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Human whole-brain functional connectivity networks have been shown to exhibit both local/quasilocal (e.g., a set of functional sub-circuits induced by node or edge attributes) and non-local (e.g., higher-order functional coordination patterns) properties. Nonetheless, the non-local properties of topological strata induced by local/quasilocal functional sub-circuits have yet to be addressed. To that end, we proposed a homological formalism that enables the quantification of higher-order characteristics of human brain functional sub-circuits. Our results indicate that each homological order uniquely unravels diverse, complementary properties of human brain functional sub-circuits. Noticeably, the H1 homological distance between rest and motor task was observed at both the whole-brain and sub-circuit consolidated levels, which suggested the self-similarity property of human brain functional connectivity unraveled by a homological kernel. Furthermore, at the whole-brain level, the rest–task differentiation was found to be most prominent between rest and different tasks at different homological orders: (i) Emotion task (H0), (ii) Motor task (H1), and (iii) Working memory task (H2). At the functional sub-circuit level, the rest–task functional dichotomy of the default mode network is found to be mostly prominent at the first and second homological scaffolds. Also at such scale, we found that the limbic network plays a significant role in homological reconfiguration across both the task and subject domains, which paves the way for subsequent investigations on the complex neuro-physiological role of such network. From a wider perspective, our formalism can be applied, beyond brain connectomics, to study the non-localized coordination patterns of localized structures stretching across complex network fibers. 

Brain imaging genetics examines associations between imaging quantitative traits (QTs) and genetic factors such as single nucleotide polymorphisms (SNPs) to provide important insights into the pathogenesis of Alzheimer’s disease (AD). The individual level SNP-QT signals are high dimensional and typically have small effect sizes, making them hard to be detected and replicated. To overcome this limitation, this work proposes a new approach that identifies high-level imaging genetic associations through applying multigraph clustering to the SNP-QT association maps. Given an SNP set and a brain QT set, the association between each SNP and each QT is evaluated using a linear regression model. Based on the resulting SNP-QT association map, five SNP–SNP similarity networks (or graphs) are created using five different scoring functions, respectively. Multigraph clustering is applied to these networks to identify SNP clusters with similar association patterns with all the brain QTs. After that, functional annotation is performed for each identified SNP cluster and its corresponding brain association pattern. We applied this pipeline to an AD imaging genetic study, which yielded promising results. For example, in an association study between 54 AD SNPs and 116 amyloid QTs, we identified two SNP clusters with one responsible for amyloid beta clearances and the other regulating amyloid beta formation. These high-level findings have the potential to provide valuable insights into relevant genetic pathways and brain circuits, which can help form new hypotheses for more detailed imaging and genetics studies in independent cohorts.