A pervasive challenge in neuroscience is testing whether neuronal connectivity changes over time due to specific causes, such as stimuli, events, or clinical interventions. Recent hardware innovations and falling data storage costs enable longer, more naturalistic neuronal recordings. The implicit opportunity for understanding the self-organised brain calls for new analysis methods that link temporal scales: from the order of milliseconds over which neuronal dynamics evolve, to the order of minutes, days, or even years over which experimental observations unfold. This review article demonstrates how hierarchical generative models and Bayesian inference help to characterise neuronal activity across different time scales. Crucially, these methods go beyond describing statistical associations among observations and enable inference about underlying mechanisms. We offer an overview of fundamental concepts in state-space modeling and suggest a taxonomy for these methods. Additionally, we introduce key mathematical principles that underscore a separation of temporal scales, such as the slaving principle, and review Bayesian methods that are being used to test hypotheses about the brain with multiscale data. We hope that this review will serve as a useful primer for experimental and computational neuroscientists on the state of the art and current directions of travel in the complex systems modelling literature. Author Summary Exploring changes in brain connectivity over time is a major challenge in neuroscience. This review article discusses the application of hierarchical generative models and Bayesian statistical methods to investigate modulators of neuronal dynamics across different temporal scales. By utilizing these innovative techniques, researchers can move beyond describing statistical associations and ask questions about underlying mechanisms. The article provides an overview of state-space modelling, dynamics, and a taxonomy of methods. It also introduces mathematical principles that link temporal scales and reviews the use of Bayesian statistical methods in testing hypotheses about the brain using multiscale data. This review aims to serve as a resource for experimental and computational neuroscientists by presenting the current state of the art and future directions of travel in modelling literature.

Author Summary The ongoing replication crisis in neuroscience and the concurrent “paradigm shift” from task-based to resting-state fMRI raises a question about the relative quality of the data obtained from these imaging paradigms. We compared parameters of intrinsic effective connectivity estimated from resting-state and Theory-of-Mind datasets. The much weaker connectivity and consequent lower information gain of the resting condition was notable as the network was specified based on connectivity patterns observed under rest and consisted of regions associated with the default mode network, which is characterized by being active during rest. These results support the assumption that the resting connectivity of the default mode network may reflect physiological rather than neural processes, and that the neural system in question better lends itself to investigation under an active task condition. Abstract Resting-state fMRI is an increasingly popular alternative to task-based fMRI. However, a formal quantification of the amount of information provided by resting-state fMRI as opposed to active task conditions about neural responses is lacking. We conducted a systematic comparison of the quality of inferences derived from a resting-state and a task fMRI paradigm by means of Bayesian Data Comparison. In this framework, data quality is formally quantified in information-theoretic terms as the precision and amount of information provided by the data on the parameters of interest. Parameters of effective connectivity, estimated from the cross-spectral densities of resting-state- and task time series by means of dynamic causal modelling (DCM), were subjected to the analysis. Data from 50 individuals undergoing resting-state and a Theory-of-Mind task were compared, both datasets provided by the Human Connectome Project. A threshold of very strong evidence was reached in favour of the Theory-of-Mind task (>10 bits or natural units) regarding information gain, which could be attributed to the active task condition eliciting stronger effective connectivity. Extending these analyses to other tasks and cognitive systems will reveal whether the superior informative value of task-based fMRI observed here is case specific or a more general trend.

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.

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.