A systematic data-driven approach to analyze sensor-level EEG connectivity: Identifying robust phase-synchronized network components using surface Laplacian with spectral-spatial PCA

Although conventional averaging across predefined frequency bands reduces the complexity of EEG functional connectivity (FC), it obscures the identification of resting-state brain networks (RSN) and impedes accurate estimation of FC reliability. Extending prior work, we combined scalp current source density (CSD; spherical spline surface Laplacian) and spectral-spatial PCA to identify FC components. Phase-based FC was estimated via debiased weighted phase-locking index from CSD-transformed resting EEGs (71 sensors, 8 min, eyes open/closed, 35 healthy adults, 1-week retest). Spectral PCA extracted 6 robust alpha and theta factors (86.6% variance). Subsequent spatial PCA for each spectral factor revealed seven robust regionally-focused (posterior, central, frontal) and long-range (posterior-anterior) alpha components (peaks at 8, 10 and 13 Hz) and a midfrontal theta (6 Hz) component, accounting for 37.0% of FC variance. These spatial FC components were consistent with well-known networks (e.g., default mode, visual, sensorimotor), and four were sensitive to eyes open/closed conditions. Most FC components had good-to-excellent internal consistency (odd/even epochs, eyes open/closed) and test-retest reliability (ICCs ≥ .8). Moreover, the FC component structure was generally present in subsamples (session x odd/even epoch, or smaller subgroups [n = 7-10]), as indicated by similarity of factor loadings across PCA solutions. Apart from systematically reducing FC dimensionality, our approach avoids arbitrary thresholds and allows quantification of meaningful and reliable network components that may prove to be of high relevance for basic and clinical research applications.

Analysis of Minimal Channels Electroencephalography for Wearable BCI: Development and Usability Study (Preprint)

BACKGROUND Electroencephalography (EEG) is a non-invasive Brain Computer Interface (BCI) technology that has shown potential in various healthcare applications such as epilepsy treatment, sleep disorder diagnosis, and stroke rehabilitation. Usually these applications require multi-channels EEG. However, multi-channel EEG headset setup process is time consuming. This may result in low patients’ acceptance despite BCI potential benefits. OBJECTIVE To investigate the number of appropriate electrodes, which could be crucial for successful applications of BCI in wearable devices. METHODS Motor Imagery (MI) classification system is used for our analysis. Different number of EEG channels was selected. EEG Multi-frequency features were extracted by Filter Bank (FB). Support Vector Machine (SVM) was used in classifying left and right hand opening/closing MI task. RESULTS The results showed that the group of nine electrodes gave high classification accuracy while requiring moderate set-up time, and hence is suggested as the minimal number of channels. Spherical spline interpolation (SSI) was also applied to investigate the feasibility of generating EEG signal from limited channels of EEG headset. The classification accuracies of the interpolated groups only, and the combined interpolated and collected group, were significantly lower than those of measured groups CONCLUSIONS For wearable device, one of the key factors that need to be concerned is wearability. The number of channels of EEG device adversely affects to set-up time. With FB feature and session dependent training, the investigation of number of channels provides the possibility to develop a successful BCI application using minimal channels EEG device. Interpolation technique which could approximate additional electrode data from nearby electrodes should be also explored.

Virtual EEG-electrodes: Convolutional neural networks as a method for upsampling or restoring channels

ABSTRACTBackgroundIn clinical practice, EEGs are assessed visually. For practical reasons, recordings often need to be performed with a reduced number of electrodes and artifacts make assessment difficult. To circumvent these obstacles, different interpolation techniques can be utilized. These techniques usually perform better for higher electrode densities and values interpolated at areas far from electrodes can be unreliable. Using a method that learns the statistical distribution of the cortical electrical fields and predicts values may yield better results.New MethodGenerative networks based on convolutional layers were trained to upsample from 4 or 14 channels or to dynamically restore single missing channels to recreate 21 channel EEGs. 5,144 hours of data from 1,385 subjects of the Temple University Hospital EEG database were used for training and evaluating the networks.Comparison with Existing MethodThe results were compared to spherical spline interpolation. Several statistical measures were used as well as a visual evaluation by board certified clinical neurophysiologists. Overall, the generative networks performed significantly better. There was no difference between real and network generated data in the number of examples assessed as artificial by experienced EEG interpreters whereas for data generated by interpolation, the number was significantly higher. In addition, network performance improved with increasing number of included subjects, with the greatest effect seen in the range 5 – 100 subjects.ConclusionsUsing neural networks to restore or upsample EEG signals is a viable alternative to interpolation methods.

Construction of spline curves on smooth manifolds by action of Lie groups

Polynomials for blending parametric curves in Lie groups are defined. Properties of these polynomials are proved. Blending parametric curves in Lie groups with these polynomials is considered. Then application of the proposed technique to construction of spline curves on smooth manifolds is presented. As an example, construction of spherical spline curves using the proposed approach is depicted.

Spherical Spline Application to Radio Occultation Data

Spherical Spline Application to Radio Occultation DataIn recent years, the importance of the Radio Occultation Method (ROM), an observation procedure of atmospheric quantities such as temperature, density, pressure, and water vapor, increased in value. Based on the global distribution and the high accuracy of the measurements between the Earth's surface up to 35km altitude, ROM offers new perspectives for climate monitoring. In order to compare the measurements, the data have to be visualized. This paper gives the basic definitions and theorems of spline approximation on the sphere. Via its adjustable smoothing parameters, ROM can be suitably adapted to approximate the given data. Further on, it demonstrates, splines as approximation structures realizing a minimal bending energy of their graphs provide a good approximation of the data at hand. Our results demonstrate that spherical spline approximation is an appropriate method to visualize the change over time of a given layer and to illustrate the vertical composition of the Earth's atmosphere. Moreover, ROM enables us to compare the layers of the atmosphere at different points in time as well as the approximation of parameters between the measurements on arbitrary points on the Earth.