Evidence from imaging studies suggests that the human brain has a small-world network topology that might be disrupted in certain brain disorders. However, current methodology is based on global graph theory measures, such as clustering, C, characteristic path length, L, and small-worldness, S, that lack spatial specificity and are insufficient to identify regional brain abnormalities. Here we propose novel ultra-fast methodology for mapping local properties of brain network topology such as local C, L and S (lC, lL and lS) in the human brain at 3-mm isotropic resolution from 'resting-state' magnetic resonance imaging data. Test-retest datasets from 40 healthy children/adolescents were used to demonstrate the overall good reliability of the measures across sessions and computational parameters (intraclass correlation > 0.5 for lC and lL) and their low variability across subjects (< 29%). Whereas regions with high local functional connectivity density (lFCD; local degree) in posterior parietal and occipital cortices demonstrated high lC and short lL, subcortical regions (globus pallidus, thalamus, hippocampus and amygdala), cerebellum (lobes and vermis), cingulum and temporal cortex also had high, lS, demonstrating stronger small-world topology than other hubs. Children/adolescents had stronger lFCD, higher lC and longer lL in most cortical regions and thalamus than 74 healthy adults, consistent with pruning of functional connectivity during maturation. In contrast, lFCD, lC and lL were weaker in thalamus and midbrain, and lL was shorter in frontal cortical regions and cerebellum for 69 schizophrenia patients than for 74 healthy controls, suggesting exaggerated pruning of connectivity in schizophrenia. Follow up correlation analyses for seeds in thalamus and midbrain uncovered lower positive connectivity of these regions in thalamus, putamen, cerebellum and frontal cortex (cingulum, orbitofrontal, inferior frontal) and lower negative connectivity in auditory, visual, motor, premotor and somatosensory cortices for schizophrenia patients than for controls, consistent with prior findings of thalamic disconnection in schizophrenia.
Tomasi, D., & Volkow, N. D. (2014). Mapping small-world properties through development in the human brain: Disruption in schizophrenia. PLoS ONE, 9(4). https://doi.org/10.1371/journal.pone.0096176