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. 2017 Jun 1;284:103-111.
doi: 10.1016/j.jneumeth.2017.04.009. Epub 2017 Apr 23.

An Information Theory Framework for Dynamic Functional Domain Connectivity

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Free PMC article

An Information Theory Framework for Dynamic Functional Domain Connectivity

Victor M Vergara et al. J Neurosci Methods. .
Free PMC article

Abstract

Background: Dynamic functional network connectivity (dFNC) analyzes time evolution of coherent activity in the brain. In this technique dynamic changes are considered for the whole brain. This paper proposes an information theory framework to measure information flowing among subsets of functional networks call functional domains.

New method: Our method aims at estimating bits of information contained and shared among domains. The succession of dynamic functional states is estimated at the domain level. Information quantity is based on the probabilities of observing each dynamic state. Mutual information measurement is then obtained from probabilities across domains. Thus, we named this value the cross domain mutual information (CDMI).

Results: Strong CDMIs were observed in relation to the subcortical domain. Domains related to sensorial input, motor control and cerebellum form another CDMI cluster. Information flow among other domains was seldom found.

Comparison with existing methods: Other methods of dynamic connectivity focus on whole brain dFNC matrices. In the current framework, information theory is applied to states estimated from pairs of multi-network functional domains. In this context, we apply information theory to measure information flow across functional domains.

Conclusion: Identified CDMI clusters point to known information pathways in the basal ganglia and also among areas of sensorial input, patterns found in static functional connectivity. In contrast, CDMI across brain areas of higher level cognitive processing follow a different pattern that indicates scarce information sharing. These findings show that employing information theory to formally measured information flow through brain domains reveals additional features of functional connectivity.

Keywords: Dynamic functional network connectivity; Entropy; Functional MRI; Mutual information.

Figures

Fig. 1
Fig. 1
The same clustering technique used in dFNC is also used in dFDC to cluster data from domain pairs. The difference strives in the use of submatrices instead of the whole functional connectivity matrix.
Fig. 2
Fig. 2
Entropy and cluster probability results. Triangles and arrows facing upward and downwards indicate significant increment and decrement related to age and sex correspondingly. There was no significant relationship with sex. Significance was assessed at p<0.01. Completely random situations are described by an entropy value of 1.58.
Fig. 3
Fig. 3
This figure compares sFNC and mutual information matrices. Both matrices show a similar relationship among SEN, VIS, AUD and CER domains. Also, the SBC domain exhibits a strong connection and mutual information with other domains in both matrices. The patterns are different in the case of DMN, ECN, LAN, SAL and PRC domains.
Fig. 4
Fig. 4
Mutual information matrix displaying values complying two different significant thresholds: p<0.05 and p<0.01. Mutual information was bootstrapped to obtain the p-value thresholds. Green circles display 15 points with p<0.01. The points where p<0.05 are displayed to better illustrate the matrix structure where the SBC domain have strong within mutual information. The other noticeable pattern is the appearance of strong mutual information within and among cerebellum, sensorial and motor domains.
Fig. 5
Fig. 5
This figure illustrates the differences of joint probability values between those passing the p<0.01 threshold and those that do not pass. The nine joint probabilities (since there are three dynamic states per dFDC) of ally dFDC pairs were sorted in ascending order. The two largest probabilities were significantly higher (p<0.01) for the group of 15 cross domain information measures with p<0.01 (displayed with green circles in Fig. 4) compared to the rest. In addition, the two smallest joint probabilities were significantly lower. This difference explains the enhanced cross domain information measure observed.
Fig. 6
Fig. 6
Displayed result was selected from the set that showed significant relationships with considered covariant. The cross domain information for SBC-DMN vs. SEN-VIS (mean I=0.06) showed significant increment with age (beta = 0.0063 and p=0.0018). The circles on the state centroids axis designate the brain region displayed. The two joint probabilities 0.22 and 0.24 drive the cross information measure since both are similarly larger than the rest.

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