Causal Functional Connectivity from Neural Dynamics

Abstract

Representation of brain network interactions is fundamental to the translation of neural structure to brain function. As such, methodologies for mapping neural interactions into structural models, i.e., inference of functional connectome from neural recordings, are key for the study of brain networks. While multiple approaches have been proposed for functional connectomics based on statistical associations between neural activity, association does not necessarily incorporate causation. Additional approaches have been proposed to incorporate aspects of causality to turn functional connectomes into causal functional connectomes, however, these methodologies typically focus on specific aspects of causality. This warrants a systematic statistical framework for causal functional connectomics that defines the foundations of common aspects of causality, to assist in contrasting existing approaches and guide development of further causal methodologies. In this research, we first develop such a statistical guide and perform a comparative study of existing approaches of causal modeling for finding the causal functional connectome (CFC). Thereafter, we consider a popular framework for inferring causal connectivity from observations - Directed Probabilistic Graphical Models. Its common formulation is not suitable for neural time series since it was developed for variables with independent and identically distributed static samples. In this work, we propose to model and estimate the causal functional connectivity from neural time series using a novel approach that adapts directed probabilistic graphical modeling to the time series scenario. In particular, we develop the Time-Aware PC (TPC) algorithm for estimating the causal functional connectivity, which adapts the Peter-Clark (PC) algorithm—a state-of-the-art method for statistical causal inference. We show that the model outcome of TPC has the properties of reflecting causality of neural interactions such as being non-parametric, exhibits the directed Markov property in a time-series setting, and is predictive of the consequence of counterfactual interventions on the time series. We demonstrate the utility of the methodology to obtain the causal functional connectome for several datasets including simulations, benchmark datasets, and recent multi-array electro-physiological recordings from the mouse visual cortex. We establish mathematical guarantees of estimation by the TPC algorithm under a standard set of assumptions on the underlying time series involving $\rho$-mixing that encompasses popular time series models such as vector auto-regressive moving average and linear processes. These findings are supported by simulations and benchmark real data analyses with TPC algorithm using different candidates of conditional dependence tests and with/without subsampling. Finally, we compute the CFC from time series resting state functional magnetic resonance imaging (rs-fMRI) data recorded in studies of Alzheimer's disease. We apply the TPC algorithm to infer the CFC for the whole brain from rs-fMRI recordings for subjects from three clinical groups: cognitively normal, mild cognitive impairment, and Alzheimer’s disease. We compare the CFC outcome of TPC with that of other related approaches in the literature. Then, we use the CFC outcomes of TPC and perform an exploratory analysis of the difference in strengths of CFC edges between Alzheimer’s and cognitively normal groups, based on edge-wise p-values obtained by Welch’s t-test. The brain regions thus identified are found to be in agreement with literature on brain regions impacted by Alzheimer’s disease, published by researchers from clinical/medical institutions.