On the Detection of Activation Patterns Using Principal Components Analysis

This chapter demonstrates that difficulties can be overcome by using the Fisher's linear discriminant analysis (FLDA) to obtain an activation pattern as a linear combination of all PCs and applying a nonparametric statistical method in order to test the significance of activation.

Abstract

Principal components analysis (PCA) of images obtained from positron emission tomography (PET) activation studies reveals an inter- and intrasubject subspace in data. The activation pattern is usually contained in the first component of the intrasubject subspace. However, this observation alone is not always sufficient to define the activated regions because (a) the activation pattern may not lie entirely on a single principal component (PC) but may be spread across several components (this is particularly true when the number of subjects increases and/or multicenter data are used) and (b) it is difficult to apply conventional parametric models in order to assess the statistical significance of the resulting activation image. This chapter demonstrates that these difficulties can be overcome by (a) using the Fisher's linear discriminant analysis (FLDA) to obtain an activation pattern as a linear combination of all PCs and (b) applying a nonparametric statistical method in order to test the significance of activation. Multicenter [15O]water PET scans were collected at three different centers in Japan, Denmark, and the United States. Each center scanned three right-handed subjects while performing a sequential finger-to-thumb opposition task. Four "baseline" and four "activation" scans were obtained from each subject. Data were analyzed using PCA. The activation pattern was extracted using FLDA. The statistical significance of activated regions was tested using a nonparametric method. The results were compared with pooled variance t-statistic images for which significance levels were obtained using a Gaussian random field model.