When two become one: the limits of causality analysis of brain dynamics

Abstract

Biological systems often consist of multiple interacting subsystems, the brain being a prominent example. To understand/nthe functions of such systems it is important to analyze if and how the subsystems interact and to describe the effect of/nthese interactions. In this work we investigate the extent to which the cause-and-effect framework is applicable to such/ninteracting subsystems. We base our work on a standard notion of causal effects and define a new concept called natural/ncausal effect. This new concept takes into account that when studying interactions in biological systems, one is often not/ninterested in the effect of perturbations that alter the dynamics. The interest is instead in how the causal connections/nparticipate in the generation of the observed natural dynamics. We identify the constraints on the structure of the causal/nconnections that determine the existence of natural causal effects. In particular, we show that the influence of the causal/nconnections on the natural dynamics of the system often cannot be analyzed in terms of the causal effect of one subsystem/non another. Only when the causing subsystem is autonomous with respect to the rest can this interpretation be made. We/nnote that subsystems in the brain are often bidirectionally connected, which means that interactions rarely should be/nquantified in terms of cause-and-effect. We furthermore introduce a framework for how natural causal effects can be/ncharacterized when they exist. Our work also has important consequences for the interpretation of other approaches/ncommonly applied to study causality in the brain. Specifically, we discuss how the notion of natural causal effects can be/ncombined with Granger causality and Dynamic Causal Modeling (DCM). Our results are generic and the concept of natural/ncausal effects is relevant in all areas where the effects of interactions between subsystems are of interest.