r Human Brain Mapping 32:1141���1160 (2011) r fMRI Functional Networks for EEG Source Imaging Xu Lei,1 Peng Xu,1 Cheng Luo,1 Jinping Zhao,1 Dong Zhou,2 and Dezhong Yao1* 1The Key Laboratory for NeuroInformation of Ministry of Education, School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu, China 2Department of Neurology, West China Hospital, Si Chuan University, Chengdu, China r r Abstract: The brain exhibits temporally coherent networks (TCNs) involving numerous cortical and sub-cortical regions both during the rest state and during the performance of cognitive tasks. TCNs represent the interactions between different brain areas, and understanding such networks may facili- tate electroencephalography (EEG) source estimation. We propose a new method for examining TCNs using scalp EEG in conjunction with data obtained by functional magnetic resonance imaging (fMRI). In this approach, termed NEtwork based SOurce Imaging (NESOI), multiple TCNs derived from fMRI with independent component analysis (ICA) are used as the covariance priors of the EEG source reconstruction using Parametric Empirical Bayesian (PEB). In contrast to previous applications of PEB in EEG source imaging with smoothness or sparseness priors, TCNs play a fundamental role among the priors used by NESOI. NESOI achieves an efficient integration of the high temporal resolution EEG and TCN derived from the high spatial resolution fMRI. Using synthetic and real data, we directly compared the performance of NESOI with other distributed source inversion methods, with and with- out the use of fMRI priors. Our results indicated that NESOI is a potentially useful approach for EEG source imaging. Hum Brain Mapp 32:1141���1160, 2011. V C 2010 Wiley-Liss, Inc. Key words: EEG source imaging parametric empirical bayesian temporally coherence networks fMRI face perception epileptic EEG r r INTRODUCTION Functional magnetic resonance imaging (fMRI) and elec- troencephalography (EEG) are complementary imaging techniques, due to their respective strengths and weak- nesses in terms of spatial and temporal resolution. fMRI is a measure of changes in the blood oxygen level-dependent (BOLD) signal. Because this index is the product of a com- plex convolution of brain activity, its temporal resolution is relatively low. Following an impulse of activity, the BOLD signal indexed by fMRI takes several seconds to rise, and even longer to fall. EEG, in contrast, measures neuronal electrical potentials that are generated by the postsynaptic excitatory and inhibitory potentials of pyram- idal cells that are positioned perpendicular to the cortical surface. The temporal resolution of EEG is thus compara- tively high, in the order of milliseconds. However, because of the complex influence of the spatiotemporal characteris- tics of skull volume conduction on the EEG signal, the spatial resolution of this technique is relatively poor. Therefore, integrating EEG and fMRI may provide a com- bined imaging technique with a high level of dynamic temporal information and high spatial resolution. Because of the different physiological mechanisms for fMRI and EEG, however, there is likely to be a disparity between the Contract grant sponsor: National Nature Science Foundation of China Contract grant number: 30525030, 60736029, 30870655, 60701015 Contract grant sponsor: 863 Project Contract grant number: 2009AA02Z301. *Correspondence to: Dezhong Yao, School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu 610054, China. E-mail: dyao@uestc.edu.cn Received for publication 10 May 2009 Revised 28 March 2010 Accepted 23 April 2010 DOI: 10.1002/hbm.21098 Published online 2 September 2010 in Wiley Online Library (wileyonlinelibrary.com). V C 2010 Wiley-Liss, Inc.

activated areas revealed by EEG and fMRI [Disbrow et al., 2000]. As such, the development of techniques for success- fully integrating EEG and fMRI is an important research goal. A large number of previous studies have proposed pos- sible approaches for tackling the problems involved in combining EEG and fMRI [Dale and Halgren, 2001 Gerloff et al., 1996 Whittingstall et al., 2007]. One proposed method is an ������EEG-informed fMRI������ algorithm [Benar �� et al., 2002 Goldman et al., 2002 Jacobs et al., 2008 Scheeringa et al., 2009]. This method requires the precise onset information of events or blocks and details of the actual hemodynamic response function (HRF). Differences between the actual HRF and the assumed HRF may reduce the feasibility of this approach [Jacobs et al., 2008]. An alternative method, the ������feature fusion������ approach uses independent component analysis (ICA) to simultaneously analyze electromagnetic and hemodynamic data [Mantini et al., 2009 Moosmann et al., 2008]. A spatial pattern derived from fMRI can then be associated with a temporal waveform of EEG according to a common feature. How- ever, as EEG must be down-sampled to temporal resolu- tion of fMRI, this method neglects a large amount of temporal information in EEG. This considerable disparity is an approximate 4-s delay between impulses of electric neural activity and the corresponding BOLD change. Because of the mismatch between the lower sampling rate of fMRI compared to the high sampling rate of EEG, there are not corresponding BOLD samples for most EEG sam- ple points. A third approach is to use a Statistical Paramet- ric Map (SPM) obtained from fMRI to improve EEG source estimation. In this approach, SPM information can be used either to constrain the spatial locations of the likely sources of EEG [Dale et al., 2000 Liu et al., 1998], or to initially seed dipoles within the active regions found in the SPM for further dipole fittings [Ahlfors et al., 1999 Auranen et al., 2009 Stancak �� et al., 2005]. Recently, fMRI SPM information was introduced into a Parametric Empir- ical Bayesian (PEB) framework for use in EEG source esti- mation [Friston et al., 2002 Phillips et al., 2002, 2005]. In practice, the hierarchical statistical model in PEB allows a variety of fMRI information to be introduced as priors, controlled by hyperparameters determined by scalp EEG data [Sato et al., 2004 Trujillo-Barreto et al., 2004]. Recent studies have shown that PEB-based EEG source imaging is a promising tool for reliable estimation of EEG sources [Henson et al., 2009], because it can utilize various priors from other modalities or assumptions. Both model- driven and data-driven methods can be used to obtain pri- ors from fMRI. However, a model-driven method such as the general linear model (GLM) requires an actual HRF to solve concrete problems. In contrast, a data-driven method allows the user to neglect the exact form of the response by relying upon an assumption of independence or ortho- gonality. In recent years, ICA, a data-driven approach, has been increasingly utilized to examine brain activation [Beckmann et al., 2005 Calhoun et al., 2009 Chen and Yao, 2004]. ICA is an intrinsically multivariate approach, and ICA component provides a grouping of active brain regions that share the same response pattern. Taken to- gether, ICA components thus provide us with temporally coherent networks (TCNs). fMRI has been used to identify TCNs during a resting state (resting state networks), and while participants perform cognitive tasks (task-related networks). In addition, ICA can simultaneously extract diverse functional networks while removing unexpected modulation effects induced by head motion, cardiac pulsa- tion or the respiration. In this study, we sought establish a framework for using multiple TCN patterns obtained by fMRI examination to facilitate EEG imaging. Our framework utilized ICA to iden- tify the multiple, widely distributed TCNs from fMRI. TCNs are then used as covariance components of a PEB model for EEG source imaging. We term this framework the NEtwork based SOurce Imaging (NESOI) approach. The main differ- ence between our method and previous PEB-based EEG source estimations methods is the utilization of multiple TCN priors instead of the various neuronal-anatomical smoothness, functional activation, or sparseness constraints, that are used in the Minimum Norm Model (MNM) [Tikho- nov and Arsenin, 1977], LOw-Resolution electromagnetic to- mography (LOR) [Pascual-Marqui, 2002], dynamic Statistical Parametric Mapping (dSPM) [Dale et al., 2000] and the Mul- tiple Sparse Prior model (MSP) [Friston et al., 2008]. The NESOI approach aims to generate accurate solutions by combining information of high temporal resolution from EEG, and TCNs derived from information of high spatial re- solution obtained by fMRI. METHODS Parametric Empirical Bayesian Model We used the following PEB model [Friston et al., 2008 Lei and Yao, 2009 Mattout et al., 2006 Phillips et al., 2002, 2005] for EEG imaging: Y �� Lh �� e1 e1eN��0 T C1�� h �� 0 �� e2 e2eN��0 T C2�� (1) where Y [ Rn3s is the EEG recording with n electrodes and s samples. L [ Rn3d is the known lead-field matrix, and y [ Rd3s is the unknown source dynamics for d dipoles. N(lT,C) denotes a multivariate Gaussian distribu- tion on a matrix, namely e $ N(lT,C) , vec(e) $ N(lT 3 C), with mean l and covariance T 3 C. vec denotes the column-stacking operator, and 3 is the Kronecker tensor product. The terms e1 and e2 represent random fluctuations in sensor and source spaces, respectively. The temporal correlations are denoted by T, which, for simplicity, is assumed to be fixed and known. The spatial covariances of e1 and e2 are mixtures of covariance components at each r Lei et al. r r 1142 r

level. In sensor space, we assume C1 a21In to encode the covariance of sensor noise, where In is the n-by-n identity matrix. In source space, we express this in a covariance component form: C2 �� Xk i��1 ciVi (2) where c : [c1,c2,. . .,ck]T is a vector of k non-negative hyperparameters that control the relative contribution of each covariance basis matrix, Vi. To ensure non-negativity of the hyperparameters, we used a log-transform ci exp(/i) and imposed a Gaussian hyperprior on / [/1,/2,. . .,/k]T as, /eN��s C��: (3) In Eq. (2), the hyperparameters c are unknown, and the components set, V �� {V1,V2, : : : ,Vk}, is assumed to be fixed and known. Such a formulation is extremely flexible, because a rich variety of candidate covariance bases can be easily combined in such a PEB framework using Eq. (2). We will briefly introduce some covariance constraints in the following sections (see [Wipf and Nagarajan, 2009] for a large number of other specific situations). Empirical Priors Once the lead-field and the form of spatial correlations of the sensor noises are given, the model is determined by the number and composition of the empirical priors related to the sources. We will explore these priors and the ensuing source space. The number of components could range from one (such as V �� {I} in the classical min- imum norm model MNM), to hundreds. Each component accounts for a certain compact spatial support [Friston et al., 2008]. Harrison et al. [2007] considered a LORETA- like [Pascual-Marqui, 2002] prior, LOR, with two covari- ance components V �� {I, G} to model independent and anatomic coherent sources, respectively, where G �� exp��rA�� �� ��q1 q2 : : : qd�� (4) is the Green function of an adjacency matrix, A, and repre- sents a spatial coherent prior. Matrix A with Aij [ [0,1] enc- odes the neighboring relationships among nodes of the cortical mesh in the source space [Harrison et al., 2007]. If j is the adjacent node with link to i, then Aij 1 otherwise, Aij 0. Here, the d mesh nodes are approximately uni- formly distributed over the cortex surface. G is usually approximated with the Taylor form as G % P 8 i��0 ri i! Ai, which ensures that only the first eight nearby neighbors are maintained to enforce the priors with compact and sparse supports on the cortical mesh nodes [Friston et al., 2008]. As a result, the ith column of G, qi, defines a subset of neighboring nodes, weighted by their surface proximity to their centre, the ith node. The smoothness parameter, r, can be regarded as an auto-regression coefficient varying between zero and one. This parameter is set to 0.6 in the current study [Friston et al., 2008]. On the basis of uniform sampling from the columns of the above coherence matrix, Friston et al. [2008] proposed a multiple sparse prior (MSP) model to describe activities in k patterns with the components as V �� fq1q1 T q2q2 T : : : qkqk Tg. In this framework, the conven- tional minimum norm prior, V �� I, indicates that the sour- ces are uncorrelated and widely distributed with equal amplitude. MSP has been shown to be a much better prior than MNM and LOR for EEG responses [Friston et al., 2008 Henson et al., 2009]. In addition to the above anatomical priors, other priors such as the functional activations derived from fMRI can also be considered in EEG source imaging [Dale et al., 2000 Liu et al., 1998 Phillips et al., 2002]. The dSPM approach, for example, adopts the fMRI SPM result obtained using a common GLM [Dale et al., 2000]. In dSPM, the off-diagonal terms of the covariance compo- nent, VdSPM in the source space, are set to 0.0, while the diagonal terms of VdSPM corresponding to supra-threshold nodes are assigned a weight of 1.0. Those to sub-threshold nodes are assigned a weight of 0.1. NEtworks SOurce Imaging The priors of LOR and MSP are based on the relation of anatomically spatially adjacent sources, where the neigh- boring nodes are assumed to have similar neuronal activ- ities. dSPM, in contrast, involves fMRI activation priors. However, TCNs, which exist both during a resting state and while performing a cognitive task, have not previ- ously been utilized as priors for EEG imaging. TCNs can involve cortical areas that are spatially distant. As thus, they differ from relations between spatially adjacent source information or local functional activation informa- tion. Our system of temporally coherent NESOI is a natu- ral extension of the above PEB framework, modified to include TCNs derived from the BOLD signal as priors. In the NESOI approach, the same PEB approach is used for suited EEG/fMRI recordings on the same subject within the same paradigm, regardless of whether the re- cording are simultaneous or conducted at different times. To obtain TCN priors, NESOI adopts ICA to group brain areas that share response patterns [Beckmann et al., 2005 Calhoun et al., 2009 Chen and Yao, 2004 Hyvarinen �� and Oja, 1997]. The spatial ICA decomposition of fMRI is implemented as: x �� BS (5) where x is an fMRI dataset. Columns represent the time series for voxels. S is the spatial independent components r Network EEG Source Imaging r r 1143 r