PII S0730-725X(99)00028-4 ● Original Contribution PRINCIPAL COMPONENT ANALYSIS OF THE DYNAMIC RESPONSE MEASURED BY fMRI: A GENERALIZED LINEAR SYSTEMS FRAMEWORK ANDERS H. ANDERSEN,*§ DON M. GASH,*§ AND MALCOLM J. AVISON†‡§ Departments of *Anatomy & Neurobiology, †Neurology, ‡Biochemistry, §Magnetic Resonance Imaging & Spectroscopy Center, University of Kentucky College of Medicine, Lexington, KY 40536, USA Principal component analysis (PCA) is one of several structure-seeking multivariate statistical techniques, exploratory as well as inferential, that have been proposed recently for the characterization and detection of activation in both PET and fMRI time series data. In particular, PCA is data driven and does not assume that the neural or hemodynamic response reaches some steady state, nor does it involve correlation with any pre-defined or exogenous experimental design template. In this paper, we present a generalized linear systems framework for PCA based on the singular value decomposition (SVD) model for representation of spatio– temporal fMRI data sets. Statistical inference procedures for PCA, including point and interval estimation will be introduced without the constraint of explicit hypotheses about specific task-dependent effects. The principal eigenvectors capture both the spatial and temporal aspects of fMRI data in a progressive fashion; they are inherently matched to unique and uncorrelated features and are ranked in order of the amount of variance explained. PCA also acts as a variation reduction technique, relegating most of the random noise to the trailing components while collecting systematic structure into the leading ones. Features summarizing variability may not directly be those that are the most useful. Further analysis is facilitated through linear subspace methods involving PC rotation and strategies of projection pursuit utilizing a reduced, lower-dimensional natural basis representation that retains most of the information. These properties will be illustrated in the setting of dynamic time-series response data from fMRI experiments involving pharmacological stimulation of the dopaminergic nigro-striatal system in primates. © 1999 Elsevier Science Inc. INTRODUCTION For more than a century now, the functional organization of the brain has been studied indirectly by comparing the behavioral consequences in terms of deficits due to le- sions in different parts of the brain. More recently, func- tional imaging techniques such as positron emission to- mography (PET) and now also magnetic resonance imaging (MRI) have made it possible to study functional connectivity of the brain directly and at an ever-increas- ing spatial resolution and sensitivity. However, appropri- ate data analysis strategies are required in order to dis- tinguish between regionally specific focal activation or “functional localization” and functional organization me- diated by coupling, suggesting “functional integration.” 1 The traditional voxel-based analyses of functional imag- ing studies within the context of regional specialization ignore the heterogeneity of the experimentally measured covariance structure of the data. Rather, they use univar- iate null-hypothesis testing approaches based on paired- image subtraction or parametric temporal correlation to- gether with intersubject averaging and only address the correlation between spatially distributed voxels post hoc. While providing powerful tests for sites of focal activa- tion, these methods are limited by the very nature of the data processing involved, which is optimized to the de- tection of only a particular, pre-defined response pattern in the scan-to-scan variation—largely a cognitive sub- traction approach. Emerging and complementary multivariate techniques with roots in PET imaging use descriptive and data-led approaches to characterizing neurophysiological dynam- ics in terms of distributed systems, so-called eigenimages or spatial modes, and their associated temporal response RECEIVED 2/11/99; ACCEPTED 3/9/99. Address correspondence to Anders H. Andersen, Ph.D., Rm. 106 MRISC Building, University of Kentucky Medical Center, 800 Rose St., Lexington, KY 40536-0098. Phone: (606) 323-1108; Fax: (606) 323-1068; E-mail anders@mri.uky.edu Magnetic Resonance Imaging, Vol. 17, No. 6, pp. 795– 815, 1999 © 1999 Elsevier Science Inc. All rights reserved. Printed in the USA. 0730-725X/99 $–see front matter 795