Marcos E. Bolanos

A weighted small world network measure for assessing functional connectivity

There is a growing need to develop measures that can characterize complex patterns of functional connectivity among brain regions. Graph theoretic measures have emerged as an important way to characterize the multivariate connectivity between nodes in a network, which have been successfully applied to neurophysiologic activity. In this paper, we propose a new small-world measure based on advances in both the bivariate measures underlying the graph theoretic approach, as well as in the definition of the measure for weighted graphs. Specifically, we recently proposed a new bivariate time-frequency phase-synchrony (TFPS) measure, which quantifies the dynamic nature of the interactions between neuronal oscillations with a higher time-frequency resolution than previous approaches and is better at isolating relevant activity. The proposed graph theoretic measures, weighted clustering coefficient and path length, represent a new approach to the calculation of weighted graph measures based on this improved bivariate TFPS measure. The new graph theoretic measures are applied to two datasets. The first is a well-known social network, Zacharys Karate Club. The second application contains event-related potential (ERP) indexing the well-known error-related negativity (ERN) component related to cognitive control. Results indicate that the new measures outperform the previously published weighted graph measures, and produces expectable results for both applications.

A PDA-based electrocardiogram/blood pressure telemonitor for telemedicine

An electrocardiogram (ECG) / blood pressure (BP) telemonitor consisting of comprehensive integration of various electrical engineering concepts, devices, and methods was developed. This personal digital assistant-based (PDAbased) system focused on integration of biopotential amplifiers, photoplethysmographic measurement of blood pressure, microcontroller devices, programming methods, wireless transmission, signal filtering and analysis, interfacing, and long term memory devices (24 hours) to develop a state-of-the-art ECG/BP telemonitor. These instrumentation modules were developed and tested to realize a complete and compact system that could be deployed to assist in telemedicine applications and heart rate variability studies. The specific objective of this device was to facilitate the long term monitoring and recording of ECG and blood pressure signals. This device was able to acquire ECG/BP waveforms, transmit them wirelessly to a PDA, save them onto a compact flash memory, and display them on the LCD screen of the PDA. It was also capable of calculating the heart rate (HR) in beats per minute, and providing systolic and diastolic blood pressure values.

Graph entropy rate minimization and the compressibility of undirected binary graphs

With the increasing popularity of complex network analysis through the use of graphs, a method for computing graph entropy has become important for a better understanding of a networks structure and for compressing large complex networks. There have been many different definitions of graph entropy in the literature which incorporate random walks, degree distribution, and node centrality. However, these definitions are either computationally complex or seemingly ad hoc. In this paper we propose a new approach for computing graph entropy with the intention of quantifying the compressibility of a graph. We demonstrate the effectiveness of our measure by identifying the lower bound of the entropy rate for scale-free, lattice, star, random, and real-world networks.

Identification of small world topologies in neural functional connections quantified by phase synchrony measures

The brain is a complex biological system with dynamic interactions between its sub-systems. One particular challenge in the study of this complex system is the identification of dynamic functional networks underlying observed neural activity. Current imaging approaches index local neural activity very well, but there is an increasing need for methods that quantify the interaction between regional activations. In this paper, we focus on inferring the functional connectivity of the brain based on electroencephalography (EEG) data. The interactions between the different neuronal populations are quantified through a recently proposed dynamic measure of phase synchrony. Small world measures, which include clustering coefficient, path length, global efficiency, and local efficiency, are computed on graphs obtained through the phase synchrony measure to study the underlying functional networks. The proposed measures are applied to an EEG study containing the error-related negativity (ERN), a brain potential response that indexes endogenous action monitoring, to determine the organization of the brain during a decision making task and determine the differences between Error and Correct responses.

Quantifying the functional importance of neuronal assemblies in the brain using Laplacian Hückel graph Energy

Determining the functional relationships between nodes in complex networks such as the neuronal networks is important. In recent years, graph theory has been employed to characterize the functional network structure of the brain from neurophysiological data such as the electroencephalogram (EEG). Current work on graph theoretic analysis of brain networks focuses on global characteristics of the network such as small world network measures. However, it is as important to be able to extract local features of the graph and quantify the vulnerability and robustness of different brain regions. In this paper, we explore how a well-known measure in signal processing, energy, can be extended toward understanding the functional role of neural assemblies in the brain network as represented by a graph. For this purpose, we introduce the Laplacian-Hückel Energy to quantify the local contribution of the nodes to the organization of any scale-free graph and determine anomalies in the graph. The proposed measure is evaluated for both the well-known Zachery karate network and a brain network constructed from an electroencephalogram study.

Graph analysis of neuronal interactions for the error-related negativity

The brain is a biological system with dynamic interactions between its sub-systems. The complexity of this system poses a challenge for identifying functional networks underlying observed neural activity. Current imaging approaches index local neural activity very well, but there is an increasing need for methods that quantify the interaction between regional activations. In this paper, we focus on inferring the functional connectivity of the brain based on electroencephalography (EEG) data. The interactions between the different neuronal populations are quantified through a dynamic measure of phase synchrony which is used to form sparsely connected networks that can be evaluated using measures of graph theory. These measures are applied to an EEG study containing the error-related negativity (ERN), a brain potential response that indexes endogenous action monitoring, to determine the organization of the brain during a decision making task and determine the differences between Error and Correct responses from subjects grouped according to an Externalizing Inventory. Results conclude weighted clustering coefficient and binary path length measures demonstrate significant differences between error low externalizers with all other response/externalizer types (error/high, correct/low, and correct/high).

Multivariate synchrony modules identified through multiple subject community detection in functional brain networks

The functional connectivity of the human brain may be described by modeling interactions among its neural assemblies as a graph composed of vertices and edges. It has recently been shown that functional brain networks belong to a class of scale-free complex networks for which graphs have helped define an association between function and topology. These networks have been shown to possess a heterogenous structure composed of clusters, dense regions of strongly associated nodes, which represent multivariate relationships among nodes. Network clustering algorithms classify the nodes based on a similarity measure representing the bivariate relationships and similar to unsupervised learning is performed without a priori information. In this paper, we propose a method for partitioning a set of networks representing different subjects and reveal a community structure common to multiple subjects. We apply this community identifying algorithm to functional brain networks during a cognitive control task, in particular the error-related negativity (ERN), to evaluate how the brain organizes itself during error-monitoring.

Identifying multivariate EEG synchronization networks through multiple subject community detection

In neurophysiological studies, it is important to infer the functional networks underlying the observed physiological data. In recent years, measures of functional connectivity as well as tools from graph theory have characterized the human brain as a complex network composed of segregated modules linked by short path lengths. However, the current studies of functional connectivity focus on either solely quantifying the pairwise relationships or describing the global characteristics of the network using graph theoretic metrics. In order to understand the multivariate relationships within the network, it is important to determine the functional modules underlying the complex networks. Moreover, the study of these functional networks is confounded by the fact that most neurophysiological studies consist of data collected from multiple subjects, thus, it is important to identify functional modules representative of all subjects. We propose a hierarchical consensus spectral clustering approach based on the Fiedler vector to address these issues. Furthermore, measures based on hypothesis testing and information theory are introduced for selecting the optimal modular structure. The proposed framework is applied to EEG data collected during a study of error-related negativity (ERN) to better understand the functional networks involved in cognitive control.

Identifying centralized hubs within neural functional connections

The brain is a complex biological system with dynamic interactions between its sub-systems. One particular challenge in the study of this complex system is the identification of dynamic functional networks underlying observed neural activity. The interactions between different neural activity are quantified through measures of functional connectivity such as the phase synchrony measure. In previous studies, graph theoretical approaches have been implemented on the pairwise connectivity matrices to analyze these interactions and quantify them using clustering coefficient and path length. In this paper, we focus on finding specific nodes that demonstrate high degrees of centrality. The centrality measure helps pinpoint which nodes are important for maintaining an efficiently connected neural network. One challenge in applying graph theoretic measures to connectivity matrices is the lack of a unique relationship between the connectivity matrix and the corresponding binary graph. In this paper, we propose a new algorithm which finds the ‘optimal’ binary graph based on different criteria including connectivity, clustering and the scale-free distribution of the network. The proposed framework is applied to an EEG study containing the error-related negativity (ERN) to identify hubs, a brain potential response that indexes endogenous action monitoring, to identify nodes with high centrality.