We present a didactic introduction to spectral dynamic causal modeling (DCM), a Bayesian state-space modeling approach used to infer effective connectivity from noninvasive neuroimaging data. Spectral DCM is currently the most widely applied DCM variant for resting-state functional MRI analysis. Our aim is to explain its technical foundations to an audience with limited expertise in state-space modeling and spectral data analysis. Particular attention will be paid to cross-spectral density, which is the most distinctive feature of spectral DCM and is closely related to functional connectivity, as measured by (zero-lag) Pearson correlations. In fact, the model parameters estimated by spectral DCM are those that best reproduce the cross-correlations between all measurements—at all time lags—including the zero-lag correlations that are usually interpreted as functional connectivity. We derive the functional connectivity matrix from the model equations and show how changing a single effective connectivity parameter can affect all pairwise correlations. To complicate matters, the pairs of brain regions showing the largest changes in functional connectivity do not necessarily coincide with those presenting the largest changes in effective connectivity. We discuss the implications and conclude with a comprehensive summary of the assumptions and limitations of spectral DCM.

Progress in scientific disciplines is accompanied by standardization of terminology. Network neuroscience, at the level of macroscale organization of the brain, is beginning to confront the challenges associated with developing a taxonomy of its fundamental explanatory constructs. The Workgroup for HArmonized Taxonomy of NETworks (WHATNET) was formed in 2020 as an Organization for Human Brain Mapping (OHBM)–endorsed best practices committee to provide recommendations on points of consensus, identify open questions, and highlight areas of ongoing debate in the service of moving the field toward standardized reporting of network neuroscience results. The committee conducted a survey to catalog current practices in large-scale brain network nomenclature. A few well-known network names (e.g., default mode network) dominated responses to the survey, and a number of illuminating points of disagreement emerged. We summarize survey results and provide initial considerations and recommendations from the workgroup. This perspective piece includes a selective review of challenges to this enterprise, including (1) network scale, resolution, and hierarchies; (2) interindividual variability of networks; (3) dynamics and nonstationarity of networks; (4) consideration of network affiliations of subcortical structures; and (5) consideration of multimodal information. We close with minimal reporting guidelines for the cognitive and network neuroscience communities to adopt.

Hunger and satiety drive eating behaviours via changes in brain function. The hypothalamus is a central component of the brain networks that regulate food intake. Animal research parsed the roles of the lateral hypothalamus (LH) and medial hypothalamus (MH) in hunger and satiety, respectively. Here, we examined how hunger and satiety change information flow between human LH and MH brain networks, and how these interactions are influenced by body mass index (BMI). Forty participants (16 overweight/obese) underwent two resting-state functional MRI scans while being fasted and sated. The excitatory/inhibitory influence of information flow between the MH and LH was modelled using spectral dynamic causal modelling. Our results revealed two core networks interacting across homeostatic state and weight: subcortical bidirectional connections between the LH, MH and the substantia nigra pars compacta (prSN), and cortical top-down inhibition from fronto-parietal and temporal areas. During fasting, we found higher inhibition between the LH and prSN, whereas the prSN received greater top-down inhibition from across the cortex. Individuals with higher BMI showed that these network dynamics occur irrespective of homeostatic state. Our findings reveal fasting affects brain dynamics over a distributed hypothalamic-midbrain-cortical network. This network is less sensitive to state-related fluctuations among people with obesity. Author Summary The hypothalamus is a central component of the brain networks regulating food intake. Animal research subdivided the hypothalamus anatomically and functionally into lateral hypothalamus (LH) and medial hypothalamus (MH). This is the first study showing how the LH and MH causally interact with other neural regions and how their dynamics change with weight and homeostasis in humans. Adopting state-of-the-art spectral dynamic causal modelling of resting-state fMRI data, we provide new insights into how homeostasis affect hypothalamic circuit dynamics, which involve a distributed network of midbrain and cortical areas with a key role of the substantia nigra. We identified unique aspects of network organisation associated with obesity involving reciprocal connections between the LH and MH, and input from the substantia nigra to the MH.

At the inception of human brain mapping, two principles of functional anatomy underwrote most conceptions—and analyses—of distributed brain responses: namely, functional segregation and integration . There are currently two main approaches to characterizing functional integration. The first is a mechanistic modeling of connectomics in terms of directed effective connectivity that mediates neuronal message passing and dynamics on neuronal circuits. The second phenomenological approach usually characterizes undirected functional connectivity (i.e., measurable correlations), in terms of intrinsic brain networks, self-organized criticality, dynamical instability, and so on. This paper describes a treatment of effective connectivity that speaks to the emergence of intrinsic brain networks and critical dynamics. It is predicated on the notion of Markov blankets that play a fundamental role in the self-organization of far from equilibrium systems. Using the apparatus of the renormalization group , we show that much of the phenomenology found in network neuroscience is an emergent property of a particular partition of neuronal states, over progressively coarser scales. As such, it offers a way of linking dynamics on directed graphs to the phenomenology of intrinsic brain networks. Author Summary This paper describes a treatment of effective connectivity that speaks to the emergence of intrinsic brain networks and critical dynamics. It is predicated on the notion of Markov blankets that play a fundamental role in the self-organization of far from equilibrium systems. Using the apparatus of the renormalization group , we show that much of the phenomenology found in network neuroscience is an emergent property of a particular partition of neuronal states, over progressively coarser scales. As such, it offers a way of linking dynamics on directed graphs to the phenomenology of intrinsic brain networks.

Bridging the gap between symmetric, direct white matter brain connectivity and neural dynamics that are often asymmetric and polysynaptic may offer insights into brain architecture, but this remains an unresolved challenge in neuroscience. Here, we used the graph Laplacian matrix to simulate symmetric and asymmetric high-order diffusion processes akin to particles spreading through white matter pathways. The simulated indirect structural connectivity outperformed direct as well as absent anatomical information in sculpting effective connectivity, a measure of causal and directed brain dynamics. Crucially, an asymmetric diffusion process determined by the sensitivity of the network nodes to their afferents best predicted effective connectivity. The outcome is consistent with brain regions adapting to maintain their sensitivity to inputs within a dynamic range. Asymmetric network communication models offer a promising perspective for understanding the relationship between structural and functional brain connectomes, both in normalcy and neuropsychiatric conditions. Author Summary Measures of white matter connectivity can usefully inform models of causal and directed brain communication (i.e., effective connectivity). However, due to the inherent differences in biophysical correlates, recording techniques and analytic approaches, the relationship between anatomical and effective brain connectivity is complex and not fully understood. In this study, we use simulation of heat diffusion constrained by the anatomical connectivity of the network to model polysynaptic (high-order) anatomical connectivity. The outcomes afford more useful constraints on effective connectivity than conventional, typically monosynaptic white matter connectivity. Furthermore, asymmetric network diffusion best predicts effective connectivity. In conclusion, the data provide insights into how anatomical connectomes give rise to asymmetric neuronal message passing and brain communication.

The brain is a complex, multiscale dynamical system composed of many interacting regions. Knowledge of the spatiotemporal organization of these interactions is critical for establishing a solid understanding of the brain’s functional architecture and the relationship between neural dynamics and cognition in health and disease. The possibility of studying these dynamics through careful analysis of neuroimaging data has catalyzed substantial interest in methods that estimate time-resolved fluctuations in functional connectivity (often referred to as “dynamic” or time-varying functional connectivity; TVFC). At the same time, debates have emerged regarding the application of TVFC analyses to resting fMRI data, and about the statistical validity, physiological origins, and cognitive and behavioral relevance of resting TVFC. These and other unresolved issues complicate interpretation of resting TVFC findings and limit the insights that can be gained from this promising new research area. This article brings together scientists with a variety of perspectives on resting TVFC to review the current literature in light of these issues. We introduce core concepts, define key terms, summarize controversies and open questions, and present a forward-looking perspective on how resting TVFC analyses can be rigorously and productively applied to investigate a wide range of questions in cognitive and systems neuroscience.

This paper considers the identification of large directed graphs for resting-state brain networks based on biophysical models of distributed neuronal activity, that is, effective connectivity . This identification can be contrasted with functional connectivity methods based on symmetric correlations that are ubiquitous in resting-state functional MRI (fMRI). We use spectral dynamic causal modeling (DCM) to invert large graphs comprising dozens of nodes or regions. The ensuing graphs are directed and weighted, hence providing a neurobiologically plausible characterization of connectivity in terms of excitatory and inhibitory coupling. Furthermore, we show that the use of Bayesian model reduction to discover the most likely sparse graph (or model) from a parent (e.g., fully connected) graph eschews the arbitrary thresholding often applied to large symmetric (functional connectivity) graphs. Using empirical fMRI data, we show that spectral DCM furnishes connectivity estimates on large graphs that correlate strongly with the estimates provided by stochastic DCM. Furthermore, we increase the efficiency of model inversion using functional connectivity modes to place prior constraints on effective connectivity. In other words, we use a small number of modes to finesse the potentially redundant parameterization of large DCMs. We show that spectral DCM—with functional connectivity priors—is ideally suited for directed graph theoretic analyses of resting-state fMRI. We envision that directed graphs will prove useful in understanding the psychopathology and pathophysiology of neurodegenerative and neurodevelopmental disorders. We will demonstrate the utility of large directed graphs in clinical populations in subsequent reports, using the procedures described in this paper.