Differential Covariance: A New Method to Estimate Functional Connectivity in fMRI

Abstract

Measuring functional connectivity from fMRI recordings is important in understanding processing in cortical networks. However, because the brain's connection pattern is complex, currently used methods are prone to producing false functional connections. We introduce differential covariance analysis, a new method that uses derivatives of the signal for estimating functional connectivity. We generated neural activities from dynamical causal modeling and a neural network of Hodgkin-Huxley neurons and then converted them to hemodynamic signals using the forward balloon model. The simulated fMRI signals, together with the ground-truth connectivity pattern, were used to benchmark our method with other commonly used methods. Differential covariance achieved better results in complex network simulations. This new method opens an alternative way to estimate functional connectivity.

Functional connectivity of fMRI using differential covariance predicts structural connectivity and behavioral reaction times

“…Backward reconstruction based on the forward Balloon model Friston, Mechelli, Turner, and Price (2000) has been shown to work well together with dCov applied to synthetic datasets Lin et al (2020).…”

“…Differential covariance (dCov) , which is the focus of this study, reduces false positive connections and recovers the ground truth connectivity from data generated by simulated models ( Lin et al, 2020 ; Lin, Das, Krishnan, Bazhenov, & Sejnowski, 2017 ). 1 Compared with other statistical methods, dCov seeks to estimate connectivity from a dynamical system perspective.…”

“…The calculation of dCov based FC was detailed in Section of main text. In our previous workLin et al (2020Lin et al ( , 2017, the advantages of differential covariance based methods over covariance -23-== / Title:…”

Dynamical differential covariance recovers directional network structure in multiscale neural systems

“…For performance evaluation in the brain surface model, c-sensitivity ( 6 ) (equation 17 in ref. 43 ) was adopted. It is defined as the fraction of the estimated true positive values that are higher than the 95th percentile of the false positive values.…”

Dynamical differential covariance recovers directional network structure in multiscale neural systems

“…We previously introduced differential covariance (dCov) ( 14, 15 ), a directed FC estimation method, and highlighted the performance of two matrices, Δc, which calculates the correlation between the derivative signal and the signal itself, and Δp, which evaluates the partial covariance between them. In simulated test cases, they detected network connections with higher sensitivity than many of the methods reviewed in Smith et al ( 1 ).…”