The choice of the source space and the Laplacian matrix in LORETA and the spatio-temporal Kalman filter EEG inverse methods

Abstract

The discretization of the brain and the definition of the Laplacian matrix influence the results of methods based on spatial and spatio-temporal smoothness, since the Laplacian operator is used to define the smoothness based on the neighborhood of each grid point. In this paper, the results of low resolution electromagnetic tomography (LORETA) and the spatiotemporal Kalman filter (STKF) are computed using, first, a greymatter source space with the standard definition of the Laplacian matrix and, second, using a whole-brain source space and a modified definition of the Laplacian matrix. Electroencephalographic (EEG) source imaging results of five inter-ictal spikes from a pre-surgical patient with epilepsy are used to validate the two aforementioned approaches. The results using the whole-brain source space and the modified definition of the Laplacian matrix were concentrated in a single source activation, stable, and concordant with the location of the focal cortical dysplasia (FCD) in the patient's brain compared with the results which use a grey-matter grid and the classical definition of the Laplacian matrix. This proof-of-concept study demonstrates a substantial improvement of source localization with both LORETA and STKF and constitutes a basis for further research in a large population of patients with epilepsy.

Source imaging of deep-brain activity using the regional spatiotemporal Kalman filter

“…The SNR values of the five selected spikes are 7.45, 11.74, 9.33, 13.28, and 6.26, respectively [28]. The dominant electrodes for the first and fifth spikes were F7 and AF7.…”

“…Additionally, the EEG data was re-referenced to the common average reference before applying LORETA, STKF or RSTKF. For every spike, the SNR was calculated as described in [28,44]. The (negative) peak to (positive) peak amplitude of the spike, which is defined to fall within 175 ms around the spike peak, at the dominant electrode was calculated and divided by the root mean square (rms) value of the background activity of the same electrode, which occurs in the 300 ms preceding the spike duration (175 ms around the spike peak).…”

“…Unlike the methods that rely on dynamic lead field mapping or the DBA forward model, RSTKF uses a standard forward model based on a 3D volumetric grid. LORETA and STKF may suffer from the choice of the 3D grid or the definition of the Laplacian matrix [27,28]. The RSTKF, however, does not seem to be affected by these factors.…”

“…In addition to the grid choice, we used only the classical definition of the Laplacian matrix in this study since it results in a non-singular Laplacian matrix. The use of this Laplacian matrix, however, suppresses the activity at the borders of the grid, since it always assumes the presence of six neighbors to each grid point, which is not true for grid points at the borders of the grid [28,64]. The use of the six neighbors in the x, y, and z directions was also chosen because it is common in these kinds of studies.…”

“…Since both LORETA and STKF use spatial smoothness constraints, we consider it useful to compare their performance, in order to ascertain the additional advantages of temporal smoothness in the STKF model. In previous work, the original STKF model was found to be superior to LORETA with respect to the localization of sources of alpha rhythms, epileptiform discharges, and focal seizures from EEG recordings [27][28][29][30][31][32]. When applied to localize sources of a focal seizure from an EEG recording, STKF showed more accurate and consistent localizations of the seizure onset, compared to LORETA [27].…”