Multivariate source prelocalization (MSP): Use of functionally informed basis functions for better conditioning the MEG inverse problem J. Mattout, a,c,d,e, * M. Pe ´le ´grini-Issac, b,e L. Garnero, c,e and H. Benali d,e a Wellcome Department of Imaging Neuroscience, London, UK b INSERM U483, Paris, France c CNRS UPR640, Paris, France d INSERM U494, Paris, France e IFR49, Paris, France Received 16 April 2004; revised 29 October 2004; accepted 21 January 2005 Available online 16 March 2005 Spatially characterizing and quantifying the brain electromagnetic response using MEG/EEG data still remains a critical issue since it requires solving an ill-posed inverse problem that does not admit a unique solution. To overcome this lack of uniqueness, inverse methods have to introduce prior information about the solution. Most existing approaches are directly based upon extrinsic anatomical and functional priors and usually attempt at simultaneously localizing and quantifying brain activity. By contrast, this paper deals with a preprocessing tool which aims at better conditioning the source reconstruction process, by relying only upon intrinsic knowledge (a forward model and the MEG/ EEG data itself) and focusing on the key issue of localization. Based on a discrete and realistic anatomical description of the cortex, we first define functionally Informed Basis Functions (fIBF) that are subject specific. We then propose a multivariate method which exploits these fIBF to calculate a probability-like coefficient of activation associated with each dipolar source of the model. This estimated distribution of activation coefficients may then be used as an intrinsic functional prior, either by taking these quantities into account in a subsequent inverse method, or by thresholding the set of probabilities in order to reduce the dimension of the solution space. These two ways of constraining the source reconstruction process may naturally be coupled. We successively des- cribe the proposed Multivariate Source Prelocalization (MSP) approach and illustrate its performance on both simulated and real MEG data. Finally, the better conditioning induced by the MSP process in a classical regularization scheme is extensively and quantitatively evaluated. D 2005 Elsevier Inc. All rights reserved. Keywords: MEG/EEG; Inverse problem; Regularization; Better condition- ing; Functionally Informed Basis Functions (fIBF); Activation probability; Multivariate Source Prelocalization (MSP) Introduction As main tools for mapping the cognitive functions of the human brain, functional imaging has a twofold objective: localizing the populations of neurons involved in cognitive or behavioral tasks and characterizing the temporal dynamics between those popula- tions. To this end, functional imaging techniques should con- sequently and ideally offer optimal spatial and temporal resolutions. Quantifying those resolutions is still an open issue. Nevertheless, the spatial and temporal resolutions should reach the order of 1 mm and 1 ms, respectively, to adequately describe the underlying physiological phenomenon of brain activity. Current functional imaging techniques, Positron Emission Tomography (PET), Single Photon Emission Computed Tomog- raphy (SPECT) and functional Magnetic Resonance Imaging (fMRI) present rather a good and even an excellent spatial resolution (~5 mm, ~1 cm and ~3 mm, respectively (Hoffman et al., 1979; Moonen and Bandettini, 1999). However, they all fail to offer a high enough temporal precision. fMRI offers the best trade-off, acquiring the signal of the whole brain in about 1 s, but remains limited by the hemodynamic delay. Because of their excellent temporal resolution (of the order of 1 ms, which roughly corresponds to the sampling rate), electro- encephalography (EEG) and magnetoencephalography (MEG) provide the most relevant data for studying the temporal dynamics of brain activity. Unfortunately, substantial difficulties lie in the inverse problem one has to solve in order to localize the electromagnetic sources that induce both EEG and MEG scalp recordings. This so-called ill-posed mathematical issue is indeed largely ill conditioned due to the non-uniqueness of the solution and numerical instability. The solution space (the brain) is much larger than the data space (up to about 128 EEG electrodes or 250 MEG sensors) and furthermore, an infinite number of different source arrangements can lead to the same measurements (Malmi- vuo and Plonsey, 1995). 1053-8119/$ - see front matter D 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.neuroimage.2005.01.026 * Corresponding author. Wellcome Department of Imaging Neuroscience, 12 Queen Square, WC1N 3BG London, UK. Fax: +44 207 807 1420. E-mail address: jmattout@fil.ion.ucl.ac.uk (J. Mattout). Available online on ScienceDirect (www.sciencedirect.com). www.elsevier.com/locate/ynimg NeuroImage 26 (2005) 356 – 373