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Structurally informed models of directed brain connectivity

Nature Reviews Neuroscience volume 26, pages 23–41 (2025)Cite this article

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Abstract

Understanding how one brain region exerts influence over another in vivo is profoundly constrained by models used to infer or predict directed connectivity. Although such neural interactions rely on the anatomy of the brain, it remains unclear whether, at the macroscale, structural (or anatomical) connectivity provides useful constraints on models of directed connectivity. Here, we review the current state of research on this question, highlighting a key distinction between inference-based effective connectivity and prediction-based directed functional connectivity. We explore the methods via which structural connectivity has been integrated into directed connectivity models: through prior distributions, fixed parameters in state-space models and inputs to structure learning algorithms. Although the evidence suggests that integrating structural connectivity substantially improves directed connectivity models, assessments of reliability and out-of-sample validity are lacking. We conclude this Review with a strategy for future research that addresses current challenges and identifies opportunities for advancing the integration of structural and directed connectivity to ultimately improve understanding of the brain in health and disease.

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Fig. 1: Generative and generic state-space models used in the context of functional MRI.
Fig. 2: Bayesian, embedded and machine-learning-based approaches to structurally informing directed connectivity models.
Fig. 3: Emerging directions for structurally informed models of directed connectivity.

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Acknowledgements

The authors thank C. Seguin for valuable discussions that contributed to the development of this Review. M.D.G. is supported by an Australian Government Research Training Program Scholarship. M.D.G., L.N. and A.R. are funded by the Australian Research Council (ref. DP200100757). A.R. is also funded by Australian National Health and Medical Research Council Investigator Grant (ref. 1194910). A.R. is affiliated with The Wellcome Centre for Human Neuroimaging supported by core funding from Wellcome (203147/Z/16/Z). A.R. is a CIFAR Azrieli Global Scholar in the Brain, Mind & Consciousness Programme.

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Authors and Affiliations

  1. School of Psychological Sciences, Monash University, Clayton, Victoria, Australia

    Matthew D. Greaves, Leonardo Novelli & Adeel Razi

  2. Monash Biomedical Imaging, Monash University, Clayton, Victoria, Australia

    Matthew D. Greaves, Leonardo Novelli & Adeel Razi

  3. Centre for Sleep and Cognition, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore

    Sina Mansour L.

  4. Centre for Translational Magnetic Resonance Research, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore

    Sina Mansour L.

  5. Department of Psychiatry, The University of Melbourne, Parkville, Victoria, Australia

    Sina Mansour L. & Andrew Zalesky

  6. Wellcome Centre for Human Neuroimaging, University College London, London, UK

    Adeel Razi

  7. CIFAR Azrieli Global Scholars Program, CIFAR, Toronto, Ontario, Canada

    Adeel Razi

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  1. Matthew D. Greaves
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  2. Leonardo Novelli
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  3. Sina Mansour L.
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  4. Andrew Zalesky
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  5. Adeel Razi
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M.D.G. wrote the article. All authors researched data for the article, contributed substantially to discussion of the content and reviewed and/or edited the manuscript before submission.

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Correspondence to Matthew D. Greaves or Adeel Razi.

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Glossary

Bayes factor

A ratio comparing the evidence for two competing models, quantifying how much more likely the data are under one model than the other.

Biologically annotated connectomes

Connectome maps that include detailed biological information about the properties and functions of neural connections and regions.

Connectome

A comprehensive map of neural connections in the brain, representing the wiring diagram of the brain at the level of neurons or brain regions.

Construct validity

The degree to which a model accurately represents and measures the theoretical concepts or constructs it is intended to reflect, often evaluated through comparisons with other established models.

Cross-species validity

The extent to which a model or finding can be consistently applied and can produce similar results across different species, such as humans and non-human animals, which demonstrates robustness and generalizability.

Cross-spectral density

A frequency-domain measure that captures the amplitude and phase relationships between two signals across different frequencies, indicating their coherence and interaction strength.

Double-gamma

A predefined, standard model of the brain’s BOLD response to neuronal activity, using a function that captures both the primary peak and subsequent undershoot.

Effective mechanism

An insufficient, non-redundant part of an unnecessary but sufficient condition for bringing about certain observations (such as the influence that a specific gene expression pattern exerts on the development of a particular phenotype).

Embeddings

Representations of complex data in a lower-dimensional space that preserves relevant information and relationships.

Face validity

Refers (in modelling) to the extent to which a model seems effective and plausible, and is often assessed through simulations.

Free energy principle

A theoretical framework that suggests that the brain minimizes a quantity called free energy to maintain a stable internal state and reduce uncertainty about its environment.

Generative models

Describes how data are produced by underlying causes or processes, allowing for the simulation or generation of new data based on its structure and parameters.

Gradient descent

A fundamental optimization algorithm used in machine learning and statistics to minimize the error of a model by iteratively adjusting its parameters in the direction that reduces the error, based on the gradient of the loss function with respect to the parameters.

Graph-theoretical models

A mathematical model that uses the principles of graph theory and can be used to describe and analyse the network structure of the brain.

Grid search

A systematic, exhaustive search process used to tune hyperparameters by evaluating a model for each combination of specified parameter values.

Inverse problem

Involves inferring the unknown parameters or unobserved states of a system from observed data.

Kalman filtering

A recursive algorithm that estimates the state of a dynamic system by predicting the state and error covariance and then updating them with new observations weighted by the Kalman gain, which determines the influence of the new observations based on their estimated reliability.

Neural elements

Any component of a neural network that can process or transmit information, ranging from single neurons to larger, macroscale brain regions.

Neuronal populations

Groups of neurons that are treated as a single unit for the purpose of modelling the neural dynamics and interactions within and between different regions of the brain.

Optogenetics

A technique that involves the use of light to control cells within living tissue, typically neurons, that have been genetically modified to express light-sensitive ion channels.

Out-of-sample validity

The extent to which the results of a statistical model or analysis generalize to new, unseen data not used during the model training or fitting process.

Power-law

A mathematical relationship in which one quantity varies as a power of another, often seen in the spectral density of neural signals, in which lower frequencies have higher power, typically following a 1/f pattern.

Predictive coding

A theoretical framework that suggests the brain constantly generates and updates predictions about sensory inputs and uses the resulting prediction errors to refine its internal models of the environment.

Predictive validity

The extent to which a measurement or model accurately forecasts or predicts outcomes or behaviours in future, unseen situations, thereby demonstrating its effectiveness and applicability beyond the initial data used to create it.

Random effects

Here, a random effects model is a statistical model that accounts for variability across individuals by treating group-level parameters as random variables and is often used in Bayesian frameworks to improve the robustness of group-level inferences.

Regularization

A technique used in modelling to impose constraints or add information to prevent overfitting and improve generalizability by penalizing complex models.

Reliability

The consistency of a measurement, particularly emphasizing its ability to produce stable and consistent results upon repeated testing within the same subjects under similar conditions.

Savage–Dickey density ratio

A special case of the Bayes factor that compares the prior and posterior densities of a parameter at a specific value, used for efficiently testing point hypotheses in nested models.

Second-order statistics

Statistical measures that capture the relationships between pairs of data points, such as covariance and correlation, which describe the variability and dependencies in a data set.

Statistical conclusion validity

The degree to which conclusions about the relationship among variables based on the data are correct or reasonable.

Streamline

A space curve traced via a tractography algorithm and guided by the local orientations of a vector field computed from diffusion-weighted imaging.

Structural covariance analysis

A method that identifies relationships between brain regions by examining correlations in morphological features, such as cortical thickness or grey matter volume, across individuals.

Structure learning

The process of identifying the underlying structure or dependencies among variables in a data set, applicable in probabilistic graphical models and graph neural networks for predicting or inferring graph topologies.

Temporal precedence

The concept that one event occurs before another in time, serving as a necessary condition for directionality in neural interactions, helping to establish which brain region is likely influencing another.

Time constants

In the context of neural dynamics and functional MRI, time constants represent the rate at which a system returns to equilibrium after a perturbation, and to accurately capture these dynamics, the sampling rate must meet the Nyquist criterion, sampling at least twice the highest frequency present.

Tractography

Various algorithms applied to diffusion-weighted imaging to piece together streamline trajectories that correspond to probable nerve tract pathways.

Transcranial magnetic stimulation

A non-invasive procedure that uses magnetic fields to stimulate neurons, often used to study brain function and — increasingly — to treat neuropsychiatric disorders.

Unimodal–transmodal cortical hierarchy

A gradient or axis in the cerebral cortex that reflects increasing complexity of information processing, from sensory (unimodal) areas that handle basic sensory inputs to higher-order (transmodal) areas that integrate multisensory information and support complex cognitive functions.

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Greaves, M.D., Novelli, L., Mansour L., S. et al. Structurally informed models of directed brain connectivity. Nat. Rev. Neurosci. 26, 23–41 (2025). https://doi.org/10.1038/s41583-024-00881-3

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