The anatomical distance of functional connections predicts brain network topology in health and schizophrenia

Abstract

The human brain is a topologically complex network embedded in anatomical space. Here, we systematically explored relationships between functional connectivity, complex network topology, and anatomical (Euclidean) distance between connected brain regions, in the resting-state functional magnetic resonance imaging brain networks of 20 healthy volunteers and 19 patients with childhood-onset schizophrenia (COS). Normal between-subject differences in average distance of connected edges in brain graphs were strongly associated with variation in topological properties of functional networks. In addition, a club or subset of connector hubs was identified, in lateral temporal, parietal, dorsal prefrontal, and medial prefrontal/cingulate cortical regions. In COS, there was reduced strength of functional connectivity over short distances especially, and therefore, global mean connection distance of thresholded graphs was significantly greater than normal. As predicted from relationships between spatial and topological properties of normal networks, this disorder-related proportional increase in connection distance was associated with reduced clustering and modularity and increased global efficiency of COS networks. Between-group differences in connection distance were localized specifically to connector hubs of multimodal association cortex. In relation to the neurodevelopmental pathogenesis of schizophrenia, we argue that the data are consistent with the interpretation that spatial and topological disturbances of functional network organization could arise from excessive "pruning" of short-distance functional connections in schizophrenia.

Figure 1.

Anatomical distance of functional connectivity in fMRI brain networks of healthy participants and patients with COS. (A) The mean network connection distance increases as a function of connection density or cost, indicating that the sparsest networks formed from the most strongly correlated edges are dominated by short-distance connections. The longer distance, less strongly correlated connections are added as the networks become denser. We focus on sparsely connected networks (1–10% cost). (B) The empirical probability density of functional connection distance is highly skewed toward short-distance connections. An exponential probability distribution, P(edge) ∼ e^−ηx, where x is the anatomical distance of the edge, provides a reasonable (though imperfect) fit to the data. (C) Across the whole range of connection densities, the healthy volunteers have a lower mean network connection distance than the patients. (D) The empirical probability densities reveal proportionally more short-distance connections and proportionally less long-distance connections in the healthy volunteers compared with the patients with schizophrenia. (E,F) More long-distance and fewer short-distance connections are evident in a representative network from the patient group, compared with a representative network from the healthy volunteer group.

Figure 2.

Interplay between the anatomical distance of functional connections and topological (nonspatial) attributes of brain networks in health and schizophrenia. (A) Across subjects, the mean anatomical distance of brain networks is related to complex network properties including modularity (a measure of decomposability of the network into component modules), clustering (the “cliquishness” of connections), global efficiency (the capacity for parallel information transfer), and small worldness (the normalized ratio of clustering to path length). (B) The average functional connectivity (absolute wavelet correlation at 0.05–0.11 Hz) is lower in the schizophrenia population than in the control population, most notably for short-distance anatomical connections <5 cm. (C) Triangular or triangle-containing network motifs tend to have shorter anatomical distances in both groups. (D) Intermodular edges are longer than intramodular edges in both groups. (E) As illustrated in the population of healthy participants, nodes with longer distance anatomical connections tend to have higher degree (more connections), higher participation coefficient (more connections between different modules or communities), and lower clustering.

Figure 3.

Anatomical locations of long-distance connector hubs, in health and schizophrenia. Cortical surface maps show the distance strength of each node, defined as the degree (number of connections) of each node multiplied by its average connection distance to the rest of the network, Z-scored for each participant relative to the mean and SD of their group. Connector hubs are shown as regions of multimodal association cortex with high distance strength in (A) the healthy volunteer group and (B) the patients with schizophrenia. (C) Distance strength was significantly reduced for some connector hubs in frontal and parietal cortex in the healthy participants compared with the patients with schizophrenia (false positive correction; t-test P < 0.003).

Figure 4.

The topological and spatial abnormalities of functional networks in COS are not attributable simply to randomization of networks. (A) The schizophrenia networks are far from fully random networks, and they are also not consistent with a process of subtle randomization where 10% of normal network edges are randomized. Partial randomization of healthy brain networks causes excessive reduction in clustering and insufficient increase in connection distance compared with the results on COS networks. (B) Between-group differences in clustering and connection distance persist when networks are constructed over a range of identical threshold values, thus ensuring that all edges in all networks represent between-regional correlations greater than the same minimum value. (C) The relationships between connection distance, efficiency, modularity, and clustering persist when the topological metrics are normalized by their values in comparable random networks.