The Neuroelectromagnetic Inverse Problem and the Zero Dipole Localization Error

Abstract

A tomography of neural sources could be constructed from EEG/MEG recordings once the neuroelectromagnetic inverse problem (NIP) is solved. Unfortunately the NIP lacks a unique solution and therefore additional constraints are needed to achieve uniqueness. Researchers are then confronted with the dilemma of choosing one solution on the basis of the advantages publicized by their authors. This study aims to help researchers to better guide their choices by clarifying what is hidden behind inverse solutions oversold by their apparently optimal properties to localize single sources. Here, we introduce an inverse solution (ANA) attaining perfect localization of single sources to illustrate how spurious sources emerge and destroy the reconstruction of simultaneously active sources. Although ANA is probably the simplest and robust alternative for data generated by a single dominant source plus noise, the main contribution of this manuscript is to show that zero localization error of single sources is a trivial and largely uninformative property unable to predict the performance of an inverse solution in presence of simultaneously active sources. We recommend as the most logical strategy for solving the NIP the incorporation of sound additional a priori information about neural generators that supplements the information contained in the data.

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

“…These nonlinear methods are hard to evaluate in a generalizable way, and their results strongly depend on the validity of the underlying assumptions (Krishnaswamy et al, 2017). For example, perfect performance for point sources in isolation does not directly imply perfect performance for multiple simultaneously active sources (Grave de Peralta, Hauk, & Gonzalez, 2009). The simulation setups for non-linear methods have to be chosen and evaluated carefully in order to represent source scenarios that can be realistically assume to underlie measure brain activity in certain types of experiments.…”

Hierarchical Bayesian inference for the EEG inverse problem using realistic FE head models: Depth localization and source separation for focal primary currents

“…This is a well-known systematic error (e.g., Ahlfors et al, 1992;Gencer and Williamson, 1998;Wang et al, 1992) and was subject of many studies (e.g., Fuchs et al, 1999;Grave de Peralta et al, 2009;Greenblatt et al, 2005;Ioannides et al, 1990;Lin et al, 2006;Pascual-Marqui, 1999, 2002Sekihara et al, 2005;Wagner et al, 2004). The depth bias can be a crucial error, e.g., in the presurgical functional mapping of the eloquent cortex (Schiffbauer et al, 2002).…”

“…However, it is important to stress that the above results were only attained for the specific source scenario examined in this study. Without further examination, their significance might be very limited because the ability to localize single dipoles is a rather trivial and a largely uninformative property, as shown by Grave de Peralta et al (2009). Nevertheless, reconstructing single dipoles is a starting test for every inverse method for CDR, and the results for the methods based on the HBM clearly motivate the examination of their use in more detail.…”

MEG-guided analysis of 7T-MRI in patients with epilepsy

“…The (partial) mismatch between MEG and possible 7T MRI abnormalities might reflect the intrinsic limitation of MEG analysis, being based upon determining the source of a signal using a mathematical model, trying to explain the recorded signal given a certain number of assumptions and limitations [30,47]; the inverse problem (as already first described in 1847 [48]). Convexity source localization errors of up to 2 cm are reported using MEG [49].…”