Marisel Villafane-Delgado

Dynamic Graph Fourier Transform on temporal functional connectivity networks

Graph signal processing extends the notion of frequency from signals in the time domain to signals defined on graphs. Graph signals arise in many applications including brain signals defined on functional connectivity networks. Most of the current work on graph signal processing focuses on static graphs. However, functional connectivity networks are dynamic and the signals on these networks change with time. In this paper, we introduce a new transform for dynamic networks named as Dynamic Graph Fourier Transform (DGFT). The proposed approach extends the notion of graph Laplacian from the static case to the dynamic case through the network Laplacian tensor. The basis functions for the transform are obtained through the Tucker decomposition of this Laplacian tensor. The proposed method detects nonstationary activity in the network structure and allows us to obtain information about the regions in the brain that contribute to different frequency contents in a cognitive control experiment.

Graph Signal Processing on Neuronal Networks

Abstract Advanced neuroimaging technology has enabled the study of both the structure and function of the brain in more detail than before. The high volume of multisubject, multimodal neuroimaging data poses challenges to the signal processing community as the data is high-dimensional, sensitive to noise, and suffers from high variability across subjects. While many discoveries in neuroscience have been made using massively univariate statistics or time-series analysis, there has been a paradigm shift toward the use of multivariate analysis, graph theoretic methods, and machine learning to decode brain function. Tools from network science and graph theory have been employed to analyze the functional connectivity of the brain by associating nodes with distinct brain regions and edges with pairwise interactions between them. However, these methods focus solely on the network topology and organization without directly correlating the activity in these brain regions with the underlying network. Graph signal processing (GSP) offers a promising tool to address this important gap in the study of neuronal networks. This new framework merges neuroimaging data such as functional magnetic resonance imaging (fMRI) and electroencephalography (EEG) with the underlying graphical structure to extract rich brain activity missed by analyzing the networks or the signals alone. Given a connectivity network and neuroimaging signals defined on this network, we first illustrate how GSP can be used for robust dimensionality reduction, signal detection and classification, and filtering to extract brain activity corresponding to different levels of spatial variation. We then present GSP-based methods for learning functional connectivity networks given the observed neuroimaging data and the use of graph-based spectral analysis for data and network denoising. Finally, we present how GSP methods can be extended to study the temporal dynamics of functional connectivity networks of the brain.

Multi-scale higher order singular value decomposition (MS-HoSVD) for resting-state FMRI compression and analysis

Advances in information technology are making it possible to collect increasingly massive amounts of multidimensional, multi-modal neuroimaging data such as functional magnetic resonance imaging (fMRI). Current fMRI datasets involve multiple variables including multiple subjects, as well as both temporal and spatial data. These high dimensional datasets pose a challenge to the signal processing community to develop data reduction methods that can exploit their rich structure and extract meaningful summarizations. In this paper, we propose a tensor-based framework for data reduction and low-dimensional structure learning with a particular focus on reducing high dimensional fMRI data sets into physiologically meaningful network components. We develop a multiscale tensor factorization method for higher order data inspired by hybrid linear modeling and subspace clustering techniques. In particular, we develop a multi-scale HoSVD approach where a given tensor is first permuted and then partitioned into several sub-tensors each of which can be represented more efficiently. This multi-scale framework is applied to resting state fMRI data to identify the default mode network from compressed data.

Functional significance of spectrotemporal response functions obtained using magnetoencephalography

The spectrotemporal response function (STRF) model of neural encoding quantitatively associates dynamic auditory neural (output) responses to a spectrogram-like representation of a dynamic (input) stimulus. STRFs were experimentally obtained via whole-head human cortical responses to dynamic auditory stimuli using magnetoencephalography (MEG). The stimuli employed consisted of unpredictable pure tones presented at a range of rates. The predictive power of the estimated STRFs was found to be comparable to those obtained from the cortical single and multiunit activity literature. The STRFs were also qualitatively consistent with those obtained from electrophysiological studies in animal models; in particular their local-field-potential-generated spectral distributions and multiunit-activity-generated temporal distributions. Comparison of these MEG STRFs with others obtained using natural speech and music stimuli reveal a general structure consistent with common baseline auditory processing, including evidence for a transition in low-level neural representations of natural speech by 100 ms, when an appropriately chosen stimulus representation was used. It is also demonstrated that MEG-based STRFs contain information similar to that obtained using classic auditory evoked potential based approaches, but with extended applications to long-duration, non-repeated stimuli.

Neural Coding of Noisy and Reverberant Speech in Human Auditory Cortex

Speech communication in daily listening environments is complicated by the phenomenon of reverberation, wherein any sound reaching the ear is a mixture of the direct component from the source and multiple reflections off surrounding objects and the environment. The brain plays a central role in comprehending speech accompanied by such distortion, which, frequently, is further complicated by the presence of additional noise sources in the vicinity. Here, using magnetoencephalography (MEG) recordings from human subjects, we investigate the neural representation of speech in noisy, reverberant listening conditions as measured by phase-locked MEG responses to the slow temporal modulations of speech. Using systems-theoretic linear methods of stimulus encoding, we observe that the cortex maintains both distorted and distortion-free (cleaned) representations of speech. Also, we show that, while neural encoding of speech remains robust to additive noise in absence of reverberation, it is detrimentally affected by noise when present along with reverberation. Further, using linear methods of stimulus reconstruction, we show that theta-band neural responses are a likely candidate for the distortion free representation of speech, whereas delta band responses are more likely to carry non-speech specific information regarding the listening environment.

Functional connectivity brain network analysis through network to signal transform based on the resistance distance

Functional connectivity brain networks have been shown to demonstrate interesting complex network behavior such as small-worldness. Transforming networks to time series has provided an alternative way of characterizing the structure of complex networks. However, previously proposed deterministic methods are limited to unweighted graphs. In this paper, we propose to employ the resistance distance matrix of weighted graphs as the distance matrix for transforming networks to signals based on classical multidimensional scaling. We present a framework for obtaining information about the networks structure through the mapped signals and recovering the original network using properties of the resistance matrix. Finally, the proposed method is applied to characterizing functional connectivity networks constructed from electroencephalogram data.

Temporal network tracking based on tensor factor analysis of graph signal spectrum

A wide variety of networks, ranging from biological to social, evolve, adapt and change over time. Recent methods employed in the assessment of temporal networks include tracking topological graph metrics, evolutionary clustering, tensor based anomaly methods and, more recently, graph to signal transformations. In this paper, we propose to assess the temporal evolution of networks by first transforming networks into signals through Classical Multidimensional Scaling based on the resistance distance and then constructing a tensor based on the spectra of each signal across time. The proposed method is first evaluated on simulated temporal networks with varying structural properties. Next, the method is applied to temporal functional connectivity networks constructed from multichannel electroencephalogram (EEG) data collected during a study of cognitive control. This analysis shows that the proposed method is more sensitive to changes in the network structure and more robust to variations in edge weights.

A time-frequency based bivariate synchrony measure for reducing volume conduction effects in EEG

Phase synchrony measures computed on electrophysiological signals play an important role in the assessment of cognitive and sensory processes. However, due to the effects of volume conduction false synchronization values may arise between time series. Measures such as the imaginary part of coherence (ImC), phase-lag index (PLI) and an enhanced version of it, the weighted PLI (WPLI) have been proposed in order to attenuate the effects of volume conduction. In this work, the computation of the WPLI based on the phase difference from the Reduced Interference Distribution-Rihaczek (RID-Rihaczek) time-frequency distribution is proposed. The proposed WPLI measure is shown to be less susceptible to volume conduction effects when compared to that based on phase difference estimates obtained from the continuous wavelet transform. The proposed measure has also been applied to real EEG data collected during a study of event-related negativity and has been shown to differentiate between real synchrony and synchrony due to volume conduction.

Computation of resting state networks from fMRI through a measure of phase synchrony

Resting-state fMRI (rs-fMRI) studies of the human brain have demonstrated that low-frequency fluctuations can define functionally relevant resting state networks (RSNs). The majority of these methods rely on Pearsons correlation for quantifying the functional connectivity between the time series from different regions. However, it is well-known that correlation is limited to quantifying only linear relationships between the time series and assumes stationarity of the underlying processes. Many empirical studies indicate nonstationarity of the BOLD signals. In this paper, we adapt a measure of time-varying phase synchrony to quantify the functional connectivity and modify it to distinguish between synchronization and desynchronization. The proposed measure is compared to the conventional Pearsons correlation method for rs-fMRI analyses on two subjects (six scans per subject) in terms of their reproducibility.

Effective connectivity in FMRI from mutual prediction approach

Effective connectivity aims to quantify how a neural system influences another. Estimation of effective connectivity in neurophysiological signals has gained great popularity in recent years. Lag-based methods, such as Granger causality, depend strongly on the amplitudes of the signals and assume the signals are linear and stationary. In this paper, we extend a previously proposed model-free method for estimation of directionality of coupling. Mutual prediction approach is implemented by estimating the instantaneous phases from the Reduced Interference Rihaczek time-frequency distribution and calculating the directionality index as function of frequency. The proposed method is evaluated on both simulated signal models and resting state fMRI time series.