A fundamental means for understanding the brain's organizational structure is to group its spatially disparate regions into functional subnetworks based on their interactions. Most community detection techniques are designed for generating partitions, but certain brain regions are known to interact with multiple subnetworks. Thus, the brain's underlying subnetworks necessarily overlap. In this paper, we propose a technique for identifying overlapping subnetworks from weighted graphs with statistical control over false node inclusion. Our technique improves upon the replicator dynamics formulation by incorporating a graph augmentation strategy to enable subnetwork overlaps, and a graph incrementation scheme for merging subnetworks that might be falsely split by replicator dynamics due to its stringent mutual similarity criterion in defining subnetworks. To statistically control for inclusion of false nodes into the detected subnetworks, we further present a procedure for integrating stability selection into our subnetwork identification technique. We refer to the resulting technique as stable overlapping replicator dynamics (SORD). Our experiments on synthetic data show significantly higher accuracy in subnetwork identification with SORD than several state-of-the-art techniques. We also demonstrate higher test-retest reliability in multiple network measures on the Human Connectome Project data. Further, we illustrate that SORD enables identification of neuroanatomically-meaningful subnetworks and network hubs.

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Tractography refers to the in vivo reconstruction of fiber bundles, e.g., in brain, via the analysis of anisotropic diffusion patterns measured by diffusion weighted magnetic resonance imaging (DWI). The data provides a probabilistic model of local diffusion which was shown to correlate with the underlying fibrous structure under certain assumptions. Deterministic tractography suffers from uncertainties at kissing and crossing fibers, at different levels depending on the diffusion model employed (e.g., DTI, HARDI), yet it is easy to interpret and use in clinic. In this study, a novel generic algorithm, split and merge tractography (SMT), is proposed that provides a real-time, interactive and reliability ranked assessment of potential pathways, communicating the true information content of the data without sacrificing the usability of tractography. Specifically, SMT takes in a precomputed set of tracts and the diffusion data (e.g., DTI, HARDI) as its input, generates a set of short (reliable) tracts via splitting at unreliable points and forms quasi-random clusters of short tracts by means of which the space of short tract clusters, representing complete tracts, is sampled. A histogram of thus formed clusters is built in an efficient way and used for real-time, interactive assessment of pathways. The current implementation uses DTI and fourth-order Runge-Kutta integration based streamline tractography as its input. The method is qualitatively assessed on phantom DTI data and real DTI data. Phantom experiments demonstrated that SMT is capable of highlighting the problematic regions and suggesting pathways that are completely overseen by input streamline tractography. Real data experiment results correlate well with known anatomy and also demonstrate that the reliability ranking can efficiently suppress the erroneous tracts interactively. The method is compared to a recent method that also pursues a similar approach, yet in a global optimization based framework. The comparative study on real DTI data revealed the lower computational load of SMT and a better correlation with known anatomy.

Abstract. Functional magnetic resonance imaging (fMRI) has been widely used for inferring brain regions that tend to work in tandem and grouping them into subnetworks. Despite that certain brain regions are known to interact with multiple subnetworks, few existing techniques support identification of subnetworks with overlaps. To address this limitation, we propose a novel approach based on replicator dynamics that facilitates detection of sparse overlapping subnetworks. We refer to our approach as overlapping replicator dynamics (RDOL). On synthetic data, we show that RDOL achieves higher accuracy in subnetwork identification than state-of-the-art methods. On real data, we demonstrate that RDOL is able to identify major functional hubs that are known to serve as communication channels between brain regions, in addition to detecting commonly observed functional subnetworks. Moreover, we illustrate that knowing the subnetwork overlaps enables inference of functional pathways, e.g. from primary sensory areas to the integration hubs.

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