Interaction patterns of brain activity across space, time and frequency. Part I: methods

We consider exploratory methods for the discovery of cortical functional connectivity. Typically, data for the i-th subject (i=1...NS) is represented as an NVxNT matrix Xi, corresponding to brain activity sampled at NT moments in time from NV cortical voxels. A widely used method of analysis first concatenates all subjects along the temporal dimension, and then performs an independent component analysis (ICA) for estimating the common cortical patterns of functional connectivity. There exist many other interesting variations of this technique, as reviewed in [Calhoun et al. 2009 Neuroimage 45: S163-172]. We present methods for the more general problem of discovering functional connectivity occurring at all possible time lags. For this purpose, brain activity is viewed as a function of space and time, which allows the use of the relatively new techniques of functional data analysis [Ramsay & Silverman 2005: Functional data analysis. New York: Springer]. In essence, our method first vectorizes the data from each subject, which constitutes the natural discrete representation of a function of several variables, followed by concatenation of all subjects. The singular value decomposition (SVD), as well as the ICA of this new matrix of dimension [rows=(NT*NV); columns=NS] will reveal spatio-temporal patterns of connectivity. As a further example, in the case of EEG neuroimaging, Xi of size NVxNW may represent spectral density for electric neuronal activity at NW discrete frequencies from NV cortical voxels, from the i-th EEG epoch. In this case our functional data analysis approach would reveal coupling of brain regions at possibly different frequencies.Comment: Technical report 2011-March-15, The KEY Institute for Brain-Mind Research Zurich, KMU Osak

Adaptive estimation of spectral densities via wavelet thresholding and information projection

In this paper, we study the problem of adaptive estimation of the spectral density of a stationary Gaussian process. For this purpose, we consider a wavelet-based method which combines the ideas of wavelet approximation and estimation by information projection in order to warrants that the solution is a nonnegative function. The spectral density of the process is estimated by projecting the wavelet thresholding expansion of the periodogram onto a family of exponential functions. This ensures that the spectral density estimator is a strictly positive function. Then, by Bochner's theorem, the corresponding estimator of the covariance function is semidefinite positive. The theoretical behavior of the estimator is established in terms of rate of convergence of the Kullback-Leibler discrepancy over Besov classes. We also show the excellent practical performance of the estimator in some numerical experiments

Estimation nonparamétrique de la structure de covariance des processus stochastiques

TOULOUSE3-BU Sciences (315552104) / SudocSudocFranceF

Effects of Neurofeedback on the Working Memory of Children with Learning Disorders—An EEG Power-Spectrum Analysis

Learning disorders (LDs) are diagnosed in children impaired in the academic skills of reading, writing and/or mathematics. Children with LDs usually exhibit a slower resting-state electroencephalogram (EEG), corresponding to a neurodevelopmental lag. Frequently, children with LDs show working memory (WM) impairment, associated with an abnormal task-related EEG with overall slower EEG activity (more delta and theta power, and less gamma activity in posterior sites). These EEG patterns indicate inefficient neural resource management. Neurofeedback (NFB) treatments aimed at normalizing the resting-state EEG of LD children have shown improvements in cognitive-behavioral indices and diminished EEG abnormalities. Given the typical findings of WM impairment in children with LDs, we aimed to explore the effects of an NFB treatment on the WM of children with LDs by analyzing the WM-related EEG power spectrum. EEGs of 18 children (8–11 y.o.) with LDs were recorded, pre- and post-treatment, during performance of a Sternberg-type WM task. Thirty sessions of an NFB treatment (NFB-group, n = 10) or 30 sessions of a placebo-sham treatment (sham-group, n = 8) were administered. We analyzed the before and after treatment group differences for the behavioral performance and the WM-related EEG power spectrum. The NFB group showed faster response times in the WM task post-treatment. They also exhibited a decreased theta power and increased beta and gamma power at the frontal and posterior sites post-treatment. We explain these findings in terms of NFB improving the efficiency of neural resource management, maintenance of memory representations, and improved subvocal memory rehearsal