Neural complexity: a graph theoretic interpretation

Effect of chemotherapy on default mode network connectivity in older women with breast cancer

Chemotherapy may impair cognition and contribute to accelerated aging. The purpose of this study was to assess the effects of chemotherapy on the connectivity of the default mode network (DMN) in older women with breast cancer. This prospective longitudinal study enrolled women aged ≥ 60 years with stage I-III breast cancer (CTx group) and matched healthy controls (HC group). Study assessments, consisting of resting-state functional MRI (rs-fMRI) and the Picture Sequence Memory (psm) test for episodic memory from the NIH Toolbox for Cognition, were obtained at baseline and within one month after the completion of chemotherapy for the CTx group and at matched intervals for the HC group. Two-sample t-test and FDR multiple comparison were used for statistical inference. Our analysis of the CTx group (N = 19; 60-82 years of age, mean = 66.6, SD = 5.24) compared to the HC group (N = 14; 60-78 years of age, mean = 68.1, SD = 5.69) revealed weaker DMN subnetwork connectivity in the anterior brain but stronger connectivity in the posterior brain at baseline. After chemotherapy, this pattern was reversed, with stronger anterior connectivity and weaker posterior connectivity. In addition, the meta-level functional network connectivity (FNC) among the DMN subnetworks after chemotherapy was consistently weaker than the baseline FNC as seen in the couplings between anterior cingulate cortex (ACC) and retrosplenial (rSplenia) region, with ΔFNC('ACC','rSplenia')=-0.14, t value=-2.44, 95 %CI=[-0.27,-0.10], p_FDR<0.05). The baseline FNC matrices of DMN subnetworks were correlated with psm scores (corr = 0.58, p < 0.05). Our results support DMN alterations as a potential neuroimaging biomarker for cancer-related cognitive impairment and accelerated aging.

Deriving pairwise transfer entropy from network structure and motifs

Transfer entropy (TE) is an established method for quantifying directed statistical dependencies in neuroimaging and complex systems datasets. The pairwise (or bivariate) TE from a source to a target node in a network does not depend solely on the local source-target link weight, but on the wider network structure that the link is embedded in. This relationship is studied using a discrete-time linearly coupled Gaussian model, which allows us to derive the TE for each link from the network topology. It is shown analytically that the dependence on the directed link weight is only a first approximation, valid for weak coupling. More generally, the TE increases with the in-degree of the source and decreases with the in-degree of the target, indicating an asymmetry of information transfer between hubs and low-degree nodes. In addition, the TE is directly proportional to weighted motif counts involving common parents or multiple walks from the source to the target, which are more abundant in networks with a high clustering coefficient than in random networks. Our findings also apply to Granger causality, which is equivalent to TE for Gaussian variables. Moreover, similar empirical results on random Boolean networks suggest that the dependence of the TE on the in-degree extends to nonlinear dynamics.

Framework to study dynamic dependencies in networks of interacting processes

The analysis of dynamic dependencies in complex systems such as the brain helps to understand how emerging properties arise from interactions. Here we propose an information-theoretic framework to analyze the dynamic dependencies in multivariate time-evolving systems. This framework constitutes a fully multivariate extension and unification of previous approaches based on bivariate or conditional mutual information and Granger causality or transfer entropy. We define multi-information measures that allow us to study the global statistical structure of the system as a whole, the total dependence between subsystems, and the temporal statistical structure of each subsystem. We develop a stationary and a nonstationary formulation of the framework. We then examine different decompositions of these multi-information measures. The transfer entropy naturally appears as a term in some of these decompositions. This allows us to examine its properties not as an isolated measure of interdependence but in the context of the complete framework. More generally we use causal graphs to study the specificity and sensitivity of all the measures appearing in these decompositions to different sources of statistical dependence arising from the causal connections between the subsystems. We illustrate that there is no straightforward relation between the strength of specific connections and specific terms in the decompositions. Furthermore, causal and noncausal statistical dependencies are not separable. In particular, the transfer entropy can be nonmonotonic in dependence on the connectivity strength between subsystems and is also sensitive to internal changes of the subsystems, so it should not be interpreted as a measure of connectivity strength. Altogether, in comparison to an analysis based on single isolated measures of interdependence, this framework is more powerful to analyze emergent properties in multivariate systems and to characterize functionally relevant changes in the dynamics.

Information storage, loop motifs, and clustered structure in complex networks

We use a standard discrete-time linear Gaussian model to analyze the information storage capability of individual nodes in complex networks, given the network structure and link weights. In particular, we investigate the role of two- and three-node motifs in contributing to local information storage. We show analytically that directed feedback and feedforward loop motifs are the dominant contributors to information storage capability, with their weighted motif counts locally positively correlated to storage capability. We also reveal the direct local relationship between clustering coefficient(s) and information storage. These results explain the dynamical importance of clustered structure and offer an explanation for the prevalence of these motifs in biological and artificial networks.

Neural complexity and structural connectivity

Tononi [Proc. Natl. Acad. Sci. U.S.A. 91, 5033 (1994)] proposed a measure of neural complexity based on mutual information between complementary subsystems of a given neural network, which has attracted much interest in the neuroscience community and beyond. We develop an approximation of the measure for a popular Gaussian model which, applied to a continuous-time process, elucidates the relationship between the complexity of a neural system and its structural connectivity. Moreover, the approximation is accurate for weakly coupled systems and computationally cheap, scaling polynomially with system size in contrast to the full complexity measure, which scales exponentially. We also discuss connectivity normalization and resolve some issues stemming from an ambiguity in the original Gaussian model.