Estimation of the electric conductivity from scalp measurements: feasibility and application to source localization.

OBJECTIVES: The accuracy of electrical impedance tomography was investigated. METHODS: The conductivities of the different compartments of the volume conductor were estimated by utilizing the boundary element method. The approach was tested for realistic head models with either 3 or 4 compartments. The impact of a geometrical error in the head model was investigated and the estimated conductivities were assigned to the compartments of the volume conductor used for the source imaging. The localization errors were quantified. RESULTS: The method used allowed the estimation of the conductivity of the compartments. The poor conductivity of the skull decreased the precision with which the conductivity of deeper structures could be estimated. A geometrical error in the head model was compensated by the estimated conductivities. However, the estimated conductivities did not cancel the geometrical error in the head model as localization errors of the order of 10-20 mm were obtained. CONCLUSIONS: In principle, the conductivity estimation of the distinct regions in the head is possible. The application of conductivity estimation to increase the accuracy of source localization remains questionable.

Functional imaging of postmovement beta event-related synchronization.

The linear estimation (LE) and spline surface Laplacian (SL) method were applied to single-trial EEG data. EEG was recorded in three subjects during voluntary, self-paced movements of the index finger. The EEG data were bandpass-filtered in the lower beta frequency range and showed short-lasting bursts of oscillations after termination of movement. These oscillations are termed postmovement beta synchronization. The realistic head geometry and the digitized positions of the electrodes were taken into account for accurate modeling of the anatomy. Regularization of the LE method was achieved by the truncated singular value decomposition. The LE and SL distribution of the postmovement beta synchronization showed similar spatial and temporal patterns. A clear increase of the LE source activity was found over the primary motor area. These results indicate that the postmovement beta synchronization is generated over the anterior bank of the central sulcus.

EEG and implanted sources in the brain.

Localisation procedures are based on models of the EEG that are relatively simple. The models are based on assumptions and choices of parameters that can be mistaken. Thus, it is crucial to validate the localisation procedures used in EEG. One of the options is to use the data obtained with electrodes that are implanted within the brain of an epileptic patient as part of the pre-surgical evaluation. When one of two neighbouring electrodes is used as a current source and the other as a current sink this can be regarded as a current dipole. The current injected has to be below the threshold for activation of cells. The position of this dipole can be deduced from magnetic resonance or X-ray images. The current dipole gives rise to a potential distribution at the scalp that can be measured by EEG. The measurements can be compared with the potential distribution that is calculated in a forward computation. Another method is to use the measured potential at the scalp to localize the source and to compare the result with the actual position of the dipole. In this paper the measured potential distributions at the scalp due to implanted dipoles were used to evaluate different volume conductor models. Since intracerebral and subdural electrodes were introduced through trephine holes over the fronto-central areas, and the diameter of the holes was rather large, approximately 23 mm, special effort was put into modelling the skull. Two important assumptions could be validated in this study: the electric currents within the head are Ohmic and a dipole can be used to model the induced electric activity of pairs of contacts on subdural electrodes or intra cerebral electrodes.

Post-movement beta oscillations studied with linear estimation.

The application of surface laplacian and linear estimation methods to single trial EEG data was studied. EEG was recorded in 3 subjects during voluntary, self-paced extensions and flexions of the index finger. In each subject a post-movement beta synchronisation was found in specific frequency bands. The surface laplacian estimates were calculated using spherical splines and cortical current distributions were constructed using the linear estimation method. Both methods yield similar results and reveal a maximal event-related synchronisation over the left sensorimotor area approximately 500-750 ms after termination of movement.

Post-movement EEG synchronization studied with different high resolution methods.

In this paper we present a study of spline surface Laplacian (LP), linear estimation (LE) and analytical deblurring (AD) utilized to improve the spatial resolution of single trial EEG data. AD is a method to reconstruct the potential distribution on the cortical surface. The dependency of AD on the electrode grid size as well as the sensitivity to uncorrelated noise and errors in the volume conductor model are investigated in detail and compared with LP. Finally, all methods (LP,LE and AD) are applied to single trial EEG data recorded in three subjects during voluntary and self-paced extension and flexion movements of the right index finger. In each subject postmovement beta oscillations were found in specific frequency bands. Cortical dipolar source strengths were reconstructed by LE and cortex potentials were estimated with AD. Both results are compared with LP calculated from the scalp EEG. All methods, although having different theoretical basis, yield similar results and reveal a maximal event-related synchronization over the left sensorimotor area approximately 500-875 ms after termination of the movement.