Understanding the functional architecture of the brain in terms of networks is becoming increasingly common. In most fMRI applications functional networks are assumed to be stationary, resulting in a single network estimated for the entire time course. However recent results suggest that the connectivity between brain regions is highly non-stationary even at rest. As a result, there is a need for new brain imaging methodologies that comprehensively account for the dynamic (i.e., non-stationary) nature of the fMRI data. In this work we propose the Smooth Incremental Graphical Lasso Estimation (SINGLE) algorithm which estimates dynamic brain networks from fMRI data. We apply the SINGLE algorithm to functional MRI data from 24 healthy patients performing a choice-response task to demonstrate the dynamic changes in network structure that accompany a simple but attentionally demanding cognitive task. Using graph theoretic measures we show that the Right Inferior Frontal Gyrus, frequently reported as playing an important role in cognitive control, dynamically changes with the task. Our results suggest that the Right Inferior Frontal Gyrus plays a fundamental role in the attention and executive function during cognitively demanding tasks and may play a key role in regulating the balance between other brain regions.
@cite_2: In recent years there has been explosive growth in the number of neuroimaging studies performed using functional Magnetic Resonance Imaging (fMRI). The field that has grown around the acquisition and analysis of fMRI data is intrinsically interdisciplinary in nature and involves contributions from researchers in neuroscience, psychology, physics and statistics, among others. A standard fMRI study gives rise to massive amounts of noisy data with a complicated spatio-temporal correlation structure. Statistics plays a crucial role in understanding the nature of the data and obtaining relevant results that can be used and interpreted by neuroscientists. In this paper we discuss the analysis of fMRI data, from the initial acquisition of the raw data to its use in locating brain activity, making inference about brain connectivity and predictions about psychological or disease states. Along the way, we illustrate interesting and important issues where statistics already plays a crucial role. We also seek to illustrate areas where statistics has perhaps been underutilized and will have an increased role in the future.
Finally, the SINGLE algorithm is formally related to the Joint Graphical Lasso (JGL) . The JGL was designed with the motivation of improving network inference by leveraging information across related observations and data sets. However, while the JGL focuses on stationary network estimation the SINGLE algorithm is designed to estimate dynamic networks. This manifests itself in two main differences to the overall objective functions of each of the algorithms. Firstly, the SINGLE algorithm only employs the Fused Lasso penalty as the Group Lasso penalty proposed in @cite_2 cannot be used in the context of temporal homogeneity. This is due to the fact that the Group Lasso penalty encourages all coefficients to either be zero or non-zero in unison and therefore ignores temporal behaviour. Secondly, while both algorithms contain a Fused Lasso penalty the nature of these penalties are vastly different. In the case of the JGL there is no natural ordering to observations and therefore are present between all networks (i.e., the penalty is of the form @math ). This is not the case in the SINGLE algorithm where there is a chronological ordering. This results in a penalty of the form @math .