Estimating effective connectivity in neural networks: comparison of derivative-based and correlation-based methods

Abstract

Inferring and understanding the underlying connectivity structure of a system solely from the observed activity of its constituent components is a challenge in many areas of science. In neuroscience, such link inference techniques for estimating connectivity are paramount when attempting to understand the network structure of neural systems from their recorded activity patterns. To date, no universally accepted method exists for the inference of effective connectivity, which describes how the activity of a neural node mechanistically affects the activity of other nodes. One practical challenge is that, without ground truth structural connectivity data, the inferred underlying structural connections cannot be validated. In this case, information on the nodal dynamics is needed to obtain a more complete causal understanding of the system in the form of its effective connectivity. Here, we describe a systematic comparison of different approaches for estimating effective connectivity. Starting with the Hopf neuron model with known ground truth structural connectivity, we reconstruct the system’s structural connectivity matrix using a variety of algorithms. We show that, in sparse networks, combining a lagged-cross-correlation (LCC) approach with a recently published derivative-based correlation analysis method provides the most reliable estimation of the known ground truth connectivity matrix. We then use the estimated structural connectivity matrix as the basis for a forward simulation of the system dynamics, in order to recreate the observed node activity patterns. We show that, under certain conditions, our best method, LCC, works better than derivative-based methods for sparse noise-driven systems. Finally, we apply our LCC method to empirical biological data. Specifically, we reconstruct the structural connectivity of a subset of the nervous system of the nematodeC. Elegans. We show that our computationally simple method performs better than another recently published, computationally more expensive reservoir computing-based method. Our results show that a comparatively simple method can be used to reliably estimate directed effective connectivity in sparse neural systems in the presence of noise. We provide a perspective for future work by advocating the combined use of structural network estimation and activity recreation techniques for system identification, thus bridging the gap between structural and effective connectivity.