Using an ordinary differential equation model to separate rest and task signals in fMRI

Amrit Kashyap (), Eloy Geenjaar, Patrik Bey, Kiret Dhindsa, Katharina Glomb, Sergey Plis, Shella Keilholz and Petra Ritter
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Amrit Kashyap: Charite University Medizin
Eloy Geenjaar: Georgia Institute of Technology
Patrik Bey: Charite University Medizin
Kiret Dhindsa: Charite University Medizin
Katharina Glomb: Charite University Medizin
Sergey Plis: Georgia State University
Shella Keilholz: Georgia Institute of Technology
Petra Ritter: Charite University Medizin

Nature Communications, 2025, vol. 16, issue 1, 1-19

Abstract: Abstract Cortical activity results from the interplay between network-connected regions that integrate information and stimulus-driven processes originating from sensory motor networks responding to specific tasks. Separating the information due to each of these components has been challenging, and the relationship as measured by fMRI in each of these cases Rest (network) and Task (stimulus-driven) remains a significant open question in the study of large-scale brain dynamics. In this study, we develop a network ordinary differential equation (ODE) model using advanced system identification tools to analyze fMRI data from both rest and task conditions. We demonstrate that task-specific ODEs are essentially a subset of rest-specific ODEs across four different tasks from the Human Connectome Project. By assuming that task activity is a relative complement of rest activity, our model significantly improves predictions of reaction times on a trial-by-trial basis, leading to a 9% increase in explanatory power (R2) across the 14 sub-tasks tested. We have additionally shown that these results hold for predicting missing trials and accuracy on a per individual basis as well as classifying Tasks trajectories or resulting dynamic Task functional connectivity. Our findings establish the principle of the Active Cortex Model, which posits that the cortex is always active and that Rest State encompasses all processes, while certain subsets of processes get elevated to perform specific task computations. Thus, this study is an important milestone in the development of the fMRI equation - to causally link large-scale brain activity, brain structural connectivity, and behavioral variables within a single framework.

Date: 2025
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DOI: 10.1038/s41467-025-62491-6

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