Towards an Objective Evaluation of EEG/MEG Source Estimation Methods: The Linear Tool Kit

Abstract

The question "What is the spatial resolution of EEG/MEG?" can only be answered with many ifs and buts, as the answer depends on a large number of parameters. Here, we describe a framework for resolution analysis of EEG/MEG source estimation, focusing on linear methods. The spatial resolution of linear methods can be evaluated using the resolution matrix, which contains the point-spread and cross-talk functions (PSFs and CTFs), respectively. Both of them have to be taken into account for a full characterization of spatial resolution. They can be used to compute a range of quantitative resolution metrics, which should cover at the last three aspects of those functions: localization accuracy, spatial extent, and relative amplitude. Here, we first provide a tutorial-style introduction to resolution analysis of linear source estimation methods. We then apply these concepts to evaluate the benefit of combining EEG and MEG measurements, and to compare weighted and normalized L2-minimum-norm estimation and spatial filters. We confirm and extend previous results, showing that adding EEG to MEG improves spatial resolution, and that different methods offer different compromises among different resolution criteria. We hope that our approach will help EEG/MEG researchers in the interpretation of source estimation results, the design of new experiments, and the development of new MEG systems.

Cortical source imaging of resting-state MEG with a high resolution atlas: An evaluation of methods

“…There was a significant effect of algorithm on LE ( Figure 3D and Figure 4A, χ 2 = 55, p = 1.31 × 10 −10 ), with significant differences between all pairs of algorithms (p = 0.0012 for all pairwise tests) except for comparisons between wLCMV, sLORETA, and eLORETA (p = 1). As previously reported numerically (Pascual-Marqui et al, 2018;Hauk et al, 2019) and theoretically expected (Pascual-Marqui, 2007), eLORETA and sLORETA had zero localization error. Interestingly, wLCMV also had zero LE in our results.…”

“…Notable exceptions include dynamic statistical parameter mapping (dSPM) (Dale et al, 2000), LORETA (Pascual Marqui et al, 1994), and the empirical Bayesian beamformer (EBB) (Belardinelli et al, 2012). Comparisons between dSPM and sLORETA have been studied using resolution metrics (Hauk et al, 2011;Hedrich et al, 2017;Hauk et al, 2019) and simulated dipoles (Pascual-Marqui et al, 2018), generally finding that sLORETA outperforms dSPM in terms of localization error, leakage, and false positive activity. Similarly, in a variance explained analysis of resting-state MEG, LORETA performed similarly to the MNE solution .…”

“…The i'th column of R is called the point spread function of dipole i (PSF i ), which corresponds to the influence of activity at dipole i on the estimate at all dipoles in the source reconstruction. The localization error of dipole i (LE i ) (Hauk et al, 2019) is thus given by…”

“…leakage using a metric previously called 'spatial dispersion' (Hauk et al, 2019), but here called the spatial extent of cross talk (SECT) to avoid misinterpretation (see section 4.3 for a justification of this difference in naming convention). The SECT influencing dipole i is calculated as…”

“…Hence an algorithm optimized for task-based source localization is not necessarily optimal for resting-state source reconstruction, and it is currently no consensus on which algorithm to use for source space reconstruction of resting-state dynamics. Here, we address this question by analysing the variance of sensor space data explained by the source estimates and by analysing theoretical resolution properties (Hauk et al, 2019) of six widely used algorithms: the linearly constrained minimum variance (LCMV) beamformer (Van Veen et al, 1997) and its depth normalized counterpart (weighted LCMV, Hillebrand et al, 2012), three methods based on least-squares minimum norms under different prior assumptions of source covariance, namely the minimum norm estimate (MNE) (Hämäläinen and Ilmoniemi, 1994), weighted MNE (Fuchs et al, 1999;Lin et al, 2006), and eLORETA (Pascual-Marqui, 2007, 2009)), as well as a variance-normalized MNE, sLORETA (Pascual-Marqui, 2002).…”