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. 2016 May;6(4):298-311.
doi: 10.1089/brain.2015.0408. Epub 2016 Mar 29.

A Mapping Between Structural and Functional Brain Networks

Jil Meier  1 , Prejaas Tewarie  2 , Arjan Hillebrand  3 , Linda Douw  4   5 , Bob W van Dijk  3 , Steven M Stufflebeam  5   6 , Piet Van Mieghem  1
Affiliations

A Mapping Between Structural and Functional Brain Networks

Jil Meier et al. Brain Connect. 2016 May.

Abstract

The relationship between structural and functional brain networks is still highly debated. Most previous studies have used a single functional imaging modality to analyze this relationship. In this work, we use multimodal data, from functional MRI, magnetoencephalography, and diffusion tensor imaging, and assume that there exists a mapping between the connectivity matrices of the resting-state functional and structural networks. We investigate this mapping employing group averaged as well as individual data. We indeed find a significantly high goodness of fit level for this structure-function mapping. Our analysis suggests that a functional connection is shaped by all walks up to the diameter in the structural network in both modality cases. When analyzing the inverse mapping, from function to structure, longer walks in the functional network also seem to possess minor influence on the structural connection strengths. Even though similar overall properties for the structure-function mapping are found for different functional modalities, our results indicate that the structure-function relationship is modality dependent.

Keywords: DT1; MEG; brain networks; fMRI; functional connectivity; functional networks; matrix mapping; structural connectivity; structural networks.

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Figures

<b>FIG. 1.</b>
FIG. 1.
(a) Visualization of the structural and functional brain network (for fMRI and MEG) for the group-averaged data set, the colors of the different regions represent here their node strength (i.e., the sum of their surrounding link weights). (b) Visualization of the mapping between their adjacency matrices. fMRI, functional MRI; MEG, magnetoencephalography. Color images available online at www.liebertpub.com/brain
<b>FIG. 2.</b>
FIG. 2.
Visualization of the fitted matrices for different maximally fitted exponents K (abbreviation: maxexp) for the function f: A → WfMRI and f: A → WMEG versus the empirical matrices for the group-averaged data set. Color images available online at www.liebertpub.com/brain
<b>FIG. 3.</b>
FIG. 3.
SSEnorm for the group-averaged data set for different maximally fitted exponents K displayed together with the results of the reshuffled matrices. For each mapping, we ran the same analysis with 100 reshuffled versions of the matrix A and with 100 reshuffled versions of matrix W. SSE, sum of squared errors. Color images available online at www.liebertpub.com/brain
<b>FIG. 4.</b>
FIG. 4.
SSEnorm for the individual data set for different maximally fitted exponents K (after averaging over all 11 individual SSEnorm results) displayed together with the averaged result of the reshuffled matrices. For each mapping, we ran the same analysis with 100 reshuffled versions of the matrix V and with 100 reshuffled versions of matrix W. Color images available online at www.liebertpub.com/brain
<b>FIG. 5.</b>
FIG. 5.
Estimated coefficients for the mapping f: A → WMEG for K = 5 together with their 95% confidence interval for the first group-averaged data set and a second group-averaged data set. Color images available online at www.liebertpub.com/brain
<b>FIG. 6.</b>
FIG. 6.
Estimated coefficients for the mapping f: A → WfMRI for K = 5 together with their 95% confidence interval for the first group-averaged data set and a second group-averaged data set. Color images available online at www.liebertpub.com/brain
<b>FIG. 7.</b>
FIG. 7.
Visualization of the fitted matrices for different maximally fitted exponents K (abbreviation: maxexp) for the function f−1: WfMRI→A and f−1: WMEG→A versus the empirical matrices for the group-averaged data set. Color images available online at www.liebertpub.com/brain
<b>FIG. 8.</b>
FIG. 8.
SSEnorm for the group-averaged data set for different maximally fitted exponents K displayed together with the results of the reshuffled matrices. For each mapping, we ran the same analysis with 100 reshuffled versions of the matrix A and with 100 reshuffled versions of matrix W. Color images available online at www.liebertpub.com/brain
<b>FIG. 9.</b>
FIG. 9.
SSEnorm for the individual data set for different maximally fitted exponents K (after averaging over all 11 individual SSEnorm results) displayed together with the averaged result of the reshuffled matrices. For each mapping, we ran the same analysis with 100 reshuffled versions of the matrix V and with 100 reshuffled versions of matrix W. Color images available online at www.liebertpub.com/brain
<b>FIG. 10.</b>
FIG. 10.
Estimated coefficients for the mapping f−1: WMEG→A for K = 5 together with their 95% confidence interval for the first group-averaged data set and a second group-averaged data set. Color images available online at www.liebertpub.com/brain
<b>FIG. 11.</b>
FIG. 11.
Estimated coefficients for the mapping f−1: WfMRI→A for K = 5 together with their 95% confidence interval for the first group-averaged data set and a second group-averaged data set. Color images available online at www.liebertpub.com/brain
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