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Modelling and prediction of the dynamic responses of large-scale brain networks during direct electrical stimulation


Direct electrical stimulation can modulate the activity of brain networks for the treatment of several neurological and neuropsychiatric disorders and for restoring lost function. However, precise neuromodulation in an individual requires the accurate modelling and prediction of the effects of stimulation on the activity of their large-scale brain networks. Here, we report the development of dynamic input–output models that predict multiregional dynamics of brain networks in response to temporally varying patterns of ongoing microstimulation. In experiments with two awake rhesus macaques, we show that the activities of brain networks are modulated by changes in both stimulation amplitude and frequency, that they exhibit damping and oscillatory response dynamics, and that variabilities in prediction accuracy and in estimated response strength across brain regions can be explained by an at-rest functional connectivity measure computed without stimulation. Input–output models of brain dynamics may enable precise neuromodulation for the treatment of disease and facilitate the investigation of the functional organization of large-scale brain networks.

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Fig. 1: Input design, stimulation experiments and IO modelling framework.
Fig. 2: Dynamic IO models accurately predict brain network dynamics in response to stimulation.
Fig. 3: Dynamic IO models predict the response to stimulation across multiple brain regions.
Fig. 4: The dynamic structure of the IO model is essential for accurate prediction.
Fig. 5: At-rest functional controllability explains the variability in the IO prediction accuracy at different network nodes.
Fig. 6: Nonlinear dynamic IO modelling does not outperform the linear dynamic IO models.
Fig. 7: The overall brain network dynamics can be decomposed into input-driven dynamics and intrinsic dynamics to explain two possible sources for forward-prediction error.
Fig. 8: The fitted IO models enable closed-loop control of a simulated internal brain state.

Data availability

The main data supporting the results in this study are available within the paper and its Supplementary Information. The raw and analysed datasets generated during the study are too large to be publicly shared, but are available for research purposes from the corresponding author on reasonable request.

Code availability

The custom computer code in this study is available at


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We acknowledge support of the Army Research Office under contract W911NF-16-1-0368 (to M.M.S.) as part of the collaboration between the US Department of Defense, the UK Ministry of Defence and the UK Engineering and Physical Research Council under the Multidisciplinary University Research Initiative. We also acknowledge support of US National Institutes of Health BRAIN grant R01-NS104923 (to B.P. and M.M.S.). Finally, the we acknowledge the Defense Advanced Research Projects Agency under Cooperative Agreement Number W911NF-14-2-0043 (to M.M.S. and B.P.), issued by the Army Research Office contracting office in support of the DARPA SUBNETS programme. The views, opinions and/or findings expressed are those of the author(s) and should not be interpreted as representing the official views or policies of the Department of Defense or the US Government. We thank B. Goodell, C. Gray, J. E. Kleinbart and A. Orsborn for assistance with chamber and microdrive system design; S. Frey and B. Hynes for custom modifications to the Brainsight system; R. Shewcraft, J. Choi, M. Rubiano, Y. Jang and O. Martin for help with animal preparation and care; and K. Brown for help with MRI analysis.

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M.M.S. and Y.Y. conceived the study and developed the IO modelling framework. Y.Y. and M.M.S. designed the multi-trial stochastic stimulation and cross-validation. Y.Y., O.G.S., S.Q., B.P. and M.M.S. designed the stimulation experiments. S.Q. and B.P. implemented the stimulation experiments. S.Q., J.I.S, B.F. and B.P. performed the experiments and data collection. Y.Y. and M.M.S. implemented and performed the modelling and analyses. O.G.S., Y.Y. and M.M.S. designed and implemented the closed-loop simulations. M.M.S. supervised all the modelling and analysis work. B.P. supervised all the experimental work. Y.Y. and M.M.S. wrote the manuscript with input from S.Q., O.G.S. and B.P.

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Correspondence to Maryam M. Shanechi.

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Yang, Y., Qiao, S., Sani, O.G. et al. Modelling and prediction of the dynamic responses of large-scale brain networks during direct electrical stimulation. Nat Biomed Eng 5, 324–345 (2021).

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