Statistical Methods for fMRI Activation and Effective Connectivity Studies

Functional magnetic resonance imaging (fMRI) is a technique to indirectly measure activity in the brain through the flow of blood. fMRI has been a powerful tool in helping us gain a better understanding of the human brain since it appeared over 20 years ago. However, fMRI poses many challenges for engineers. In particular, to detect and interpret the blood oxygen level-dependent (BOLD) signals on which fMRI is based is a challenge; For example, fMRI activation may be caused by a local neural population (activation detection) or by a distant brain region (effective connectivity). Although many advanced statistical methods have been developed for fMRI data analysis, many problems are still being addressed to maximize the accuracy in activation detection and effective connectivity analysis. This chapter presents general statistical methods for activation detection and effective connectivity analysis in fMRI scans of the human brain. A linear regression model for activation detection is introduced (Sect. 38.2.1), and a detailed statistical inference method for activation detection (Sect. 38.2.2) when applying an autoregression model to correct residual terms of the linear model is presented in Sect. 38.2.3. We adopt a two-stage mixed model to combine different subjects (Sect. 38.3) for second-level data analysis. To estimate the variance for the mixed model, a modified expectation-maximization algorithm is employed. Finally, due to the false positives in the activation map, a Bonferroni-related threshold correction method is developed to control the false positives (Sect. 38.3.3). An fMRI dataset from retinotopic mapping experiments was employed to test the feasibility of the methods for both first- and second-level analysis.In Sect. 38.4, we present a nonlinear system identification method (NSIM) for effective connectivity study. The mathematical theory of the method is presented in Sect. 38.4.1. An F statistical test is proposed to quantify the magnitude of the relationship based on two-connection and three-connection visual networks (Sect. 38.4.3). To circumvent the limitation of the model overfitting in NSIM, a model selection algorithm is suggested subsequently. In the model selection, we propose a nongreedy search method, e.g., least angle regression for effective connectivity analysis (Sects. 38.4.7 and 38.4.8). Three datasets obtained from standard block and random block designs are used to verify the method, and we outline some research directions and conclude our study in Sect. 38.5.