S Baillet

Publications of S Baillet

• Diffeomorphic Brain Registration Under Exhaustive Sulcal Constraints

  Authors: G. Auzias, O. Colliot, J.A. Glaunes, M. Perrot, J.-F. Mangin, A. Trouve, S. Baillet

  Medical Imaging, IEEE Transactions on. 07/2011;

  The alignment and normalization of individual brain structures is a prerequisite for group-level analyses of structural and functional neuroimaging data. The techniques currently available are eitherThe alignment and normalization of individual brain structures is a prerequisite for group-level analyses of structural and functional neuroimaging data. The techniques currently available are either based on volume and/or surface attributes, with limited insight regarding the consistent alignment of anatomical landmarks across individuals. This article details a global, geometric approach that performs the alignment of the exhaustive sulcal imprints (cortical folding patterns) across individuals. This DIffeomorphic Sulcal-based COrtical (DISCO) technique proceeds to the automatic extraction, identification and simplification of sulcal features from T1-weighted Magnetic Resonance Image (MRI) series. These features are then used as control measures for fully-3-D diffeomorphic deformations. Quantitative and qualitative evaluations show that DISCO correctly aligns the sulcal folds and gray and white matter volumes across individuals. The comparison with a recent, iconic diffeomorphic approach (DARTEL) highlights how the absence of explicit cortical landmarks may lead to the misalignment of cortical sulci. We also feature DISCO in the automatic design of an empirical sulcal template from group data. We also demonstrate how DISCO can efficiently be combined with an image-based deformation (DARTEL) to further improve the consistency and accuracy of alignment performances. Finally, we illustrate how the optimized alignment of cortical folds across subjects improves sensitivity in the detection of functional activations in a group-level analysis of neuroimaging data.

• Canonical correlation analysis applied to functional connectivity in MEG

  Authors: J.L.P. Soto, D. Pantazis, K. Jerbi, S. Baillet, R.M. Leahy

  Biomedical Imaging: From Nano to Macro, 2010 IEEE International Symposium on; 05/2010

  We present a multivariate method based on canonical correlation analysis for the study of functional connectivity in the brain with MEG data. We obtain a time-frequency representation of the brainWe present a multivariate method based on canonical correlation analysis for the study of functional connectivity in the brain with MEG data. We obtain a time-frequency representation of the brain activity on the cortical surface, and use the signal power at specific frequency bands as inputs to our model. Our measure of interaction between two spatial locations is the canonical correlation, and the vectors associated with it indicate the contribution of each individual frequency band to the interaction. The resulting canonical correlation maps are thresholded for significance using false discovery rate. We further provide a novel way to control for linear mixing by testing whether the correlation vectors are collinear. We apply our method to simulations and experimental data from an MEG visuomotor study, and demonstrate that it is able to detect functional interactions across space as well as the frequency bands that contribute to these interactions.

• A two-step imaging procedure for MEG characterization of cortical currents: Location and spatial extent

  Authors: S. Khan, B. Cottereau, R.M. Leahy, J.C. Mosher, H. Amman, S. Baillet

  Biomedical Imaging: From Nano to Macro, 2008. ISBI 2008. 5th IEEE International Symposium on; 06/2008

  There is theoretical and experimental evidence that the spatial extent of mass neural activity is an important factor of brain response in neuroimaging studies. Direct estimation of the surface areaThere is theoretical and experimental evidence that the spatial extent of mass neural activity is an important factor of brain response in neuroimaging studies. Direct estimation of the surface area of activated regions would importantly complement the quantitative analysis of amplitude variations of cortical currents. These latter are accessible at the regional scale through source modeling of magnetoencephalographic signals. Here we present a joint approach to the estimation of both the local spatial extent and amplitude variations of neural current sources. The technique operates in two consecutive steps: 1) the compact modeling of regional cortical currents using equivalent current multipoles and 2) the remapping of these latter back onto the cortical surface using a sparse-focal imaging model. This Multipole Cortical Remapping technique operates in a Bayesian framework. Performances are evaluated using extensive Monte-Carlo simulations and are complemented with real data from a somatosensory mapping MEG experiment.

• Cortical flow: Investigating the spatiotemporal dynamics of the brain

  Authors: J. Lefevre, S. Baillet

  Biomedical Imaging: From Nano to Macro, 2008. ISBI 2008. 5th IEEE International Symposium on; 06/2008

  Magneto- and electro-encephalography (MEG/EEG) offer probably the best trade-off between a superlative time resolution and a fair spatial one. At the scale of sensors, MEG/EEG signals reflect theMagneto- and electro-encephalography (MEG/EEG) offer probably the best trade-off between a superlative time resolution and a fair spatial one. At the scale of sensors, MEG/EEG signals reflect the global dynamic of the brain whereas sources imaging through inverse problem provide more regional behaviors. In both case, the data can be seen as spatiotemporal structures from which we can features such as optical flow, reflecting the amount of changes in the sequence of brain activations. After having recalled the theoretical basis of the so-called cortical flow, we present two applications in different experimental paradigms. We first show that our tool yields a temporal sequencing of brain events at a global scale. At last we focus on more local neural behaviors occurring in the visual cortex.

• Multi-scale diffeomorphic cortical registration under manifold sulcal constraints

  Authors: G. Auzias, J.-A. Glaunes, A. Cachia, P. Cathier, E. Bardinet, O. Colliot, J.-F. Mangin, A. Trouve, S. Baillet

  Biomedical Imaging: From Nano to Macro, 2008. ISBI 2008. 5th IEEE International Symposium on; 06/2008

  Neuroimaging at the group level requires spatial normalization across individuals. This issue has been receiving considerable attention from multiple research groups. Here we suggest a surface-basedNeuroimaging at the group level requires spatial normalization across individuals. This issue has been receiving considerable attention from multiple research groups. Here we suggest a surface-based geometric approach that consists in matching a set of cortical surfaces through their sulcal imprints. We provide the proof-of-concept of this approach by showing 1) how sulci may be automatically identified and simplified from Tl-weighted MRI data series, and 2) how this sulcal information may be considered as landmarks for recent measure-based diffeomorphic deformation approaches. In our framework, the resulting 3D transforms are naturally applied to the entire cortical surface and MRI volumes.

• Mapping and Tracking the Flow of Brain Activations using MEG/EEG: Hypothesis and Methods

  Authors: J. Lefevre, S. Baillet

  Noninvasive Functional Source Imaging of the Brain and Heart and the International Conference on Functional Biomedical Imaging, 2007. NFSI-ICFBI 2007. Joint Meeting of the 6th International Symposium on; 11/2007

  We introduce a mathematical tool for the exploration of spatiotemporal dynamics of brain activations as revealed by time-resolved brain mapping techniques. In that respect, Magneto (MEG) andWe introduce a mathematical tool for the exploration of spatiotemporal dynamics of brain activations as revealed by time-resolved brain mapping techniques. In that respect, Magneto (MEG) and Electroencephalography (EEG) source imaging has been considerably maturing in terms of leading access to the dynamics of brain activity. Here we suggest that the local analysis in space and time of the resulting source measures might be performed through the computation of a cortical displacement field within the optical flow framework. The theoretical principles of the method are briefly introduced and are subsequently illustrated by simulations. Finally, this technique was applied on brain image sequences from a ball-catching paradigm, in which significant structures of the resulting optical flow during the early brain response that accompanied the fall of the ball could be revealed.

• A MEG Multiresolution Model Selection Procedure Reveals the Cortical Somatotopy of Hand-Fingers

  Authors: B. Cottereau, K. Jerbi, S Baillet

  Noninvasive Functional Source Imaging of the Brain and Heart and the International Conference on Functional Biomedical Imaging, 2007. NFSI-ICFBI 2007. Joint Meeting of the 6th International Symposium on; 11/2007

  We introduce a new model selection procedure (MiMS) to the MEG source estimation problem, based on a multireso-lution approach. The technique uses an explicit piecewise image model of corticalWe introduce a new model selection procedure (MiMS) to the MEG source estimation problem, based on a multireso-lution approach. The technique uses an explicit piecewise image model of cortical currents that is iteratively updated through increasing spatial resolution according to the generalized cross-validation (GCV) error principle. The method is illustrated on MEG data testing for the somatotopic organization of early brain responses following stimulation of hand fingers. In addition to the canonical somatotopic organization of brain responses along the post-central gyrus, these data suggest that the MiMS approach could help revealing the spatial extent of mass-neural responses as a pertinent parameter of brain activation, in complement to measures of amplitude variations of cortical currents.

• Modeling and Detecting Deep Brain Activity with MEG & EEG

  Authors: Y. Attal, M. Bhattacharjee, J. Yelnik, B. Cottereau, J. Lefevre, Y. Okada, E. Bardinet, M. Chupin, S. Baillet

  Engineering in Medicine and Biology Society, 2007. EMBS 2007. 29th Annual International Conference of the IEEE; 09/2007

  We introduce an anatomical and electrophysiological model of deep brain structures dedicated to magnetoencephalography (MEG) and electroencephalography (EEG) source imaging. So far, most imagingWe introduce an anatomical and electrophysiological model of deep brain structures dedicated to magnetoencephalography (MEG) and electroencephalography (EEG) source imaging. So far, most imaging inverse models considered that MEG/EEG surface signals were predominantly produced by cortical, hence superficial, neural currents. Here we question whether crucial deep brain structures such as the basal ganglia and the hippocampus may also contribute to distant, scalp MEG and EEG measurements. We first design a realistic anatomical and electrophysiological model of these structures and subsequently run Monte-Carlo experiments to evaluate the respective sensitivity of the MEG and EEG to signals from deeper origins. Results indicate that MEG/EEG may indeed localize these deeper generators, which is confirmed here from experimental MEG data reporting on the modulation of alpha brain waves.

• Challenging the estimation of cortical activity from MEG with simulated fMRI-constrained retinotopic maps

  Authors: A. Gramfort, B. Cottereau, M. Clerc, B. Thirion, S. Baillet

  Engineering in Medicine and Biology Society, 2007. EMBS 2007. 29th Annual International Conference of the IEEE; 09/2007

  Detection of activity from the primary visual cortex is a difficult challenge to magneto-encephalography (MEG) source imaging techniques: the geometry of the visual cortex is intricate, withDetection of activity from the primary visual cortex is a difficult challenge to magneto-encephalography (MEG) source imaging techniques: the geometry of the visual cortex is intricate, with structured visual field maps extending deeper along the calcarine fissure. This questions the very sensitivity of MEG to the corresponding neural responses of visual stimuli and the usage of MEG source imaging for innovative retinotopic explorations. In this context, we compare two imaging models of MEG generators in realistic simulations of activations within the visual cortex. Localization and spatial extent of neural activity in the visual cortex were extracted from retinotopic maps obtained in fMRI. We prove that the suggested approaches are robust and succeed in accurately recovering the activation patterns with satisfactory match with fMRI results. These results suggest that fast retinotopic exploration of the visual cortex could be obtained from MEG as a complementary alternative to more standard fMRI approaches. The excellent time resolution of MEG imaging further opens interesting perspectives on the temporal and spectral processes sustained by the human visual system.

• Multiresolution imaging of neural currents from MEG data using an explicit piecewise image model

  Authors: B. Cottereau, K. Jerbi, S. Baillet

  Biomedical Imaging: Nano to Macro, 2006. 3rd IEEE International Symposium on; 05/2006

  MEG source imaging is an underdetermined inverse problem that suffers from a large number of unknown source parameters in realistic source settings. While linear source estimators offer poor spatialMEG source imaging is an underdetermined inverse problem that suffers from a large number of unknown source parameters in realistic source settings. While linear source estimators offer poor spatial resolution, most recent non-linear approaches still lead to untractable computational costs. We propose a new multiresolution approach using an explicit piecewise image model of the distribution of neural currents. At each spatial resolution, the ill-posedness of the iterative estimation procedure is reduced owing to a compact parametric current model for the mass neural activity of spatially-extended brain regions. This procedure can be considered as either an imaging approach per se, or a source-selection pre-processing step to more computationally-demanding estimators

• Functional brain mapping with high-temporal resolution: introducing evolutionary activation cells

  Authors: F. Gombert, S. Baillet

  Biomedical Imaging: Nano to Macro, 2006. 3rd IEEE International Symposium on; 05/2006

  Functional image sequences obtained from image reconstruction techniques applied to magneto and electroencephalography data convey a large amount of information in the space and time domains.Functional image sequences obtained from image reconstruction techniques applied to magneto and electroencephalography data convey a large amount of information in the space and time domains. Conventional approaches to their analysis necessitate considerable input from neuroscience experts to extract pertinent information. We introduce in this paper an automatic data sequencing procedure of these brain activation maps. Our main objective consists in facilitating and accelerating the extraction of spatiotemporal activation patterns of interest called activation cells. These cells are tracked across time with a consistent labeling strategy that follows a small set of predefined evolutionary scenarios. Resulting graphical synopsis are exemplified on the analysis of epileptic spike events and indicate satisfactory consistency with human expertise

• Investigations of dipole localization accuracy in MEG using the bootstrap.

  Authors: F Darvas, M. Rautiainen, D Pantazis, S Baillet, H Benali, J C Mosher, L Garnero, R.M. Leahy

  NeuroImage. 05/2005; 25(2):355-68.

  We describe the use of the nonparametric bootstrap to investigate the accuracy of current dipole localization from magnetoencephalography (MEG) studies of event-related neural activity. The bootstrapWe describe the use of the nonparametric bootstrap to investigate the accuracy of current dipole localization from magnetoencephalography (MEG) studies of event-related neural activity. The bootstrap is well suited to the analysis of event-related MEG data since the experiments are repeated tens or even hundreds of times and averaged to achieve acceptable signal-to-noise ratios (SNRs). The set of repetitions or epochs can be viewed as a set of independent realizations of the brain's response to the experiment. Bootstrap resamples can be generated by sampling with replacement from these epochs and averaging. In this study, we applied the bootstrap resampling technique to MEG data from somatotopic experimental and simulated data. Four fingers of the right and left hand of a healthy subject were electrically stimulated, and about 400 trials per stimulation were recorded and averaged in order to measure the somatotopic mapping of the fingers in the S1 area of the brain. Based on single-trial recordings for each finger we performed 5000 bootstrap resamples. We reconstructed dipoles from these resampled averages using the Recursively Applied and Projected (RAP)-MUSIC source localization algorithm. We also performed a simulation for two dipolar sources with overlapping time courses embedded in realistic background brain activity generated using the prestimulus segments of the somatotopic data. To find correspondences between multiple sources in each bootstrap, sample dipoles with similar time series and forward fields were assumed to represent the same source. These dipoles were then clustered by a Gaussian Mixture Model (GMM) clustering algorithm using their combined normalized time series and topographies as feature vectors. The mean and standard deviation of the dipole position and the dipole time series in each cluster were computed to provide estimates of the accuracy of the reconstructed source locations and time series.

• Localization of realistic cortical activity in MEG using current multipoles.

  Authors: K. Jerbi, S Baillet, J C Mosher, G Nolte, L Garnero, R.M. Leahy

  NeuroImage. 07/2004; 22(2):779-93.

  We present a novel approach to MEG source estimation based on a regularized first-order multipole solution. The Gaussian regularizing prior is obtained by calculation of the sample mean andWe present a novel approach to MEG source estimation based on a regularized first-order multipole solution. The Gaussian regularizing prior is obtained by calculation of the sample mean and covariance matrix for the equivalent moments of realistic simulated cortical activity. We compare the regularized multipole localization framework to the classical dipole and general multipole source estimation methods by evaluating the ability of all three solutions to localize the centroids of physiologically plausible patches of activity simulated on the surface of a human cerebral cortex. The results, obtained with a realistic sensor configuration, a spherical head model, and given in terms of field and localization error, depict the performance of the dipolar and multipolar models as a function of variable source surface area (50-500 mm(2)), noise conditions (20, 10, and 5 dB SNR), source orientation (0-90 degrees ), and source depth (3-11 cm). We show that as the sources increase in size, they become less accurately modeled as current dipoles. The regularized multipole systematically outperforms the single dipole model, increasingly so as the spatial extent of the sources increases. In addition, our simulations demonstrate that as the orientation of the sources becomes more radial, dipole localization accuracy decreases substantially, while the performance of the regularized multipole model is far less sensitive to orientation and even succeeds in localizing quasi-radial source configurations. Furthermore, our results show that the multipole model is able to localize superficial sources with higher accuracy than the current dipole. These results indicate that the regularized multipole solution may be an attractive alternative to current-dipole-based source estimation methods in MEG.

• Electromagnetic brain imaging using BrainStorm

  Authors: S. Baillet, J.C. Masher, R.M. Leahy

  Biomedical Imaging: Nano to Macro, 2004. IEEE International Symposium on; 05/2004

  Electromagnetic brain imaging consists of the mapping of neural generators of magnetic fields and electric potentials measured outside the head using magnetoencephalography (MEG) andElectromagnetic brain imaging consists of the mapping of neural generators of magnetic fields and electric potentials measured outside the head using magnetoencephalography (MEG) and electroencephalography (EEC), respectively. Here we report on a collaborative project dedicated to the development and distribution of BrainStorm, a software suite for MEG-EEG data modeling and visualization, with integration of MRI information. BrainStorm is developed in Matlab, which ensures OS portability and facilitated interoperability with many other research software resources. Distribution of BrainStorm is managed under GNU licensing, with no charge to users.

• Fusion of simultaneous fMRI/EEG data based on the electro-metabolic coupling

  Authors: P.-J. Lahaye, S. Baillet, J.-B. Poline, L. Garnero

  Biomedical Imaging: Nano to Macro, 2004. IEEE International Symposium on; 05/2004

  This paper presents an algorithm of data fusion for simultaneous EEG and fMRI recordings, which provides an estimation of 'neural' signals on the cortical surface. The technique described here isThis paper presents an algorithm of data fusion for simultaneous EEG and fMRI recordings, which provides an estimation of 'neural' signals on the cortical surface. The technique described here is applied on simulation data, and can be generically applied to any event-related paradigm. The main originality of this method relative to EEG source reconstruction techniques is to take into account the observed relationship between sources energy and the size of corresponding BOLD responses, for each source and across event occurrences, resulting in a better estimation of the sources' energy. In presence of an EEC/BOLD link, simulation studies show that the method proposed here 1) has better spatial discrimination 2) better estimates the temporal course of sources 3) better estimates the coherence of sources, relative to a similar method using EEG information only. The method is also robust to noise on fMRI and EEG. To our knowledge, this is the first attempt to take advantage of the temporal variability across events.

• Imaging cortical oscillations during sustained visuomotor coordination in MEG

  Authors: K. Jerbi, J.-P. Lachaux, S. Baillet, L. Garnero

  Biomedical Imaging: Nano to Macro, 2004. IEEE International Symposium on; 05/2004

  Cortical oscillations have been shown to play an important role in a wide range of neural activities. In particular, task-related changes in spectral power and task-related modulations of couplingCortical oscillations have been shown to play an important role in a wide range of neural activities. In particular, task-related changes in spectral power and task-related modulations of coupling both within and between neuronal assemblies in specific frequency bands have been reported. In the current study, we use magnetoencephalography (MEG) recordings to produce maps of task-related changes of spectral power in the alpha (8-15Hz), beta (15-30) and gamma (30-50Hz) range during a sustained visuomotor coordination task in which 4 subjects were asked to use a track-ball device to continuously counter the quasi-random rotations of a cube in a 3D environment. We use a wavelet-based method to compute and compare the time-frequency maps corresponding to the visuomotor task to those of the control conditions. We find that, compared to rest conditions, visuomotor coordination is associated with a sustained depression of spectral power in mu and beta bands over the sensorimotor cortex throughout the whole duration of the task (8 seconds) followed by a wide-band increase in power starting within 1 to 2 seconds after the end of the coordination task. The spatial distribution of the relative power changes in relevant frequency bands are computed and displayed as topographic images on a flattened sensor geometry.

• Automated interictal spike detection and source localization in magnetoencephalography using independent components analysis and spatio-temporal clustering.

  Authors: A. Ossadtchi, S Baillet, J C Mosher, D Thyerlei, W Sutherling, R.M. Leahy

  Clinical neurophysiology : official journal of the International Federation of Clinical Neurophysiology. 04/2004; 115(3):508-22.

  OBJECTIVE: Magnetoencephalography (MEG) dipole localization of epileptic spikes is useful in epilepsy surgery for mapping the extent of abnormal cortex and to focus intracranial electrodes. VisuallyOBJECTIVE: Magnetoencephalography (MEG) dipole localization of epileptic spikes is useful in epilepsy surgery for mapping the extent of abnormal cortex and to focus intracranial electrodes. Visually analyzing large amounts of data produces fatigue and error. Most automated techniques are based on matching of interictal spike templates or predictive filtering of the data and do not explicitly include source localization as part of the analysis. This leads to poor sensitivity versus specificity characteristics. We describe a fully automated method that combines time-series analysis with source localization to detect clusters of focal neuronal current generators within the brain that produce interictal spike activity. METHODS: We first use an ICA (independent components analysis) method to decompose the multichannel MEG data and identify those components that exhibit spike-like characteristics. From these detected spikes we then find those whose spatial topographies across the array are consistent with focal neural sources, and determine the foci of equivalent current dipoles and their associated time courses. We then perform a clustering of the localized dipoles based on distance metrics that takes into consideration both their locations and time courses. The final step of refinement consists of retaining only those clusters that are statistically significant. The average locations and time series from significant clusters comprise the final output of our method. RESULTS AND SIGNIFICANCE: Data were processed from 4 patients with partial focal epilepsy. In all three subjects for whom surgical resection was performed, clusters were found in the vicinity of the resectioned area. CONCLUSIONS: The presented procedure is promising and likely to be useful to the physician as a more sensitive, automated and objective method to help in the localization of the interictal spike zone of intractable partial seizures. The final output can be visually verified by neurologists in terms of both the location and distribution of the dipole clusters and their associated time series. Due to the clinical relevance and demonstrated promise of this method, further investigation of this approach is warranted.

• On MEG forward modelling using multipolar expansions.

  Authors: K. Jerbi, J C Mosher, S Baillet, R.M. Leahy

  Physics in medicine and biology. 03/2002; 47(4):523-55.

  Magnetoencephalography (MEG) is a non-invasive functional imaging modality based on the measurement of the external magnetic field produced by neural current sources within the brain. TheMagnetoencephalography (MEG) is a non-invasive functional imaging modality based on the measurement of the external magnetic field produced by neural current sources within the brain. The reconstruction of the underlying sources is a severely ill-posed inverse problem typically tackled using either low-dimensional parametric source models, such as an equivalent current dipole (ECD), or high-dimensional minimum-norm imaging techniques. The inability of the ECD to properly represent non-focal sources and the over-smoothed solutions obtained by minimum-norm methods underline the need for an alternative approach. Multipole expansion methods have the advantages of the parametric approach while at the same time adequately describing sources with significant spatial extent and arbitrary activation patterns. In this paper we first present a comparative review of spherical harmonic and Cartesian multipole expansion methods that can be used in MEG. The equations are given for the general case of arbitrary conductors and realistic sensor configurations and also for the special cases of spherically symmetric conductors and radially oriented sensors. We then report the results of computer simulations used to investigate the ability of a first-order multipole model (dipole and quadrupole) to represent spatially extended sources, which are simulated by 2D and 3D clusters of elemental dipoles. The overall field of a cluster is analysed using singular value decomposition and compared to the unit fields of a multipole, centred in the middle of the cluster, using subspace correlation metrics. Our results demonstrate the superior utility of the multipolar source model over ECD models in providing source representations of extended regions of activity.

• Segmentation of the amygdalo-hippocampal complex by competitive region growing [MRI analysis]

  Authors: M. Chupin, D Hasboun, F Poupon, S Baillet, L Garnero

  Biomedical Imaging, 2002. Proceedings. 2002 IEEE International Symposium on; 02/2002

  Semi-automatic segmentation of amygdala and hippocampus is of major interest to neurologists but it is a challenge to numerical image analysis techniques because of intrinsic complexity of thoseSemi-automatic segmentation of amygdala and hippocampus is of major interest to neurologists but it is a challenge to numerical image analysis techniques because of intrinsic complexity of those structures. We introduce a new method to approach this problem with Markovian region growing. As we are concerned by segmenting atrophic structures, we did not use shape priors, but constrained the growth with relational and weak geometric priors. The major relational constraint is given by the simultaneous segmentation of hippocampus and amygdala. The algorithm runs quickly on a basic workstation with satisfactory results on both structures.

• On MEG forward modelling using multipolar expansions

  Authors: K. Jerbi, J. ~C. Mosher, S. Baillet, R. ~M. Leahy

  Physics in Medicine and Biology. 01/2002; 47(4):523-555.

  Magnetoencephalography (MEG) is a non-invasive functional imaging modality based on the measurement of the external magnetic field produced by neural current sources within the brain. TheMagnetoencephalography (MEG) is a non-invasive functional imaging modality based on the measurement of the external magnetic field produced by neural current sources within the brain. The reconstruction of the underlying sources is a severely ill-posed inverse problem typically tackled using either low-dimensional parametric source models, such as an equivalent current dipole (ECD), or high-dimensional minimum-norm imaging techniques. The inability of the ECD to properly represent non-focal sources and the over-smoothed solutions obtained by minimum-norm methods underline the need for an alternative approach. Multipole expansion methods have the advantages of the parametric approach while at the same time adequately describing sources with significant spatial extent and arbitrary activation patterns. In this paper we first present a comparative review of spherical harmonic and Cartesian multipole expansion methods that can be used in MEG. The equations are given for the general case of arbitrary conductors and realistic sensor configurations and also for the special cases of spherically symmetric conductors and radially oriented sensors. We then report the results of computer simulations used to investigate the ability of a first-order multipole model (dipole and quadrupole) to represent spatially extended sources, which are simulated by 2D and 3D clusters of elemental dipoles. The overall field of a cluster is analysed using singular value decomposition and compared to the unit fields of a multipole, centred in the middle of the cluster, using subspace correlation metrics. Our results demonstrate the superior utility of the multipolar source model over ECD models in providing source representations of extended regions of activity.