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

Chicharro D, Ledberg A - PLoS ONE (2012)

Bottom Line: We furthermore introduce a framework for how natural causal effects can be characterized when they exist.Specifically, we discuss how the notion of natural causal effects can be combined with Granger causality and Dynamic Causal Modeling (DCM).Our results are generic and the concept of natural causal effects is relevant in all areas where the effects of interactions between subsystems are of interest.

View Article: PubMed Central - PubMed

Affiliation: Center of Brain and Cognition, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain. chicharro31@yahoo.es

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

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Graphical representation of causal connections for subsystems changing in time.Causal graphs represent two subsystems with unidirectional causal connections from  to  (A–C), or bidirectional causal connections (D–F). From left to right the scale of the graphs changes from a microscopic level, representing the dynamic, to a macroscopic one, in which each subsystem is represented by a single node.
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pone-0032466-g003: Graphical representation of causal connections for subsystems changing in time.Causal graphs represent two subsystems with unidirectional causal connections from to (A–C), or bidirectional causal connections (D–F). From left to right the scale of the graphs changes from a microscopic level, representing the dynamic, to a macroscopic one, in which each subsystem is represented by a single node.

Mentions: The subsystems can be represented at different scales, according to the type of causal effect one is interested in. We will consider the case of two subsystems with unidirectional causal connections from to (Figure 3A–C), or alternatively with bidirectional causal connections (Figure 3D–F).


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

Chicharro D, Ledberg A - PLoS ONE (2012)

Graphical representation of causal connections for subsystems changing in time.Causal graphs represent two subsystems with unidirectional causal connections from  to  (A–C), or bidirectional causal connections (D–F). From left to right the scale of the graphs changes from a microscopic level, representing the dynamic, to a macroscopic one, in which each subsystem is represented by a single node.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3306364&req=5

pone-0032466-g003: Graphical representation of causal connections for subsystems changing in time.Causal graphs represent two subsystems with unidirectional causal connections from to (A–C), or bidirectional causal connections (D–F). From left to right the scale of the graphs changes from a microscopic level, representing the dynamic, to a macroscopic one, in which each subsystem is represented by a single node.
Mentions: The subsystems can be represented at different scales, according to the type of causal effect one is interested in. We will consider the case of two subsystems with unidirectional causal connections from to (Figure 3A–C), or alternatively with bidirectional causal connections (Figure 3D–F).

Bottom Line: We furthermore introduce a framework for how natural causal effects can be characterized when they exist.Specifically, we discuss how the notion of natural causal effects can be combined with Granger causality and Dynamic Causal Modeling (DCM).Our results are generic and the concept of natural causal effects is relevant in all areas where the effects of interactions between subsystems are of interest.

View Article: PubMed Central - PubMed

Affiliation: Center of Brain and Cognition, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain. chicharro31@yahoo.es

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

Show MeSH