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Temporal synchronization-based functional connectivity (FC) has long been used by the neuroscience community. However, topographical FC information may provide additional information to characterize the advanced relationship between two brain regions. Accordingly, we proposed a novel method, namely high-order functional connectivity (HOFC), to capture this second-level relationship using inter-regional resemblance of the FC topographical profiles. Specifically, HOFC first calculates an FC profile for each brain region, notably between the given brain region and other brain regions. Based on these FC profiles, a second layer of correlations is computed between all pairs of brain regions (i.e., correlation's correlation). On this basis, we generated an HOFC network, where "high-order" network properties were computed. We found that HOFC was discordant with the traditional FC in several links, indicating additional information being revealed by the new metrics. We applied HOFC to identify biomarkers for early detection of Alzheimer's disease by comparing 77 mild cognitive impairment patients with 89 healthy individuals (control group). Sensitivity in detection of group difference was consistently improved by ∼25% using HOFC compared to using FC. An HOFC network analysis also provided complementary information to an FC network analysis. For example, HOFC between olfactory and orbitofrontal cortices was found significantly reduced in patients, besides extensive alterations in HOFC network properties. In conclusion, our results showed promise in using HOFC to comprehensively map the human brain connectome.

Topographical Information-Based High-Order Functional Connectivity and Its Application in Abnormality Detection for Mild Cognitive Impairment