Random Field–Union Intersection tests for EEG/MEG imaging F. Carbonell, a, * L. Gala ´n, b P. Valde ´s, b K. Worsley, c R.J. Biscay, d L. Dı ´az-Comas, b M.A. Bobes, b and M. Parra b a Institute for Cybernetics, Mathematics and Physics, Havana, Cuba b Cuban Neuroscience Center, C.P. 10400 Havana, Cuba c McGill University, Montreal, Canada d Havana University, Cuba Received 14 August 2003; revised 15 January 2004; accepted 15 January 2004 Electrophysiological (EEG/MEG) imaging challenges statistics by providing two views of the same spatiotemporal data: topographic and tomographic. Until now, statistical tests for these two situations have developed separately. This work introduces statistical tests for assessing simultaneously the significance of spatiotemporal event- related potential/event-related field (ERP/ERF) components and that of their sources. The test for detecting a component at a given time instant is provided by a Hotelling’s T 2 statistic. This statistic is constructed in such a manner to be invariant to any choice of reference and is based upon a generalized version of the average reference transform of the data. As a consequence, the proposed test is a generalization of the well- known Global Field Power statistic. Consideration of tests at all time instants leads to a multiple comparison problem addressed by the use of Random Field Theory (RFT). The Union-Intersection (UI) principle is the basis for testing hypotheses about the topographic and tomographic distributions of such ERP/ERF components. The performance of the method is illustrated with actual EEG recordings obtained from a visual experiment of pattern reversal stimuli. D 2004 Elsevier Inc. All rights reserved. Keywords: Event-related potentials; Random Fields; Union Intersection test; Hotelling’s T 2 ; Global Field Power; Average reference; EEG/MEG Source Analysis Introduction Recent years have seen the emergence of some methods for electrophysiological (EEG/MEG) neuroimaging. They hold the promise of complementing other imaging modalities, such as PET or fMRI, by providing very high temporal resolution maps of neural activation. These techniques however challenge statistics in several ways. One problem is the need to detect significant components in the event-related potential/event-related field (ERP/ERF) data and their topographic distribution, that is, the spatiotemporal detection of the ERP/ERF components in high dimensional, very correlated data. In addition, interest is increasingly focusing on the identifica- tion of the current sources that generate such components. As a consequence, tomographic views of the same data should also be analyzed, for example, by the use of linear inverse solutions (Pascual-Marqui et al., 2002), which further increases the dimen- sionality of variables to be considered. In practice, temporal components and their spatial location are usually identified by visual inspection of the peaks that appear in the ERP/ERF waveforms. However, this procedure may introduce bias in the analysis due to the large amount of channels recorded and typically excludes less pronounced phenomena. It is difficult to avoid subjectivity, especially when analyzing noisy recordings. A typical example of this type of situation in a clinical setting is the analysis of auditory ERPs to decide the presence of a response to low-intensity signals (Dobie, 1993). As a consequence some statis- tical decision procedures have been introduced to address the statistical identification of ERP/ERF components. A common exploratory approach to determine ERP/ERF com- ponents in the topographic view is the use of the statistic Global Field Power (GFP). This measure, introduced by Lehmann (1987) is essentially the variance over electrodes of the potential/field of the average reference transformed data. Components are identified as maxima of the GFP as a function of time. It is difficult however to associate statistical significance to this measure. Measures based on statistical procedures are permutation t tests or MANCOVA techniques (Blair and Karniski, 1993; Friston et al., 1996; Gala ´n et al., 1997; Raz, 1989). Subsequent testing of hypothesis for the topographic view may then be carried out, for example, by repeated measurement ANOVA, general MANOVA tests (Jenning et al., 1987; Vasey and Thayer, 1987), or permutation t tests. These techniques have been limited to a moderate number of sensors and time instants. The related problem of objectively identifying the presence of the sources of the ERP/ERF component cannot be addressed by the same type of procedures due to the huge number of variables to be considered after the use of inverse solutions. For this reason, the use of novel methods based on Random Field Theory (RFT) and usually known as Statistical Parametric Mappings (SPM) (Friston et al., 1991; Worsley et al., 1992) is a promising alternative (Bosch et al., 2001; Dale et al., 2000; Park et al., 2002). 1053-8119/$ - see front matter D 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.neuroimage.2004.01.020 * Corresponding author. Departamento de Sistemas Adaptativos, Instituto de Cibernetica, Matematica y Fisica, Calle 15, No. 551, e/C y D, Vedado, La Habana 4, C.P. 10400, Cuba. E-mail address: felix@icmf.inf.cu (F. Carbonell). Available online on ScienceDirect (www.sciencedirect.com.) www.elsevier.com/locate/ynimg NeuroImage 22 (2004) 268 – 276