provided: Background cortical excitability is sufficiently high; the strength of long cortico-cortical axon systems is sufficiently high; and the bottom-up influence of local networks on the global dynamic field is sufficiently weak. The global models provide “entry points” to more detailed studies of global top-down influences, including binding of weakly connected networks, modulation of gamma oscillations by theta or alpha rhythms, and the effects of white matter deficits.

EEG functional connectivity, axon delays and white matter disease

OBJECTIVE

Both structural and functional brain connectivities are closely linked to white matter disease. We discuss several such links of potential interest to neurologists, neurosurgeons, radiologists, and non-clinical neuroscientists.

METHODS

Treatment of brains as genuine complex systems suggests major emphasis on the multi-scale nature of brain connectivity and dynamic behavior. Cross-scale interactions of local, regional, and global networks are apparently responsible for much of EEG's oscillatory behaviors. Finite axon propagation speed, often assumed to be infinite in local network models, is central to our conceptual framework.

RESULTS

Myelin controls axon speed, and the synchrony of impulse traffic between distant cortical regions appears to be critical for optimal mental performance and learning. Several experiments suggest that axon conduction speed is plastic, thereby altering the regional and global white matter connections that facilitate binding of remote local networks.

CONCLUSIONS

Combined EEG and high resolution EEG can provide distinct multi-scale estimates of functional connectivity in both healthy and diseased brains with measures like frequency and phase spectra, covariance, and coherence.

SIGNIFICANCE

White matter disease may profoundly disrupt normal EEG coherence patterns, but currently these kinds of studies are rare in scientific labs and essentially missing from clinical environments.

Determination of seizure propagation across microdomains using spectral measures of causality

The use of microelectrode arrays to measure electrical activity from the surface of the brain is increasingly being investigated as a means to improve seizure focus localization. In this work, we determine seizure propagation across microdomains sampled by such microelectrode arrays and compare the results using two widely used frequency domain measures of causality, namely the partial directed coherence and the directed direct transfer function. We show that these two measures produce very similar propagation patterns for simulated microelectrode activity over a relatively smaller number of channels. However as the number of channels increases, partial directed coherence produces better estimates of the actual propagation pattern. Additionally, we apply these two measures to determine seizure propagation over microelectrode arrays measured from a patient undergoing intracranial monitoring for seizure focus localization and find very similar patterns which also agree with a threshold based reconstruction during seizure onset.