Currently, network-oriented analysis of fMRI data has become an important tool for understanding brain organization and brain networks. Among the range of network modeling methods, partial correlation has shown great promises in accurately detecting true brain network connections. However, the application of partial correlation in investigating brain connectivity, especially in large-scale brain networks, has been limited so far due to the technical challenges in its estimation. In this paper, we propose an efficient and reliable statistical method for estimating partial correlation in large-scale brain network modeling. Our method derives partial correlation based on the precision matrix estimated via Constrained L1-minimization Approach (CLIME), which is a recently developed statistical method that is more efficient and demonstrates better performance than the existing methods. To help select an appropriate tuning parameter for sparsity control in the network estimation, we propose a new Dens-based selection method that provides a more informative and flexible tool to allow the users to select the tuning parameter based on the desired sparsity level. Another appealing feature of the Dens-based method is that it is much faster than the existing methods, which provides an important advantage in neuroimaging applications. Simulation studies show that the Dens-based method demonstrates comparable or better performance with respect to the existing methods in network estimation. We applied the proposed partial correlation method to investigate resting state functional connectivity using rs-fMRI data from the Philadelphia Neurodevelopmental Cohort (PNC) study. Our results show that partial correlation analysis removed considerable between-module marginal connections identified by full correlation analysis, suggesting these connections were likely caused by global effects or common connection to other nodes. Based on partial correlation, we find that the most significant direct connections are between homologous brain locations in the left and right hemisphere. When comparing partial correlation derived under different sparse tuning parameters, an important finding is that the sparse regularization has more shrinkage effects on negative functional connections than on positive connections, which supports previous findings that many of the negative brain connections are due to non-neurophysiological effects. An R package “DensParcorr” can be downloaded from CRAN for implementing the proposed statistical methods.

In the last decade, a number of neuroimaging studies have investigated the neurophysiological effects associated with contemplative practices. Meditation-related changes in resting state functional connectivity (rsFC) have been previously reported, particularly in the default mode network, frontoparietal attentional circuits, saliency-related regions, and primary sensory cortices. We collected functional magnetic resonance imaging data from a sample of 12 experienced Zen meditators and 12 meditation-naïve matched controls during a basic attention-to-breathing protocol, together with behavioral performance outside the scanner on a set of computerized neuropsychological tests. We adopted a network system of 209 nodes, classified into nine functional modules, and a multi-stage approach to identify rsFC differences in meditators and controls. Between-group comparisons of modulewise FC, summarized by the first principal component of the relevant set of edges, revealed important connections of frontoparietal circuits with early visual and executive control areas. We also identified several group differences in positive and negative edgewise FC, often involving the visual, or frontoparietal regions. Multivariate pattern analysis of modulewise FC, using support vector machine (SVM), classified meditators, and controls with 79% accuracy and selected 10 modulewise connections that were jointly prominent in distinguishing meditators and controls; a similar SVM procedure based on the subjects’ scores on the neuropsychological battery yielded a slightly weaker accuracy (75%). Finally, we observed a good correlation between the across-subject variation in strength of modulewise connections among frontoparietal, executive, and visual circuits, on the one hand, and in the performance on a rapid visual information processing test of sustained attention, on the other. Taken together, these findings highlight the usefulness of employing network analysis techniques in investigating the neural correlates of contemplative practices.

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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