ABSTRACT

Innovation and Information Management, School of Business, Faculty of Business and Economics, University of Hong Kong

Fan Li

Department of Statistical Science, Duke University

11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 11.2 The GLM: Single-Level Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 11.3 Modeling the Hemodynamic Response Function in the Time Domain . . . . . . . . 312

11.3.1 Parametric Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 11.3.2 Nonparametric Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 11.3.3 Comparison of Different HRF Estimation Methods . . . . . . . . . . . . . . . . . . . 320

11.4 Hemodynamic Response Estimation in the Frequency Domain . . . . . . . . . . . . . . . 321 11.5 Multi-Subject Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322

11.5.1 Semi-Parametric Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 11.6 Nonlinear Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323

11.6.1 The Balloon Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 11.6.2 Volterra Series Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 11.6.3 Bi-Exponential Nonlinear Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 11.6.4 Volterra Series Models for Multi-Subject Data . . . . . . . . . . . . . . . . . . . . . . . 326

11.7 Summary and Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

Functional magnetic resonance imaging (fMRI) measures brain activity through detecting blood oxygen-level changes in blood vessels; it provides non-invasive measurements of human brain activity with high spatial resolution (see Chapter 6 for details). FMRI has become the most popular neuroimaging technology for studying brain functions in psychology research. In typical psychology experiments, several subjects from a target human population (either a population of normal human subjects or a population of patients with a certain disease) are recruited; each subject completes a protocol comprised of one or several experimental conditions, while his or her brain activity is measured by fMRI. Then a series of preprocess-

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ing steps-as described in Chapter 10-are performed. The ensuing fMRI data can be used in statistical analysis for different research goals: (i) measuring brain response in a designed condition, (ii) locating activated brain regions, (iii) comparing brain activity under different conditions, (iv) determining brain networks, and (v) predicting brain disease development. This chapter focuses on estimation methods for the first three goals. Chapters 14, 16, and 17 review existing statistical models and methods for prediction problems using human brain data.