From correlation to causation: Estimating effective connectivity from zero-lag covariances of brain signals

Abstract

Knowing brain connectivity is of great importance both in basic research and for clinical applications. We are proposing a method to infer directed connectivity from zero-lag covariances of neuronal activity recorded at multiple sites. This allows us to identify causal relations that are reflected in neuronal population activity. To derive our strategy, we assume a generic linear model of interacting continuous variables, the components of which represent the activity of local neuronal populations. The suggested method for inferring connectivity from recorded signals exploits the fact that the covariance matrix derived from the observed activity contains information about the existence, the direction and the sign of connections. Assuming a sparsely coupled network, we disambiguate the underlying causal structure via L1-minimization, which is known to prefer sparse solutions. In general, this method is suited to infer effective connectivity from resting state data of various types. We show that our method is applicable over a broad range of structural parameters regarding network size and connection probability of the network. We also explored parameters affecting its activity dynamics, like the eigenvalue spectrum. Also, based on the simulation of suitable Ornstein-Uhlenbeck processes to model BOLD dynamics, we show that with our method it is possible to estimate directed connectivity from zero-lag covariances derived from such signals. In this study, we consider measurement noise and unobserved nodes as additional confounding factors. Furthermore, we investigate the amount of data required for a reliable estimate. Additionally, we apply the proposed method on full-brain resting-state fast fMRI datasets. The resulting network exhibits a tendency for close-by areas being connected as well as inter-hemispheric connections between corresponding areas. In addition, we found that a surprisingly large fraction of more than one third of all identified connections were of inhibitory nature.

Sparse Estimation of Resting-State Effective Connectivity From fMRI Cross-Spectra

“…Figure 4 ) is especially relevant for fMRI given the indirect nature of the measured hemodynamic signals. This further confirms previous results on the possibility to estimate sparse networks from lag-free covariances (Pernice and Rotter, 2013 ; Schiefer et al, 2018 ). Nevertheless, it is clear that hemodynamic variability still acts as an important confounder on observed time-series correlations, so that integrating hemodynamic information, either via separate HRF estimates (Wu et al, 2013 ; Proulx et al, 2014 ) or by specifically including hemodynamics in the generative model (Ryali et al, 2011 ; Friston et al, 2014b ) would be beneficial to EC estimation.…”

Advancing functional connectivity research from association to causation

“…Thus, a simple approach to remove problematic partial correlation results is to remove connections that are not present with pairwise correlation but appear with partial correlation. As a further bonus, the resulting causal graph can be oriented with causal directionality (at least in a 3-node case) because only a collider graph could have produced this pattern of results 88,94,95 .…”

Time-Delay Latency of Resting-State Blood Oxygen Level-Dependent Signal Related to the Level of Consciousness in Patients with Severe Consciousness Impairment

“…The implicit assumption in the traditional FC approach is that the correlation between brain regions occurs with zero latency (Schiefer et al, 2018). This assumption has two limitations: First, there is no consideration about the time required for information processing in each brain region, and second, this approach does not provide insights about how brain regions are communicating within themselves or with other brain areas (Mitra and Raichle, 2018).…”