Thresholding Functional Connectivity Matrices to Recover the Topological Properties of Large-Scale Neuronal Networks

Abstract

The identification of the organization principles on the basis of the brain connectivity can be performed in terms of structural (i.e., morphological), functional (i.e., statistical), or effective (i.e., causal) connectivity. If structural connectivity is based on the detection of the morphological (synaptically mediated) links among neurons, functional and effective relationships derive from the recording of the patterns of electrophysiological activity (e.g., spikes, local field potentials). Correlation or information theory-based algorithms are typical routes pursued to find statistical dependencies and to build a functional connectivity matrix. As long as the matrix collects the possible associations among the network nodes, each interaction between the neuron i and j is different from zero, even though there was no morphological, statistical or causal connection between them. Hence, it becomes essential to find and identify only the significant functional connections that are predictive of the structural ones. For this reason, a robust, fast, and automatized procedure should be implemented to discard the “noisy” connections. In this work, we present a Double Threshold (DDT) algorithm based on the definition of two statistical thresholds. The main goal is not to lose weak but significant links, whose arbitrary exclusion could generate functional networks with a too small number of connections and altered topological properties. The algorithm allows overcoming the limits of the simplest threshold-based methods in terms of precision and guaranteeing excellent computational performances compared to shuffling-based approaches. The presented DDT algorithm was compared with other methods proposed in the literature by using a benchmarking procedure based on synthetic data coming from the simulations of large-scale neuronal networks with different structural topologies.

Personalized modeling of Alzheimer's disease progression estimates neurodegeneration severity from EEG recordings

“…Mean BFC values did not differ significantly between groups (0.072 ± 0.037 for the HC group, 0.071 ± 0.035 for the SCD group, and 0.069 ± 0.031 for the MCI group). We then binarized the BFC setting using as threshold the mean BFC value 26 to study the differences in the number of relevant functional connections between groups (see Methods). The MCI group displayed an average decrease of significant connections compared to HC subjects (17.8% of connections present in the HC group are lost in MCI patients while only 7.6% of the connections present in the MCI group are gained, see Figure S3a left).…”

“…We computed envelope correlation for delta, theta and alpha bands, and for the whole 0.5−45 Hz range, to study the change in significant broadband connections 23–25 . FC values were tested for significance and only values larger than half of the average value of FC over all participants were kept 26 . The features extracted as candidate biomarkers for each patient from the FC data were as follows: (1) mean and standard deviation of broadband FC (BFC) values over all electrode pairs; (2) count of relevant connections; and (3) average connectivity in the delta, theta and alpha ranges.…”

“…[23][24][25] FC values were tested for significance and only values larger than half of the average value of FC over all participants were kept. 26 The features extracted as candidate biomarkers for each patient from the FC data were as follows:…”

Connectivity Analysis in EEG Data: A Tutorial Review of the State of the Art and Emerging Trends

“…Binary graphs indicate only the presence or absence of a connection, and weighted graphs provide information about the strength of that connection [ 239 ]. Weighted graphs can exclude non-significant links, which are generally discarded by applying arbitrary weight thresholds [ 244 , 245 , 246 ]. Undirected and directed graphs are represented by symmetric and asymmetric adjacency matrices, respectively.…”

Representation Learning and Pattern Recognition in Cognitive Biometrics: A Survey

“…In addition, deep learning models such as convolution neural networks and graph convolution neural networks are proposed to learn intrinsic structural representations from the EEG connectivity graphs [ 97 , 98 ]. Notably, an important aspect of connectivity-based methods is thresholding the functional connectivity matrices to reduce spurious connections, thereby restoring meaningful topological properties of the graphs [ 99 ].…”