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      Algorithmic procedures for Bayesian MEG/EEG source reconstruction in SPM ☆

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          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          The MEG/EEG inverse problem is ill-posed, giving different source reconstructions depending on the initial assumption sets. Parametric Empirical Bayes allows one to implement most popular MEG/EEG inversion schemes (Minimum Norm, LORETA, etc.) within the same generic Bayesian framework. It also provides a cost-function in terms of the variational Free energy—an approximation to the marginal likelihood or evidence of the solution. In this manuscript, we revisit the algorithm for MEG/EEG source reconstruction with a view to providing a didactic and practical guide. The aim is to promote and help standardise the development and consolidation of other schemes within the same framework. We describe the implementation in the Statistical Parametric Mapping (SPM) software package, carefully explaining each of its stages with the help of a simple simulated data example. We focus on the Multiple Sparse Priors (MSP) model, which we compare with the well-known Minimum Norm and LORETA models, using the negative variational Free energy for model comparison. The manuscript is accompanied by Matlab scripts to allow the reader to test and explore the underlying algorithm.

          Highlights

          • •

            We revisit the Bayesian source inversion algorithm for M/EEG source reconstruction.

          • •

            We provide a didactic and practical guide with software examples.

          • •

            The aim is to help standardize the development of other schemes.

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          Most cited references45

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          Low resolution electromagnetic tomography: a new method for localizing electrical activity in the brain.

          R.D Pascual-Marqui, C.M. Michel, D. Lehmann (1994)
          This paper presents a new method for localizing the electric activity in the brain based on multichannel surface EEG recordings. In contrast to the models presented up to now the new method does not assume a limited number of dipolar point sources nor a distribution on a given known surface, but directly computes a current distribution throughout the full brain volume. In order to find a unique solution for the 3-dimensional distribution among the infinite set of different possible solutions, the method assumes that neighboring neurons are simultaneously and synchronously activated. The basic assumption rests on evidence from single cell recordings in the brain that demonstrates strong synchronization of adjacent neurons. In view of this physiological consideration the computational task is to select the smoothest of all possible 3-dimensional current distributions, a task that is a common procedure in generalized signal processing. The result is a true 3-dimensional tomography with the characteristic that localization is preserved with a certain amount of dispersion, i.e., it has a relatively low spatial resolution. The new method, which we call Low Resolution Electromagnetic Tomography (LORETA) is illustrated with two different sets of evoked potential data, the first showing the tomography of the P100 component to checkerboard stimulation of the left, right, upper and lower hemiretina, and the second showing the results for the auditory N100 component and the two cognitive components CNV and P300. A direct comparison of the tomography results with those obtained from fitting one and two dipoles illustrates that the new method provides physiologically meaningful results while dipolar solutions fail in many situations. In the case of the cognitive components, the method offers new hypotheses on the location of higher cognitive functions in the brain.
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            Improved Localizadon of Cortical Activity by Combining EEG and MEG with MRI Cortical Surface Reconstruction: A Linear Approach.

            A M Dale, M I Sereno (1993)
            Abstract We describe a comprehensive linear approach to the problem of imaging brain activity with high temporal as well as spatial resolution based on combining EEG and MEG data with anatomical constraints derived from MRI images. The "inverse problem" of estimating the distribution of dipole strengths over the cortical surface is highly underdetermined, even given closely spaced EEG and MEG recordings. We have obtained much better solutions to this problem by explicitly incorporating both local cortical orientation as well as spatial covariance of sources and sensors into our formulation. An explicit polygonal model of the cortical manifold is first constructed as follows: (1) slice data in three orthogonal planes of section (needle-shaped voxels) are combined with a linear deblurring technique to make a single high-resolution 3-D image (cubic voxels), (2) the image is recursively flood-filled to determine the topology of the gray-white matter border, and (3) the resulting continuous surface is refined by relaxing it against the original 3-D gray-scale image using a deformable template method, which is also used to computationally flatten the cortex for easier viewing. The explicit solution to an error minimization formulation of an optimal inverse linear operator (for a particular cortical manifold, sensor placement, noise and prior source covariance) gives rise to a compact expression that is practically computable for hundreds of sensors and thousands of sources. The inverse solution can then be weighted for a particular (averaged) event using the sensor covariance for that event. Model studies suggest that we may be able to localize multiple cortical sources with spatial resolution as good as PET with this technique, while retaining a much finer grained picture of activity over time.
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              The magnetic lead field theorem in the quasi-static approximation and its use for magnetoencephalography forward calculation in realistic volume conductors.

              Guido Nolte (2003)
              The equation for the magnetic lead field for a given magnetoencephalography (MEG) channel is well known for arbitrary frequencies omega but is not directly applicable to MEG in the quasi-static approximation. In this paper we derive an equation for omega = 0 starting from the very definition of the lead field instead of using Helmholtz's reciprocity theorems. The results are (a) the transpose of the conductivity times the lead field is divergence-free, and (b) the lead field differs from the one in any other volume conductor by a gradient of a scalar function. Consequently, for a piecewise homogeneous and isotropic volume conductor, the lead field is always tangential at the outermost surface. Based on this theoretical result, we formulated a simple and fast method for the MEG forward calculation for one shell of arbitrary shape: we correct the corresponding lead field for a spherical volume conductor by a superposition of basis functions, gradients of harmonic functions constructed here from spherical harmonics, with coefficients fitted to the boundary conditions. The algorithm was tested for a prolate spheroid of realistic shape for which the analytical solution is known. For high order in the expansion, we found the solutions to be essentially exact and for reasonable accuracies much fewer multiplications are needed than in typical implementations of the boundary element methods. The generalization to more shells is straightforward.
              Article 0 comments Cited 366 times – based on 0 reviews     Review now
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                Author and article information

                Contributors
                J.D. López
                Journal
                Journal ID (nlm-ta): Neuroimage
                Journal ID (iso-abbrev): Neuroimage
                Title: Neuroimage
                Publisher: Academic Press
                ISSN (Print): 1053-8119
                ISSN (Electronic): 1095-9572
                Publication date PMC-release: 01 January 2014
                Publication date (Print): 01 January 2014
                Volume: 84
                Pages: 476-487
                Affiliations
                [a ]Departamento de Ingeniería Electrónica, Universidad de Antioquia, Medellín, Colombia
                [b ]Wellcome Trust Centre for Neuroimaging, University College London, London WC1N 3BG, UK
                [c ]Universidad Nacional de Colombia, Medellín, Colombia
                Author notes
                [* ]Corresponding author. josedavid@ 123456udea.edu.co
                Article
                Publisher ID: S1053-8119(13)00936-1
                DOI: 10.1016/j.neuroimage.2013.09.002
                PMC ID: 3913905
                PubMed ID: 24041874
                SO-VID: f069cb39-2fc4-4ae4-9576-94469f267fde
                Copyright © © 2013 The Authors
                License:

                Open Access under CC BY-NC-ND 3.0 license

                History
                Date accepted : 3 September 2013
                Categories
                Subject: Technical Note

                ScienceOpen disciplines: Neurosciences
                Keywords: meg/eeg inverse problem,multiple sparse priors,free energy,bayesian model selection
                Data availability:
                ScienceOpen disciplines: Neurosciences
                Keywords: meg/eeg inverse problem, multiple sparse priors, free energy, bayesian model selection

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