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Front. Neurosci. | doi: 10.3389/fnins.2019.00127

A Functional Data Method for Causal Dynamic Network Modeling of Task-related fMRI

  • 1Division of Applied Mathematics, Brown University, United States
  • 2Brown University, United States
  • 3The Department of Biostatistics, Brown University, United States
  • 4Carney Institute for Brain Science, Brown University, United States
  • 5Center for Statistical Sciences, School of Public Health, Brown University, United States

3 Functional MRI (fMRI) is a popular approach to investigate brain connections and activations
4 when human subjects perform tasks. Because fMRI measures the indirect and convoluted signals
5 of brain activities at a lower temporal resolution, complex differential equation modeling methods
6 (e.g. Dynamic Causal Modeling) are usually employed to infer the neuronal processes and to
7 fit the resulting fMRI signals. However, this modeling strategy is computationally expensive
8 and remains to be mostly a confirmatory or hypothesis-driven approach. One major statistical
9 challenge here is to infer, in a data-driven fashion, the underlying differential equation models
10 from fMRI data. In this paper, we propose a causal dynamic network (CDN) method to estimate
11 brain activations and connections simultaneously. Our method links the observed fMRI data with
12 the latent neuronal states modeled by an ordinary differential equation (ODE) model. Using the
13 basis function expansion approach in functional data analysis, we develop an optimization-based
14 criterion that combines data-fitting errors and ODE fitting errors. We also develop and implement
15 a block coordinate-descent algorithm to compute the ODE parameters efficiently. We illustrate the
16 numerical advantages of our approach using data from realistic simulations and two task-related
17 fMRI experiments. Compared with various effective connectivity methods, our method achieves
18 higher estimation accuracy while improving the computational speed by from tens to thousands of
19 times. Though our method is developed for task-related fMRI, we also demonstrate the potential
20 applicability of our method (with a simple modification) to resting-state fMRI, by analyzing both
21 simulated and real data from medium-sized networks.

Keywords: brain connectitvity, Dynamic data analysis, optimization, Ordinary diffeential equations, task-related fMRI

Received: 28 Jul 2018; Accepted: 05 Feb 2019.

Edited by:

Pedro A. Valdes-Sosa, Clinical Hospital of Chengdu Brain Science Institute, China

Reviewed by:

Roberto C. Sotero, University of Calgary, Canada
Philippe CIUCIU, Commissariat à l'Energie Atomique et aux Energies Alternatives (CEA), France
Gopikrishna Deshpande, Auburn University, United States  

Copyright: © 2019 Cao, Sandstede and Luo. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Dr. Xi Luo, Brown University, Providence, United States, xi.rossi.luo@gmail.com