Using an ODE model to separate Rest and Task signals in fMRI

Ongoing cortical activity is shaped by the interactions between brain regions connected on a macroscopic level. While components of the activity reflect specific processes responding to a presented stimulus, the vast majority persists as a background activity that innately exists due to cortical loops present in the connectivity. Simulations of the background activity, commonly known as resting state, have been developed over recent years using sophisticated ordinary differential equations (ODE) taking into account the macroscale organization of the cortex. However, the relationship between the rest activity compared to task or stimulus driven activity remains unclear although several different models have been proposed relating them. In this study, we develop a novel method of testing the relationship between rest and task by utilizing the framework that cortical activity can be represented by an ODE. The methodology uses a well-tested data driven approach known as Sparse Identification of Nonlinear Dynamics (SINDy) to construct an ODE to represent both rest and task functional Magnetic Response Imaging (fMRI) data separately. Since this technique is still relatively novel in the context of neuroscience, we validate the algorithm in its ability to identify an ODE that correctly predicts the signal dynamics, has a structure similar to those models currently used to recapitulate rest activity, and its ability to produce an impulse response as measured in fMRI data. Then, we systematically test the relationship between the two ODE models representing rest and task in order to model the task independent network activity. The task independent component is then subsequently removed from the measured signal and we utilize behavioral measures such as reaction time measured on a trial by trial basis to test if we have successfully separated the signal, as behavioral variables would be more correlated to the stimulus dependent activity than the raw unseparated signal. Our results show evidence that the stimulus independent signal is equivalent to all the processes in Rest that are not present in Task and can be estimated by subtracting the Task model from the Rest model. This suggests that Task can be approximated as a subset of Rest. We believe that our results are pertinent to the scientific community as they represent one of the first steps on using an ODE model to understanding the relationship of stimulus response in the cortex and allow for better decoding in terms of predicting the behavioral metrics. Significance Statement This article represents a pioneering effort in linking white matter structural connectivity, resulting in measured fMRI brain activity, and behavioral metrics within a single causal ODE model. Based solely on regression, a numerical approximation for intrinsic fMRI activity is constructed and then applied to separate aspects of the task fMRI activity based on background processes and stimulus-dependent processes. Therefore, this work represents a significant advancement towards modeling and interpreting fMRI data. ### Competing Interest Statement The authors have declared no competing interest.