Relationships Between Neuronal Oscillatory Amplitude and Dynamic Functional Connectivity

Next-generation neural mass and field modeling

The Wilson-Cowan population model of neural activity has greatly influenced our understanding of the mechanisms for the generation of brain rhythms and the emergence of structured brain activity. As well as the many insights that have been obtained from its mathematical analysis, it is now widely used in the computational neuroscience community for building large-scale in silico brain networks that can incorporate the increasing amount of knowledge from the Human Connectome Project. Here, we consider a neural population model in the spirit of that originally developed by Wilson and Cowan, albeit with the added advantage that it can account for the phenomena of event-related synchronization and desynchronization. This derived mean-field model provides a dynamic description for the evolution of synchrony, as measured by the Kuramoto order parameter, in a large population of quadratic integrate-and-fire model neurons. As in the original Wilson-Cowan framework, the population firing rate is at the heart of our new model; however, in a significant departure from the sigmoidal firing rate function approach, the population firing rate is now obtained as a real-valued function of the complex-valued population synchrony measure. To highlight the usefulness of this next-generation Wilson-Cowan style model, we deploy it in a number of neurobiological contexts, providing understanding of the changes in power spectra observed in electro- and magnetoencephalography neuroimaging studies of motor cortex during movement, insights into patterns of functional connectivity observed during rest and their disruption by transcranial magnetic stimulation, and to describe wave propagation across cortex.

Post-stimulus beta responses are modulated by task duration

Modulation of beta-band neural oscillations during and following movement is a robust marker of brain function. In particular, the post-movement beta rebound (PMBR), which occurs on movement cessation, has been related to inhibition and connectivity in the healthy brain, and is perturbed in disease. However, to realise the potential of the PMBR as a biomarker, its modulation by task parameters must be characterised and its functional role determined. Here, we used MEG to image brain electrophysiology during and after a grip-force task, with the aim to characterise how task duration, in the form of an isometric contraction, modulates beta responses. Fourteen participants exerted a 30% maximum voluntary grip-force for 2, 5 and 10 s. Our results showed that the amplitude of the PMBR is modulated by task duration, with increasing duration significantly reducing PMBR amplitude and increasing its time-to-peak. No variation in the amplitude of the movement related beta decrease (MRBD) with task duration was observed. To gain insight into what may underlie these trial-averaged results, we used a Hidden Markov Model to identify the individual trial dynamics of a brain network encompassing bilateral sensorimotor areas. The rapidly evolving dynamics of this network demonstrated similar variation with task parameters to the ‘classical’ rebound, and we show that the modulation of the PMBR can be well-described in terms of increased frequency of beta events on a millisecond timescale rather than modulation of beta amplitude during this time period. Our results add to the emerging picture that, in the case of a carefully controlled paradigm, beta modulation can be systematically controlled by task parameters and such control can reveal new information as to the processes that generate the average beta timecourse. These findings will support design of clinically relevant paradigms and analysis pipelines in future use of the PMBR as a marker of neuropathology.

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The post-movement beta rebound is modulated by task duration.

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Increasing task duration reduces amplitude of the post-movement beta rebound.

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The modulation is explained by increased frequency of short-timescale beta events.

Brain Functional Connectivity Through Phase Coupling of Neuronal Oscillations: A Perspective From Magnetoencephalography

Magnetoencephalography has gained an increasing importance in systems neuroscience thanks to the possibility it offers of unraveling brain networks at time-scales relevant to behavior, i.e., frequencies in the 1-100 Hz range, with sufficient spatial resolution. In the first part of this review, we describe, in a unified mathematical framework, a large set of metrics used to estimate MEG functional connectivity at the same or at different frequencies. The different metrics are presented according to their characteristics: same-frequency or cross-frequency, univariate or multivariate, directed or undirected. We focus on phase coupling metrics given that phase coupling of neuronal oscillations is a putative mechanism for inter-areal communication, and that MEG is an ideal tool to non-invasively detect such coupling. In the second part of this review, we present examples of the use of specific phase methods on real MEG data in the context of resting state, visuospatial attention and working memory. Overall, the results of the studies provide evidence for frequency specific and/or cross-frequency brain circuits which partially overlap with brain networks as identified by hemodynamic-based imaging techniques, such as functional Magnetic Resonance (fMRI). Additionally, the relation of these functional brain circuits to anatomy and to behavior highlights the usefulness of MEG phase coupling in systems neuroscience studies. In conclusion, we believe that the field of MEG functional connectivity has made substantial steps forward in the recent years and is now ready for bringing the study of brain networks to a more mechanistic understanding.

The road ahead in clinical network neuroscience

Clinical network neuroscience, the study of brain network topology in neurological and psychiatric diseases, has become a mainstay field within clinical neuroscience. Being a multidisciplinary group of clinical network neuroscience experts based in The Netherlands, we often discuss the current state of the art and possible avenues for future investigations. These discussions revolve around questions like "How do dynamic processes alter the underlying structural network?" and "Can we use network neuroscience for disease classification?" This opinion paper is an incomplete overview of these discussions and expands on ten questions that may potentially advance the field. By no means intended as a review of the current state of the field, it is instead meant as a conversation starter and source of inspiration to others.

How Sensitive Are Conventional MEG Functional Connectivity Metrics With Sliding Windows to Detect Genuine Fluctuations in Dynamic Functional Connectivity?

Despite advances in the field of dynamic connectivity, fixed sliding window approaches for the detection of fluctuations in functional connectivity are still widely used. The use of conventional connectivity metrics in conjunction with a fixed sliding window comes with the arbitrariness of the chosen window lengths. In this paper we use multivariate autoregressive and neural mass models with a priori defined ground truths to systematically analyze the sensitivity of conventional metrics in combination with different window lengths to detect genuine fluctuations in connectivity for various underlying state durations. Metrics of interest are the coherence, imaginary coherence, phase lag index, phase locking value and the amplitude envelope correlation. We performed analysis for two nodes and at the network level. We demonstrate that these metrics show indeed higher variability for genuine temporal fluctuations in connectivity compared to a static connectivity state superimposed by noise. Overall, the error of the connectivity estimates themselves decreases for longer state durations (order of seconds), while correlations of the connectivity fluctuations with the ground truth was higher for longer state durations. In general, metrics, in combination with a sliding window, perform poorly for very short state durations. Increasing the SNR of the system only leads to a moderate improvement. In addition, at the network level, only longer window widths were sufficient to detect plausible resting state networks that matched the underlying ground truth, especially for the phase locking value, amplitude envelope correlation and coherence. The length of these longer window widths did not necessarily correspond to the underlying state durations. For short window widths resting state network connectivity patterns could not be retrieved. We conclude that fixed sliding window approaches for connectivity can detect modulations of connectivity, but mostly if the underlying dynamics operate on moderate to slow timescales. In practice, this can be a drawback, as state durations can vary significantly in empirical data.

Complex temporal patterns processing by a neural mass model of a cortical column

It is well known that neuronal networks are capable of transmitting complex spatiotemporal information in the form of precise sequences of neuronal discharges characterized by recurrent patterns. At the same time, the synchronized activity of large ensembles produces local field potentials that propagate through highly dynamic oscillatory waves, such that, at the whole brain scale, complex spatiotemporal dynamics of electroencephalographic (EEG) signals may be associated to sensorimotor decision making processes. Despite these experimental evidences, the link between highly temporally organized input patterns and EEG waves has not been studied in detail. Here, we use a neural mass model to investigate to what extent precise temporal information, carried by deterministic nonlinear attractor mappings, is filtered and transformed into fluctuations in phase, frequency and amplitude of oscillatory brain activity. The phase shift that we observe, when we drive the neural mass model with specific chaotic inputs, shows that the local field potential amplitude peak appears in less than one full cycle, thus allowing traveling waves to encode temporal information. After converting phase and amplitude changes obtained into point processes, we quantify input-output similarity following a threshold-filtering algorithm onto the amplitude wave peaks. Our analysis shows that the neural mass model has the capacity for gating the input signal and propagate selected temporal features of that signal. Finally, we discuss the effect of local excitatory/inhibitory balance on these results and how excitability in cortical columns, controlled by neuromodulatory innervation of the cerebral cortex, may contribute to set a fine tuning and gating of the information fed to the cortex.

Mapping the topological organisation of beta oscillations in motor cortex using MEG

The spatial topology of the human motor cortex has been well studied, particularly using functional Magnetic Resonance Imaging (fMRI) which allows spatial separation of haemodynamic responses arising from stimulation of different body parts, individual digits and even spatially separate areas of the same digit. However, the spatial organisation of electrophysiological responses, particularly neural oscillations (rhythmic changes in electrical potential across cellular assemblies) has been less well studied. Mapping the spatial signature of neural oscillations is possible using magnetoencephalography (MEG), however spatial differentiation of responses induced by movement of separate digits is a challenge, because the brain regions involved are separated by only a few millimetres. In this paper we first show, in simulation, how to optimise experimental design and beamformer spatial filtering techniques to increase the spatial specificity of MEG derived functional images. Combining this result with experimental data, we then capture the organisation of the post-movement beta band (13–30 Hz) oscillatory response to movement of digits 2 and 5 of the dominant hand, in individual subjects. By comparing these MEG results to ultra-high field (7T) fMRI, we also show significant spatial agreement between beta modulation and the blood oxygenation level dependent (BOLD) response. Our results show that, when using an optimised inverse solution and controlling subject movement (using custom fitted foam padding) the spatial resolution of MEG can be of order 3–5 mm. The method described offers exciting potential to understand better the cortical organisation of oscillations, and to probe such organisation in patient populations where those oscillations are known to be abnormal.

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Aim is to map the topological organisation of neural oscillations in motor cortex.

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MEG spatial resolution optimised by temporal separation of sources.

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Subject motion controlled using foam headcasts.

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Cortical representation of Digit 2 and Digit 5 separated spatially.

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Post movement beta rebound maps motortopically in agreement with BOLD responses.