AUTHOR=Cao Xuefei , Sandstede Björn , Luo Xi 

TITLE=A Functional Data Method for Causal Dynamic Network Modeling of Task-Related fMRI

JOURNAL=Frontiers in Neuroscience

VOLUME=Volume 13 - 2019

YEAR=2019

URL=https://www.frontiersin.org/journals/neuroscience/articles/10.3389/fnins.2019.00127

DOI=10.3389/fnins.2019.00127

ISSN=1662-453X

ABSTRACT=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.