Quantifying the strength of structural connectivity underlying functional brain networks

In recent years, there has been strong interest in neuroscience studies to investigate brain organization through networks of brain regions that demonstrate strong functional connectivity (FC). Several well-known functional networks have been consistently identified in both taskrelated and resting-state fMRI across different study populations. These networks are extracted from observed fMRI using data-driven analytic methods such as independent component analysis (ICA). A notable limitation of these FC methods is that they do not include or provide any information on the underlying structural connectivity (SC) which is believed to serve as the basis for interregional interactions in brain activity. We propose a new statistical measure of the strength of SC (sSC) underlying FC networks obtained from data-driven methods. The sSC is developed using information from diffusion tensor imaging (DTI) data. A key advantage of sSC is that it is a standardized coefficient which adjusts for the different number of voxels and baseline SC of various functional networks. Hence, sSC can be applied to compare the strength of structural connections across different FC networks. Furthermore, we propose a reliability index for data-driven FC networks to measure the reproducibility of the networks through re-sampling the observed data. By evaluating the association between the sSC and the reliability index, we can investigate whether underlying SC informs the reliability of identified FC networks. To perform statistical inference such as hypothesis testing on the sSC, we develop a formal variance estimator of sSC based a spatial semivariogram model with a novel distance metric. We demonstrate the performance of the sSC measure and its estimation and inference methods with simulation studies. For real data analysis, we apply our methods to a multimodal imaging study with resting-state fMRI and DTI data from 20 healthy controls and 20 subjects with major depressive disorder. Results show that well-known resting state networks all demonstrate higher SC within the network as compared to the average structural connections across the brain. We also found that sSC is positively associated with the reliability index, indicating 1 ar X iv :1 70 3. 04 05 6v 1 [ st at .A P] 1 2 M ar 2 01 7 that the FC networks that have stronger underlying SC are more reproducible across samples. These results provide evidence that structural connections do serve as structural basis for the FC networks and that the structural information from DTI data can be leveraged to inform the reliability of functional networks derived through data-driven methods.