This paper presents a novel approach for the estimation of frequency-specific EEG scale modulations by the directional anisotropy of the brain, using the Mellin transform [1, 2, 3]. In the case of epileptic sources, the activity recorded by routine scalp EEG includes contributions not only from a seizure's primary propagation path but also from secondary paths and unrelated to the seizure activity. In addition, the anisotropy of the brain directionally modulates the seizure-related signal component. We estimated patient-specific direction-specific, frequency-locked scale shifts. During the ictal interval, these shifts occurred at frequencies ≥50 Hz. We further estimated the effect of scale modulations on time-delay estimation. Larger time-delays were estimated from EEGs that had been corrected by a scale factor prior to this estimation. Thus, corrections for non-linear scaling of EEGs may ultimately improve time-delay estimation for source localization, particularly in cases of seizures rapidly propagating to large areas of the brain.
Localization of the seizure focus in the brain is a challenging problem in the field of epilepsy. The complexity of the seizure-related EEG waveform, its non-stationarity and degradation with distance due to the dispersive nature of the brain as a propagation medium, make localization difficult. Yet, precise estimation of the focus is critical, particularly when surgical resection is the only therapeutic option. The first step to solving this inverse problem is to estimate and account for frequency- or mode-specific signal dispersion, which is present in both scalp and intracranial EEG recordings during seizures. We estimated dispersion curves in both types of signals using a spatial correlation method and mode-based semblance analysis. We showed that, despite the assumption of spatial stationarity and a simplified array geometry, there is measurable inter-modal and intra-modal dispersion during seizures in both types of EEG recordings, affecting the estimated arrival times and consequently focus localization.
Distance-preserving dimension reduction techniques can fail to separate elements of different classes when the neighborhood structure does not carry sufficient class information. We introduce a new visual technique, K-epsilon diagrams, to analyze dataset topological structure and to assess whether intra-class and inter-class neighborhoods can be distinguished.We propose a force feature space data transform that emphasizes similarities between same-class points and enhances class separability. We show that the force feature space transform combined with distance-preserving dimension reduction produces better visualizations than dimension reduction alone. When used for classification, force feature spaces improve performance of K-nearest neighbor classifiers. Furthermore, the quality of force feature space transformations can be assessed using K-epsilon diagrams.
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