A general linear model for MEG beamformer imaging

A new general linear model (GLM) beamformer method is described for processing magnetoencephalography (MEG) data. A standard nonlinear beamformer is used to determine the time course of neuronal activation for each point in a predefined source space. A Hilbert transform gives the envelope of oscillatory activity at each location in any chosen frequency band (not necessary in the case of sustained (DC) fields), enabling the general linear model to be applied and a volumetric T statistic image to be determined. The new method is illustrated by a two-source simulation (sustained field and 20 Hz) and is shown to provide accurate localization. The method is also shown to locate accurately the increasing and decreasing gamma activities to the temporal and frontal lobes, respectively, in the case of a scintillating scotoma. The new method brings the advantages of the general linear model to the analysis of MEG data and should prove useful for the localization of changing patterns of activity across all frequency ranges including DC (sustained fields).

Introduction

In recent years, beamformer techniques have been used to improve spatial localization in magnetoencephalography (MEG). See, for example, Dziewas et al., (2003), Gaetz and Cheyne (2003), Hashimoto et al., 2001a, Hashimoto et al., 2001b, Herdman et al., (2003), Hirata et al., (2002), Ihara et al., (2003), Ishii et al., 1999, Ishii et al., 2002, Ishii et al., 2003, Iwaki et al., (1999), Kamada et al., (1998), Ploner et al., (2002), Robinson and Vrba (1999), Robinson et al., (2002), Sekihara et al., 2001, Sekihara et al., 2002, Taniguchi et al., (2000), Ukai et al., (2002), van Drongelen et al., (1996), van Veen et al., (1997), Xiang et al., (2001, 2003), Hall et al., (2004), Hillebrand and Barnes (2003), Fawcett et al., (2004), and Furlong et al., (2004). In essence, a beamformer is a collection of spatial filters, each optimally tuned to a particular image voxel (Van Veen et al., 1997). Raw MEG data are projected through these spatial filters to obtain an estimate of electrical activity at each voxel. Some metric can then be applied to assess task-related change in electrical activity and, by applying it to all voxels, a spatial map of task-related change can be generated.

Typically, metrics comprise simple two-sample tests that compare the source power between predefined active and passive time–frequency windows (Barnes and Hillebrand, 2003, Vrba, 2002). A widely used nonlinear beamformer method in MEG is synthetic aperture magnetometry (SAM) (Robinson and Vrba, 1999). SAM can be used to create statistical parametric maps (SPMs) showing the spatial distribution of cortical power change. This is achieved by integrating power in specified frequency bands over active and passive time windows. By subtracting source power in the passive time window from source power in the active time window and dividing the result by an estimate of noise magnitude, a pseudo T statistic may be obtained (Robinson and Vrba, 1999, see also Discussion) for each vertex in a 3D lattice stretching across the source space. These pseudo-T statistics can then be used to create 3D volumetric images of power change across the brain. This use of SAM has greatly enhanced the potential of MEG as a functional brain imaging technique. In addition, a recent SAM study (Singh et al., 2002) has demonstrated that a striking similarity exists between the spatial distribution of oscillatory power change and the fMRI BOLD response.

Despite these successes, simple two-sample tests do not allow for complex experimental designs where, for example, the hypothesis involves the covariation of oscillatory power with some physiological metric (such as galvanic skin response). Nor does it allow for investigation of covariant temporal behavior in different frequency bands (Friston, 2000). Also, despite recent reports (Forss et al., 2001; Lammertmann and Lutkenhoner, 2000) demonstrating that low-frequency sustained field effects are observable in MEG studies, spatially mapping such fields using SAM has proved difficult. In this study, we generalize the beamformer methodology through application of the formalism of the general linear model (GLM) (Friston et al., 1996, Seber, 1977, Worsley and Friston, 1995). We demonstrate the method using simulations, showing that it can be used to obtain the spatial distribution of both low-frequency sustained fields as well as changes in oscillatory electrical activity. We go on to show the utility of the technique using experimental data through the identification of linear modulation in gamma oscillations in a scintillating scotoma study (Hall et al., 2004).