Abstract
Effective connectivity (EC), which reflects the causal interactions between brain regions, is fundamental to understanding information processing in the brain; however, traditional methods for obtaining EC, which rely on neural responses to stimulation, are often invasive or limited in spatial coverage, making them unsuitable for whole-brain EC mapping in humans. Here, to address this gap, we introduce Neural Perturbational Inference (NPI), a data-driven framework for mapping whole-brain EC. NPI employs an artificial neural network trained to model large-scale neural dynamics, serving as a computational surrogate of the brain. By systematically perturbing all regions in the surrogate brain and analyzing the resulting responses in other regions, NPI maps the directionality, strength and excitatory/inhibitory properties of brain-wide EC. Validation of NPI on generative models with known ground-truth EC demonstrates its superiority over existing methods such as Granger causality and dynamic causal modeling. When applied to resting-state functional magnetic resonance imaging data across diverse datasets, NPI reveals consistent, structurally supported EC patterns. Furthermore, comparisons with cortico-cortical evoked potential data show a strong resemblance between NPI-inferred EC and real stimulation propagation patterns. By transitioning from correlational to causal understandings of brain functionality, NPI marks a stride in decoding the brain’s functional architecture and facilitating both neuroscience studies and clinical applications.
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Data availability
The synthetic data generated using the ground-truth RNN and WBM are publicly available on GitHub at https://github.com/ncclab-sustech/NPI/. The following datasets used in this study are accessible via their respective repositories: HCP dataset (https://www.humanconnectome.org/study/hcp-young-adult/document/1200-subjects-data-release), ABCD dataset (https://abcdstudy.org/scientists/data-sharing/), CCEP dataset (https://f-tract.eu/atlas/), ABIDE dataset (https://fcon_1000.projects.nitrc.org/indi/abide/) and ADNI dataset (http://adni.loni.usc.edu). The brain atlases used in this study are also publicly available: MMP atlas (https://github.com/mbedini/The-HCP-MMP1.0-atlas-in-FSL), Schaefer atlases (https://github.com/ThomasYeoLab/CBIG/tree/master/stable_projects/brain_parcellation/Schaefer2018_LocalGlobal/Parcellations/MNI) and the AAL atlas (available from the Nilearn Python package). Source data are provided with this paper.
Code availability
The code supporting this study is available on GitHub at https://github.com/ncclab-sustech/NPI/, under the Apache License, v.2.0 (Apache-2.0). The main Python packages used in this study are numpy (v.1.26.4), torch (v.2.2.2), scipy (v.1.12.0), Nilearn (v.0.10.3), matplotlib (v.3.8.3), seaborn (v.0.13.2) and jupyter (v.1.1.1).
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Acknowledgements
Q.L. was supported by the National Natural Science Foundation of China (62472206), the National Key R&D Program of China (2021YFF1200804), Shenzhen Excellent Youth Project (RCYX20231211090405003), Shenzhen Science and Technology Innovation Committee (2022410129, KJZD20230923115221044, KCXFZ20201221173400001), Guangdong Provincial Key Laboratory of Advanced Biomaterials (2022B1212010003), and the Center for Computational Science and Engineering at Southern University of Science and Technology. C.Z. was supported by Hong Kong RGC Senior Research Fellowship Scheme (SRFS2324-2S05). Y.H. was partly supported by ECS-26303921 from the Research Grants Council of Hong Kong. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the paper. Z. Liang was supported by GuangDong Basic and Applied Basic Research Foundation (2025A1515011645). We thank the support from the Swarma-TCCI scholarship to Z. Luo and Z. Liang. We also thank H. Wu, J. Jiang, K. Du, Y. Mu, P. Zhou, S. Gu and Z. Cui, and members of the NCC laboratory including C. Wei, K. Lou, Z. Li, X. Xu and S. Wang for their valuable discussions.
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Contributions
Z. Luo designed the study, developed the NPI framework, conducted the primary analyses and drafted the paper. K.P. contributed to validating the NPI framework on synthetic and real datasets, analyzing results and preparing the paper. Z. Liang and S.C. supported the comparison of NPI with competing methods and assisted in figure generation. C.X. provided technical expertise in designing the ANN architecture and predicting fMRI signals. D.L. contributed to fMRI data preprocessing. Y.H. and C.Z. offered critical guidance on NPI validation and result analysis. Q.L., as the corresponding author, conceptualized the study, supervised the research and drafted the paper. All authors reviewed and approved the final paper.
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Extended data
Extended Data Fig. 1 Optimizing MLP architecture via grid search.
(a) The MLP architecture used in our study, which includes an input layer, two hidden layers, and an output layer, derived from grid search. (b) The R2 of one-step-ahead prediction on the training set under various sizes of hidden layer configurations, averaged across 20 participants. (c) The R2 of one-step-ahead prediction on the test set under various sizes of hidden layer configurations, averaged across 20 participants.
Extended Data Fig. 2 NPI-inferred EC is consistent with the Jacobian matrix of the trained ANN model.
(a) Jacobian matrix of an example RNN, numerically calculated using Pytorch. (b) Jacobian matrix of an ANN trained to predict the synthetic signals. (c) NPI-inferred EC by perturbing the trained ANN. (d) Jacobian of the trained ANN vs. Jacobian matrix of the ground-truth RNN across connection pairs. (e) NPI-inferred EC vs. Jacobian matrix of trained ANN across connection pairs. (f) Correlation coefficients between the NPI-inferred EC and the ground-truth EC, and between the Jacobian matrix and the ground-truth EC. There is no significant difference (P=0.87, two-sided Wilcoxon signed-rank test, n=50). Error bars represent standard deviation. (g) NPI-inferred EC on resting-state fMRI data from the HCP dataset, averaged across 800 participants. (h) Jacobian matrix of the ANN model trained on resting-state fMRI data from the HCP dataset, averaged across 800 participants. (i) NPI-inferred EC vs. Jacobian matrix of the trained ANN across connection pairs.
Extended Data Fig. 3 The performance of NPI is reliable across different network topographies.
(a) The test data are generated by generative models with predefined directed, binary structural connectivities (SC), from a public dataset23 (b) NPI is utilized to map the EC from synthetic BOLD signals. (c) Comparisons of the AUC scores of EC inference with NPI across nine different SC configurations with the inferences obtained with GC and DCM. Error bars represent standard deviations. P values for nine structures (n=60 for each bar), NPI vs. GC, GC vs. DCM, and NPI vs. DCM respectively: Net1: P = 6.25 × 10−11, 7.48 × 10−9, 8.40 × 10−11, Net2: P = 8.54 × 10−9, 1.59 × 10−7, 4.40 × 10−10, Net3: P = 1.57 × 10−10, 2.23 × 10−10, 5.82 × 10−11, Net4: P = 1.20 × 10−6, 1.63 × 10−11, 1.63 × 10−11, Net5: P = 2.08 × 10−5, 1.63 × 10−11, 1.62 × 10−11, Net6: P = 2.45 × 10−10, 1.63 × 10−11, 1.62 × 10−11, Net7: P = 7.85 × 10−9, 6.32 × 10−10, 3.37 × 10−11, Net8: P = 1.43 × 10−10, 1.63 × 10−11, 1.63 × 10−11, Net9: P = 4.80 × 10−9, 1.63 × 10−11, 1.63 × 10−11.
Extended Data Fig. 4 The EBC, binarized EBC, and excitatory and inhibitory part of EBC.
(a) The whole-brain EBC. (b) EBC binarized by a threshold of 80% strength of EC. The entries larger than the threshold are set to 1, while the rest are set to 0. (c, d) The excitatory (c) and inhibitory (d) parts of EBC.
Extended Data Fig. 5 The NPI-inferred EC derived from brain atlases with increasing numbers of regions.
(a) EBC across different resolution of parcellations in Schaefer atlases. The group-level EBC are averaged across 100 participants. (b) Inter-participant correlation of individual EC and FC across different parcellations in Schaefer atlases. Results are averaged across 100 participants.
Supplementary information
Supplementary Information (download PDF )
Supplementary Notes 1–6, Figs. 1–15 and Tables 1–5.
Supplementary Video (download MOV )
ANN’s performance of one-step-ahead prediction using real fMRI data under MMP parcellation (360 regions). The next step is predicted from three preceding steps. Real signals (ground-truth dynamics) and predicted signals (ANN-predicted dynamics) are plotted.
Source data
Source Data Fig. 3 (download ZIP )
Whole-brain EC matrix with MMP parcellation and corresponding area names.
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Luo, Z., Peng, K., Liang, Z. et al. Mapping effective connectivity by virtually perturbing a surrogate brain. Nat Methods 22, 1376–1385 (2025). https://doi.org/10.1038/s41592-025-02654-x
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DOI: https://doi.org/10.1038/s41592-025-02654-x
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