Brain dynamics and structure-function relationships via spectral factorization and the transfer function

Unified theory of alpha, mu, and tau rhythms via eigenmodes of brain activity

A compact description of the frequency structure and topography of human alpha-band rhythms is obtained by use of the first four brain activity eigenmodes previously derived from corticothalamic neural field theory. Just two eigenmodes that overlap in frequency are found to reproduce the observed topography of the classical alpha rhythm for subjects with a single, occipitally concentrated alpha peak in their electroencephalograms. Alpha frequency splitting and relative amplitudes of double alpha peaks are explored analytically and numerically within this four-mode framework using eigenfunction expansion and perturbation methods. These effects are found to result primarily from the different eigenvalues and corticothalamic gains corresponding to the eigenmodes. Three modes with two non-overlapping frequencies suffice to reproduce the observed topography for subjects with a double alpha peak, where the appearance of a distinct second alpha peak requires an increase of the corticothalamic gain of higher eigenmodes relative to the first. Conversely, alpha blocking is inferred to be linked to a relatively small attention-dependent reduction of the gain of the relevant eigenmodes, whose effect is enhanced by the near-critical state of the brain and whose sign is consistent with inferences from neural field theory. The topographies and blocking of the mu and tau rhythms within the alpha-band are explained analogously via eigenmodes. Moreover, the observation of three rhythms in the alpha band is due to there being exactly three members of the first family of spatially nonuniform modes. These results thus provide a simple, unified description of alpha band rhythms and enable experimental observations of spectral structure and topography to be linked directly to theory and underlying physiology.

Impaired time-distance reconfiguration patterns in Alzheimer's disease: a dynamic functional connectivity study with 809 individuals from 7 sites

BACKGROUND

The dynamic functional connectivity (dFC) has been used successfully to investigate the dysfunction of Alzheimer's disease (AD) patients. The reconfiguration intensity of nodal dFC, which means the degree of alteration between FCs at different time scales, could provide additional information for understanding the reconfiguration of brain connectivity.

RESULTS

In this paper, we introduced a feature named time distance nodal connectivity diversity (tdNCD), and then evaluated the network reconfiguration intensity in every specific brain region in AD using a large multicenter dataset (N = 809 from 7 independent sites). Our results showed that the dysfunction involved in three subnetworks in AD, including the default mode network (DMN), the subcortical network (SCN), and the cerebellum network (CBN). The nodal tdNCD inside the DMN increased in AD compared to normal controls, and the nodal dynamic FC of the SCN and the CBN decreased in AD. Additionally, the classification analysis showed that the classification performance was better when combined tdNCD and FC to classify AD from normal control (ACC = 81%, SEN = 83.4%, SPE = 80.6%, and F1-score = 79.4%) than that only using FC (ACC = 78.2%, SEN = 76.2%, SPE = 76.5%, and F1-score = 77.5%) with a leave-one-site-out cross-validation. Besides, the performance of the three classes classification was improved from 50% (only using FC) to 53.3% (combined FC and tdNCD) (macro F1-score accuracy from 46.8 to 48.9%). More importantly, the classification model showed significant clinically predictive correlations (two classes classification: R = -0.38, P < 0.001; three classes classification: R = -0.404, P < 0.001). More importantly, several commonly used machine learning models confirmed that the tdNCD would provide additional information for classifying AD from normal controls.

CONCLUSIONS

The present study demonstrated dynamic reconfiguration of nodal FC abnormities in AD. The tdNCD highlights the potential for further understanding core mechanisms of brain dysfunction in AD. Evaluating the tdNCD FC provides a promising way to understand AD processes better and investigate novel diagnostic brain imaging biomarkers for AD.

Partial Directed Coherence and the Vector Autoregressive Modelling Myth and a Caveat

Here we dispel the lingering myth that Partial Directed Coherence is a Vector Autoregressive (VAR) Modelling dependent concept. In fact, our examples show that it is spectral factorization that lies at its heart, for which VAR modelling is a mere, albeit very efficient and convenient, device. This applies to Granger Causality estimation procedures in general and also includes instantaneous Granger effects. Care, however, must be exercised for connectivity between multivariate data generated through nonminimum phase mechanisms as it may possibly be incorrectly captured.

Discrete spectral eigenmode-resonance network of brain dynamics and connectivity

The problem of finding a compact natural representation of brain dynamics and connectivity is addressed using an expansion in terms of physical spatial eigenmodes and their frequency resonances. It is demonstrated that this discrete expansion via the system transfer function enables linear and nonlinear dynamics to be analyzed in compact form in terms of natural dynamic "atoms," each of which is a frequency resonance of an eigenmode. Because these modal resonances are determined by the system dynamics, not the investigator, they are privileged over widely used phenomenological patterns, and obviate the need for artificial discretizations and thresholding in coordinate space. It is shown that modal resonances participate as nodes of a discrete spectral network, are noninteracting in the linear regime, but are linked nonlinearly by wave-wave coalescence and decay processes. The modal resonance formulation is shown to be capable of speeding numerical calculations of strongly nonlinear interactions. Recent work in brain dynamics, especially based on neural field theory (NFT) approaches, allows eigenmodes and their resonances to be estimated from data without assuming a specific brain model. This means that dynamic equations can be inferred using system identification methods from control theory, rather than being assumed, and resonances can be interpreted as control-systems data filters. The results link brain activity and connectivity with control-systems functions such as prediction and attention via gain control and can also be linked to specific NFT predictions if desired, thereby providing a convenient bridge between physiologically based theories and experiment. Amplitudes of modes and resonances can also be tracked to provide a more direct and temporally localized representation of the dynamics than correlations and covariances, which are widely used in the field. By synthesizing many different lines of research, this work provides a way to link quantitative electrophysiological and imaging measurements, connectivity, brain dynamics, and function. This underlines the need to move between coordinate and spectral representations as required. Moreover, standard theoretical-physics approaches and mathematical methods can be used in place of ad hoc statistical measures such as those based on graph theory of artificially discretized and decimated networks, which are highly prone to selection effects and artifacts.

Determination of Dynamic Brain Connectivity via Spectral Analysis

Spectral analysis based on neural field theory is used to analyze dynamic connectivity via methods based on the physical eigenmodes that are the building blocks of brain dynamics. These approaches integrate over space instead of averaging over time and thereby greatly reduce or remove the temporal averaging effects, windowing artifacts, and noise at fine spatial scales that have bedeviled the analysis of dynamical functional connectivity (FC). The dependences of FC on dynamics at various timescales, and on windowing, are clarified and the results are demonstrated on simple test cases, demonstrating how modes provide directly interpretable insights that can be related to brain structure and function. It is shown that FC is dynamic even when the brain structure and effective connectivity are fixed, and that the observed patterns of FC are dominated by relatively few eigenmodes. Common artifacts introduced by statistical analyses that do not incorporate the physical nature of the brain are discussed and it is shown that these are avoided by spectral analysis using eigenmodes. Unlike most published artificially discretized “resting state networks” and other statistically-derived patterns, eigenmodes overlap, with every mode extending across the whole brain and every region participating in every mode—just like the vibrations that give rise to notes of a musical instrument. Despite this, modes are independent and do not interact in the linear limit. It is argued that for many purposes the intrinsic limitations of covariance-based FC instead favor the alternative of tracking eigenmode coefficients vs. time, which provide a compact representation that is directly related to biophysical brain dynamics.