Model‐Based Analysis and Optimization of the Mapping of Cortical Sources in the Spontaneous Scalp EEG

Abstract

The mapping of brain sources into the scalp electroencephalogram (EEG) depends on volume conduction properties of the head and on an electrode montage involving a reference. Mathematically, this source mapping (SM) is fully determined by an observation function (OF) matrix. This paper analyses the OF-matrix for a generation model for the desynchronized spontaneous EEG. The model involves a four-shell spherical volume conductor containing dipolar sources that are mutually uncorrelated so as to reflect the desynchronized EEG. The reference is optimized in order to minimize the impact in the SM of the sources located distant from the electrodes. The resulting reference is called the localized reference (LR). The OF-matrix is analyzed in terms of the relative power contribution of the sources and the cross-channel correlation coefficient for five existing references as well as for the LR. It is found that the Hjorth Laplacian reference is a fair approximation of the LR, and thus is close to optimum for practical intents and purposes. The other references have a significantly poorer performance. Furthermore, the OF-matrix is analyzed for limits to the spatial resolution for the EEG. These are estimated to be around 2 cm.

An investigation of the phase locking index for measuring of interdependency of cortical source signals recorded in the EEG

“…Although each electrode reflects primarily a signal of a source located exactly below the electrode (we assume that most of the neurons in the excited cortical area are oriented towards the surface, which is a reasonable assumption ( Nunez et al 1997 ), crosstalk from other sources exists that is caused by propagation of their signals through biological tissues of the head in the form of electrical fields. The amount of crosstalk can be substantially reduced by a proper choice of the EEG reference, but it can remain sufficiently large to obscure measurements ( Nunez et al 1997 ; Sazonov et al 2007a ).…”

“…The VC has four layers with different conductivities which mimic the brain, dura, skull, and skin. The VC is described in detail in ( Sazonov et al 2007a ). The sources are located at 17mm depth from the surface of the VC, exactly below the positions corresponding to the basic 19 electrodes of the standard 10–20 system.…”

“…EEG signals c q , q = 1, 2 are obtained by solving the forward problem and using the Hjorth Laplacian reference so as to mimic the EEG recording procedure. The Hjorth Laplacian reference ( Hjorth 1975 ) effectively reduces the impact of the sources located distant to the recording electrodes, is easy to implement, and is widely used ( Nunez et al 1997 ; Sazonov et al 2007a ).…”

“… The influence of crosstalk between the sources through biological tissues of the head, known as the volume conduction effect, has not been evaluated. (Although the impact of the sources located distant from the electrodes can be reduced, e.g., by a proper choice of the EEG reference, some residual amount of crosstalk is always present that may significantly affect measurements ( Nunez et al 1997 ; Sazonov et al 2007a ; Guevara et al 2005 ). No rigorous comparison of the PLI with other (classical) measures of the interdependency such as those based on the correlation function or on the coherence function has yet been reported.…”