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

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.