A Multivariate Granger Causality Concept towards Full Brain Functional Connectivity

Abstract

Detecting changes of spatially high-resolution functional connectivity patterns in the brain is crucial for improving the fundamental understanding of brain function in both health and disease, yet still poses one of the biggest challenges in computational neuroscience. Currently, classical multivariate Granger Causality analyses of directed interactions between single process components in coupled systems are commonly restricted to spatially low- dimensional data, which requires a pre-selection or aggregation of time series as a preprocessing step. In this paper we propose a new fully multivariate Granger Causality approach with embedded dimension reduction that makes it possible to obtain a representation of functional connectivity for spatially high-dimensional data. The resulting functional connectivity networks may consist of several thousand vertices and thus contain more detailed information compared to connectivity networks obtained from approaches based on particular regions of interest. Our large scale Granger Causality approach is applied to synthetic and resting state fMRI data with a focus on how well network community structure, which represents a functional segmentation of the network, is preserved. It is demonstrated that a number of different community detection algorithms, which utilize a variety of algorithmic strategies and exploit topological features differently, reveal meaningful information on the underlying network module structure.

Tracking the Reorganization of Module Structure in Time-Varying Weighted Brain Functional Connectivity Networks

“…brain regions, the thresholding and removal of low weight edges is an integral processing step in the network analysis pipeline to yield edge noncomplete networks and to emphasize key features of network topology. 3,19,55 Heuristic and statistical thresholding approaches are controversially discussed 16 and have to be applied carefully as they are prone to introduce serious biases into the resulting network structure. 18 The common situation of having to screen various predefined edge weight thresholds and to subsequently analyze the resulting thresholded networks in an exploratory fashion 35,36 is improved with our proposed algorithm for computing a specific single Pareto optimal threshold for each network (approach #2).…”

“…Modules in brain functional networks can be interpreted in terms of functionally segregated and delineated brain areas, which yield important insights into the studied brain activity. [13][14][15][16] It can be assumed that the way interactions between functionally distinct brain regions are redistributed in the course of the neural information processing is reflected in the dynamic reconfiguration of module structure in time-varying brain functional networks. 3,[13][14][15] Still, in current neuroscience research, the analysis of the temporal reorganization of module structure is not commonly considered, despite its potential for improving the understanding of the time evolution of functional interaction patterns and the resulting functional segmentation of corresponding brain areas.…”

“…At first, the adjacency matrix of the underlying binary network that contains the information on edge positions is obtained by means of using an algorithm similar to the one we described previously. 16,65 Thereby, properties of the module structure are controlled by probabilities of intra-and inter-module edges, user-defined module memberships of nodes, specified constraints on minimum intra-module in-and out-degrees and constraints on maximum intermodule in-and out-degrees. For the testing of our computational framework, we need to simulate a sequence of weighted edge-complete networks, thus the underlying binary networks also have to be edgecomplete.…”

Methodological aspects of analyzing high resolved brain connectivity for multiple subjects

“…First, spatially highly resolved functional connectivity of each individual was quantified by means of lsGCI [3] that enables the quantification of a node-by-node (e.g. voxel-byvoxel) connectivity even for high dimensional time-series.…”

“…Networks of different sizes were used to simulate data [3]; this allows the study of the impact of all parameters by comparing the results with the known ground truth. Also, resting state fMRI (rs-fMRI) data were used to evaluate the influence of model parameters in the context of real data.…”