The EEG is a neurological diagnostic tool with high temporal resolution. However, when solving the EEG inverse problem, its localization accuracy is limited because of noise in measurements and available uncertainties of the conductivity value in the forward model evaluations. This paper proposes the reduced conductivity dependence (RCD) method for decreasing the localization error in EEG source analysis by limiting the propagation of the uncertain conductivity values to the solutions of the inverse problem. We redefine the traditional EEG cost function, and in contrast to previous approaches, we introduce a selection procedure of the EEG potentials. The selected potentials are, as low as possible, affected by the uncertainties of the conductivity when solving the inverse problem. We validate the methodology on the widely used three-shell spherical head model with a single electrical dipole and multiple dipoles as source model. The proposed RCD method enhances the source localization accuracy with a factor ranging between 2 and 4, dependent on the dipole location and the noise in measurements.
It is well known that the uncertain knowledge of the conductivity values of the head tissues has an important impact upon the accuracy of the electroencephalogram source reconstruction. Assuming a certain value of the conductivity often leads to high reconstruction error values when solving the inverse problem. It is possible to quantify the impact of multiple uncertain conductivity values on the localization accuracy. We propose an approach that reduces the impact of these multiple uncertainties on the reconstruction accuracy of the dipole parameters. This paper elaborates the numerical method and shows results of localization accuracy in a five-shell spherical head model. Sensitivity analysis, when considering multiple layers in the head model, shows the different scales of the influence of the various uncertain conductivity values on the potential values. We propose a cost function that reduces the impact of multiple uncertainties of the conductivity value on the electroencephalogram dipole reconstruction and two strategies for selecting potential values on the basis of the sensitivity analysis. Numerical simulations, when considering multiple uncertainties in the model, provide results with higher reconstruction accuracy compared with the case where only a single uncertainty is taken into account.
This paper proposes a modification of the subspace correlation cost function and the Recursively Applied and Projected Multiple Signal Classification (RAP-MUSIC) method for electroencephalography (EEG) source analysis in epilepsy. This enables to reconstruct neural source locations and orientations that are less degraded due to the uncertain knowledge of the head conductivity values. An extended linear forward model is used in the subspace correlation cost function that incorporates the sensitivity of the EEG potentials to the uncertain conductivity value parameter. More specifically, the principal vector of the subspace correlation function is used to provide relevant information for solving the EEG inverse problems. A simulation study is carried out on a simplified spherical head model with uncertain skull to soft tissue conductivity ratio. Results show an improvement in the reconstruction accuracy of source parameters compared to traditional methodology, when using conductivity ratio values that are different from the actual conductivity ratio.
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