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

Alessio Boschi,Martina Brofiga,Paolo Massobrio

doi:10.3389/fnins.2021.705103

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.

Highlights

The brain or more in general nervous systems are complex networks par excellence, made up of thousands of neurons synaptically interconnected
The network model, organized according to the RND, SW, and SF topologies described in section “Network Model,” was tuned up in order to generate firing dynamics reflecting the behavior of mature in vitro cortical cultures (Wagenaar et al, 2006)
Spiking and bursting features of the simulated dataset were characterized in terms of mean firing rate (MFR), i.e., the number of spikes per second averaged over the number of the neurons of the network, mean bursting rate (MBR), i.e., the number of bursts per minute averaged over the number of the neurons of the network, and the burst duration (BD), i.e., the temporal duration of these events averaged over the entire number of detected bursts

Summary

Introduction

The brain or more in general nervous systems are complex networks par excellence, made up of thousands of neurons synaptically interconnected. Such huge connectivity and the intrinsic topological organization make it possible to generate and integrate information from multiple external and internal sources in real time (Sporns et al, 2000). The structural connectivity matrix takes into account the physical (synaptically mediated) connections existing among neurons or small assemblies. The resolution of such CMs depends on the used technologies to acquire morphological (structural connectivity) or dynamical (functional and effective connectivity) information. The CM contains different information regarding the connectivity of the considered network, from the kind of connections (i.e., excitatory vs. inhibitory links), to the synaptic weights (i.e., an indication of the synaptic efficacy), up to the delays introduced by the synaptic transmission (Fornito et al, 2016)

Methods

Results

Conclusion