Randomization and resilience of brain functional networks as systems-level endophenotypes of schizophrenia

Significance

Using network analysis of resting-state functional MRI data, we demonstrate that significant randomization of global network metrics, and greater resilience to targeted attack on network hubs, was replicably demonstrable in Chinese patients with schizophrenia, and was also demonstrated for the first time in their nonpsychotic first-degree relatives. These results support the hypothesis that functional networks are abnormally randomized and resilient in schizophrenia and indicate that network randomization/resilience may be an endophenotype, or marker of familial risk, for schizophrenia. We suggest that the greater randomization of the brain network endophenotype of schizophrenia may confer advantages in terms of greater resilience to pathological attack that may explain the selection and persistence of risk genes for schizophrenia in the general population.

Abstract

Schizophrenia is increasingly conceived as a disorder of brain network organization or dysconnectivity syndrome. Functional MRI (fMRI) networks in schizophrenia have been characterized by abnormally random topology. We tested the hypothesis that network randomization is an endophenotype of schizophrenia and therefore evident also in nonpsychotic relatives of patients. Head movement-corrected, resting-state fMRI data were acquired from 25 patients with schizophrenia, 25 first-degree relatives of patients, and 29 healthy volunteers. Graphs were used to model functional connectivity as a set of edges between regional nodes. We estimated the topological efficiency, clustering, degree distribution, resilience, and connection distance (in millimeters) of each functional network. The schizophrenic group demonstrated significant randomization of global network metrics (reduced clustering, greater efficiency), a shift in the degree distribution to a more homogeneous form (fewer hubs), a shift in the distance distribution (proportionally more long-distance edges), and greater resilience to targeted attack on network hubs. The networks of the relatives also demonstrated abnormal randomization and resilience compared with healthy volunteers, but they were typically less topologically abnormal than the patients’ networks and did not have abnormal connection distances. We conclude that schizophrenia is associated with replicable and convergent evidence for functional network randomization, and a similar topological profile was evident also in nonpsychotic relatives, suggesting that this is a systems-level endophenotype or marker of familial risk. We speculate that the greater resilience of brain networks may confer some fitness advantages on nonpsychotic relatives that could explain persistence of this endophenotype in the population.

Schizophrenia is increasingly conceived as a brain dysconnectivity syndrome or disorder of brain network organization (1–4). Various methods have been used to demonstrate abnormal structural or functional connectivity between brain regions in patients with schizophrenia. Specifically, several recent studies have used graph theory to measure the topological pattern of connections (or edges) between regional nodes in large-scale networks derived from neuroimaging data (5–12).

The results to date of graph theoretical studies of schizophrenia are not entirely consistent, but there is some convergence around the concept of topological randomization (9, 13). For example, human brain networks (and many other complex, real-life networks) generally have a small-world topology that can be understood as intermediate between the regular, highly clustered organization of a lattice and the globally efficient organization of a random graph. Three independent functional MRI (fMRI) studies have shown that the functional brain networks of patients with schizophrenia are relatively shifted toward the random end of this small-world spectrum, i.e., they have lower clustering coefficient and greater efficiency than healthy brain networks (5, 7, 8). Previous studies have also reported schizophrenia-related disruptions in the normal community structure of fMRI networks, such as increased connectivity between modules (5), and abnormal rich clubs (14), in patients with schizophrenia. There is also some evidence that the physical (geometric) distance of edges tends to be relatively increased in structural and functional brain graphs of schizophrenia (6, 15).

There were three main objectives of this study. The first was to assess the replicability of the prior topological and geometric markers of network randomization in an independent sample of patients with schizophrenia. Specifically, we wanted to test the hypothesis that the network abnormalities most frequently reported in US or European studies of schizophrenia would also be evident in a Chinese population. Second, we tested the hypothesis that brain network randomization in patients with schizophrenia would be associated with greater resilience to targeted attack on network hubs in silico. Third, we aimed to test the hypothesis that brain network randomization/resilience is an endophenotype, or marker of familial risk for schizophrenia, that is expected to be abnormal in nonpsychotic first-degree relatives of patients as well as in the patients themselves.

We therefore analyzed resting-state fMRI data from 25 patients with schizophrenia (Sz), 25 first-degree relatives (Rel), and 29 healthy volunteers (HV). For each individual image, we constructed a functional brain graph and estimated some key topological and geometric markers of randomization (clustering coefficient, efficiency, degree distribution, distance distribution), and resilience to targeted attack and random failure. We predicted that functional brain networks would be more randomized and resilient in both Sz and Rel, compared with HV.

Results

Functional Connectivity.

At each frequency interval defined by a wavelet decomposition of the fMRI time series, the rank ordering of group mean functional connectivity HV > Rel > Sz was statistically significant [Jonckheere–Terpstra (J-T) test, P < 0.05, false discovery rate (FDR) corrected]. Post hoc t tests demonstrated that mean wavelet correlation, or functional connectivity, was significantly reduced in Sz compared with HV at all wavelet scales (Fig. 1). For consistency with many prior studies of resting-state fMRI connectivity, we focused on the frequency interval 0.05–0.1 Hz, approximately corresponding here to wavelet scale 2. However, we note that broadly similar results were obtained by analysis of other wavelet scales (Fig. S1).

Fig. 1.

Global functional connectivity strength at each of four wavelet scales (corresponding to frequency intervals) and over all frequencies (broadband) for Sz (red), Rel (green), and HV (blue). Connectivity strength (wavelet correlation) was corrected for nonsignificant age differences between groups by regression. Red asterisks denote significant rank-ordered differences in connectivity strength: Sz < Rel < HV (J-T test, P < 0.05, FDR corrected). Crosses denote values located more than 1.5× the interquartile range from the median.

Fig. S1.

Topological measures of functional brain networks in Sz (red), Rel (green), and HV (blue), at wavelet scales (A) 1 (0.1–0.2 Hz), (B) 3 (0.025–0.05. Hz) and (C) 4 (0.125–0.025 Hz). Confidence intervals on the curves represent ±1 SD. (Left) Clustering coefficient (y axis) as a function of connection density (x axis). (Right) Global efficiency as a function of connection density. The significant differences among three groups were denoted by asterisks (J-T test, P < 0.05, FDR corrected).

Global Network Topology.

There were significant between-group differences in all global topological metrics. For the clustering coefficient, the rank ordering HV > Rel > Sz was significant (J-T test; P < 0.05, FDR corrected; Fig. 2A), and post hoc t tests demonstrated significantly decreased clustering coefficient in people with schizophrenia, and their unaffected relatives, compared with healthy volunteers. In contrast, for the global efficiency, the rank ordering Sz > Rel > HV was statistically significant and post hoc t tests demonstrated significantly increased global efficiency in Sz, and Rel, compared with HV (Fig. 2B). Small worldness was generally evident over a range of graph connection densities—the so-called small-world regime corresponding to 1–24% connection density. There were significant differences in small worldness between groups: HV > Rel > Sz; and post hoc t tests demonstrated significant reductions in Sz compared with HV; small worldness was not abnormal in Rel (Fig. 2C).

Fig. 2.

Topological and geometric measures of functional brain networks in Sz (red), Rel (green), and HV (blue); confidence intervals on the curves represent ±1 SD. (A) Clustering coefficient (y axis) as a function of connection density (x axis). (B) Global efficiency (y axis) as a function of connection density (x axis). (C) Small worldness (y axis) as a function of connection density (x axis). (D) Cumulative degree distributions were best fit in each group by an exponentially truncated power law. The fitted curves with median value of the power law exponent α in each group are plotted; (Inset) boxplots represent the within-group distributions and between-group differences in the two parameters: α and the exponential cutoff, β; cross indicates significant between-group differences (t test, uncorrected P < 0.05). (E) The probability distributions of connection distance in three groups (data averaged over subjects in each group) show a greater proportion of long-distance connections, and reduced proportion of middistance connections, in schizophrenia. (F) The mean connection distance (x axis) as a function of connection density (y axis) shows a significant trend in rank ordering of the three groups, Sz > Rel = HV, where the network has longer connection distance in Sz, but not in Rel. The significant differences between groups are denoted by asterisks (J-T test, P < 0.05, FDR corrected).

Degree Distributions.

The best-fitting form of the degree distribution was generally an exponentially truncated power law. However, there were significant differences between groups in terms of mean degree distribution parameters over the small-world regime: rank ordering Sz = Rel > HV for the power law exponent, α (J-T test, uncorrected P = 0.026), but rank ordering HV > Rel = Sz for the exponential cutoff, β (J-T test, uncorrected P = 0.029). Post hoc t tests demonstrated that the power law exponent α was significantly increased but the exponential cutoff β was significantly reduced in Sz and/or Rel, compared with HV. As shown graphically in Fig. 2D, this shift in degree distribution parameters indicates that the probability of high degree hubs is abnormally reduced in both people with schizophrenia and their relatives.

Connection Distance.

The distribution of connection distance was somewhat similar in all groups (Kolmogorov–Smirnov test, pairwise comparison, P > 0.05) (Fig. 2E). However, the mean connection distance over a range of connection densities (1–24%) was different between groups: The rank ordering Sz > Rel = HV was significant (J-T test, P < 0.05, FDR corrected, Fig. 2F), and post hoc t tests demonstrated significantly longer connection distance in Sz than in HV (uncorrected P < 0.05).

Resilience.

Under random failure, the global efficiency of the networks typically remained high (about 90% of maximum efficiency), even after more than 50% of nodes had been deleted. In other words, brain networks were highly resilient to random failure (Fig. 3 A and C). However, the global efficiency of all networks was degraded more severely by targeted attack (Fig. 3 B and D). For example, after deletion of only 10% of the highest-degree hub nodes, the global efficiency of brain networks was reduced below 90% of maximum (Fig. 3D). For random failure, there were no significant between-group differences (J-T test, P > 0.05, FDR corrected). However, for targeted attack, the rank order Sz = Rel > HV was significant (J-T test, P < 0.05, FDR corrected), and post hoc t tests demonstrated that resilience to targeted attack was increased in both Sz and Rel compared with HV (Fig. 3).

Fig. 3.

Network resilience to target attack and random failure for Sz (red), Rel (green), and HV (blue); confidence intervals on the curves represent ±1 SD. (A) Network resilience against random failure (y axis) as a function of connection density (x axis). (B) Network resilience against targeted attack (y axis) as a function of connection density (x axis). The boxplots illustrate the network resilience at connection density of 10%; the significant differences between the three groups are denoted by red asterisks (J-T test, P < 0.05, FDR corrected); and cross denotes post hoc t tests with uncorrected P < 0.05. (C and D) The curves show how the global efficiency (percentage of maximum efficiency; y axis) of networks deteriorates as the proportion of nodes deleted by in silico attack (x axis) is increased, at connection density of 10%. (C) Random failure causes less rapid deterioration of global efficiency in all networks. (D) Targeted attack on network hubs causes relatively rapid deterioration in network efficiency. Sz and Rel have greater resilience to targeted attack than healthy volunteers.

Nodal Topology.

There were significant between-group differences in clustering and efficiency at a nodal level of analysis that were consistent with the results for global topology (J-T test, P < 0.05, FDR corrected). As illustrated in Fig. 4A, for nodal clustering, the rank ordering was usually HV > Rel > Sz, whereas, for nodal efficiency, the rank ordering was usually Sz > Rel > HV. Nodes demonstrating significant rank ordering of clustering HV > Rel > Sz were located mainly in bilateral precentral and postcentral cortex, and lateral and medial occipital cortex. These are areas of functionally specialized cortex (motor, somatosensory, and visual) that are known to be highly clustered in healthy functional brain networks (16). Nodes demonstrating significant rank ordering of efficiency Sz > Rel > HV were localized in dorsolateral prefrontal cortex, anterior and posterior cingulate cortex, inferior parietal cortex, superior temporal cortex, hippocampus, and caudate nucleus. All of these areas have been previously implicated in the pathophysiology of schizophrenia (11).

Fig. 4.

Nodal topological differences between groups. (A) Cortical surface maps show significant between-group differences in rank order of nodal clustering (Left) and nodal efficiency (Right) of functional brain networks (J-T trend test, P < 0.05, FDR corrected). Nodes where the rank order is Sz < Rel < HV are colored in blue; nodes where the rank order is Sz > Rel > HV are colored in red. The cortical surface maps were generated by BrainNet viewer software (www.nitrc.org/projects/bnv/) (52). (B) The mean nodal topology in the HV group (x axis) versus the difference between HV and Sz groups in mean nodal topology (y axis) are plotted for nodal clustering (Left) and nodal efficiency (Right). The colored points highlight nodes demonstrating significant between-group differences in nodal topology corresponding to the colored areas of the cortical surface maps (A). The straight lines fitted to these data have significantly nonzero negative slope, indicating that abnormally increased efficiency tends to be located in nodes with normally low efficiency whereas abnormally decreased clustering is located in nodes with normally high clustering.

Schizophrenia-related differences in nodal topology were also related to the nodal topology of the normal connectome. Specifically, the nodes that showed the greatest reduction of clustering in schizophrenia tended to have the highest clustering in the HV group (r = -0.78, P < 0.001), whereas nodes that showed the greatest increase of efficiency in schizophrenia tended to have the lowest efficiency in the HV groups (r = -0.65, P < 0.001) (Fig. 4B). Similar results were also found in Rel; see Figs. S2 and S3 and Tables S1 and S2.

Fig. S2.

Brain regions with high nodal clustering/efficiency in functional networks. Cortical surface maps show the nodal clustering (Left) and nodal efficiency (Right) of hub regions, defined as the nodal properties 1 SD greater than mean in HV (Top), Rel (Middle), and Sz (Bottom).

Fig. S3.

Hub disruption of functional networks in Rel. The mean nodal topology in HV group (x axis) versus the difference between HV and Rel groups in mean nodal topology (y axis) are plotted for nodal clustering (Left) and nodal efficiency (Right). The lines fitted to these data have significantly nonzero negative slope, indicating that abnormally increased efficiency tends to be located in nodes with normally high efficiency, whereas abnormally decreased clustering is located in nodes with normally high clustering. The colored points highlight nodes demonstrating significant between-group differences in nodal topology corresponding to the colored areas of the cortical surface maps in Fig. 4A.

Table S1.

Brain regions with significant difference between groups in nodal clustering

Brain region	Node coordinates			z score
	X	Y	Z
Left precental gyrus	−52	−2	32	3.29
Right precental gyrus	60	4	22	3.19
Left superior frontal gyrus, dorsolateral	−20	62	11	−2.55
Right superior frontal gyrus, orbital part	23	62	3	−3.53
Left middle frontal gyrus	−40	24	40	−3.21
	−28	4	57	−2.48
Right middle frontal gyrus	38	52	13	2.64
	36	48	25	2.85
Right middle frontal gyrus, orbital part	23	62	−5	−2.90
Left inferior frontal gyrus, opercular part	−48	8	15	2.57
	−48	13	17	2.63
Right inferior frontal gyrus, opercular part	51	15	4	2.44
	47	25	27	2.94
Left inferior frontal gyrus, orbital part	−38	40	−10	−2.68
Right rolandic operculum	58	−14	14	2.55
Left superior frontal gyrus, medial	−4	37	36	−2.82
Left insula	−40	−5	1	3.95
	−35	−19	10	3.20
Right anterior cingulate and paracingulate gyri	9	22	24	2.73
Left calcarine fissure and surrounding cortex	−8	−85	5	2.85
	−2	−87	−0	3.64
	1	−87	9	3.70
Right calcarine fissure and surrounding cortex	11	−85	10	3.03
Left cuneus	−7	−88	17	3.29
Right cuneus	15	−84	30	3.66
	13	−83	20	3.17
	16	−95	11	3.03
Left lingual gyrus	−18	−64	−9	2.64
Right lingual gyrus	16	−77	−10	2.58
	11	−67	−7	2.97
	15	−81	−3	2.43
Left superior occipital gyrus	−15	−87	21	2.44
	−16	−83	31	2.52
	−22	−85	29	3.16
Right superior occipital gyrus	22	−83	23	3.70
	19	−85	29	3.49
	26	−83	26	3.41
Left middle occipital gyrus	−24	−94	8	3.36
	−26	−89	16	2.77
	−34	−87	7	3.24
	−39	−82	10	2.81
	−43	−74	1	3.26
	−17	−101	3	2.54
	−21	−94	−2	3.04
	−33	−86	−1	3.05
Right middle occipital gyrus	32	−83	25	2.65
Left inferior occipital gyrus	−43	−74	−6	3.26
	−35	−82	−9	2.52
Right inferior occipital gyrus	41	−81	−6	2.53
	51	−64	−14	2.42
Left fusiform gyrus	−29	−57	−14	3.07
	−40	−52	−18	2.48
Right fusiform gyrus	32	−45	−12	2.94
	28	−53	−16	2.76
	41	−62	−18	2.45
	41	−43	−21	3.62
Left postcentral gyrus	−56	−4	18	2.96
	−44	−33	52	2.71
	−50	−19	44	2.53
	−46	−13	47	3.07
	−43	−22	52	3.12
	−51	−10	37	2.47
	−57	−9	28	4.21
	−56	−18	32	3.38
Right postcentral gyrus	65	−11	20	2.94
	55	−15	33	3.18
	63	−3	22	4.05
	53	−8	34	3.64
	52	−21	48	2.62
	40	−33	55	3.06
	37	−23	60	3.09
	45	−13	48	3.12
Left inferior parietal, but supramarginal and angular gyri	−51	−28	42	3.36
Left supramarginal gyrus	−58	−26	22	3.79
	−56	−26	34	3.37
	−57	−34	33	2.47
Right supramarginal gyrus	61	−20	29	4.41
	54	−28	39	2.78
	58	−32	30	4.66
Right angular gyrus	35	−68	45	−2.86
Left lenticular nucleus, putamen	−28	−11	4	2.46
Left thalamus	−7	−23	4	2.47
	−15	−16	8	2.72
Left heschl gyrus	−42	−20	9	3.52
Right heschl gyrus	46	−18	9	2.66
Left superior temporal gyrus	−55	−37	19	3.87
	−52	−11	−1	2.47
	−56	−34	13	2.64
Right superior temporal gyrus	62	−25	23	3.73
Right superior temporal gyrus	59	−6	1	2.76
Left middle temporal gyrus	−48	−66	4	3.20
Right middle temporal gyrus	54	−59	10	2.90
	47	−70	5	3.16
Left inferior temporal gyrus	−47	−15	−30	−2.48
	−56	−23	−24	−2.82
Right inferior temporal gyrus	49	−17	−29	−2.41

The testing order of three groups was set as Sz, Rel, and HV. The negative z score indicates the network measures were ranked in the order Sz > Rel > HV; the positive z score indicates the network measures were ranked in the order Sz < Rel < HV. The statistical criterion for between-group differences was set at P < 0.05 (J-T trend test, FDR corrected).

Table S2.

Brain regions with significant difference between groups in nodal efficiency

Brain region	Node coordinates			z score
	X	Y	Z
Left precental gyrus	−24	−22	70	3.51
Left superior frontal gyrus, dorsolateral	−18	34	48	−2.76
	−23	60	3	−2.55
	−15	25	53	−3.15
	−14	51	32	−2.36
	−15	43	42	−3.73
Right superior frontal gyrus, dorsolateral	10	54	36	−2.94
	24	25	51	−3.37
	17	30	51	−2.73
	18	59	20	−2.34
	20	16	56	−3.32
	17	42	39	−3.56
	20	53	25	−2.89
	20	38	45	−3.45
Left superior frontal gyrus, orbital part	−14	55	−15	−3.24
	−21	61	−6	−4.36
Right superior frontal gyrus, orbital part	23	62	3	−2.69
Left middle frontal gyrus	−33	27	44	−3.63
	−25	16	55	−2.33
	−36	7	51	−2.36
	−26	29	48	−3.12
	−32	17	51	−2.57
	−22	40	38	−3.08
Right middle frontal gyrus	38	21	46	−3.16
	28	54	21	−2.36
	30	28	44	−3.38
	31	15	54	−3.45
	36	48	25	−2.39
	29	38	37	−2.64
	18	50	32	−3.10
	23	38	37	−3.30
Left middle frontal gyrus, orbital part	−25	54	−11	−2.65
	−41	50	−5	−2.79
Right middle frontal gyrus, orbital part	39	55	−6	−3.07
	23	62	−5	−4.16
Left inferior frontal gyrus, triangular part	−43	39	1	−2.50
	−40	50	4	−2.61
Right inferior frontal gyrus, triangular part	53	31	2	−2.44
	47	39	1	−2.40
Left inferior frontal gyrus, orbital part	−38	40	−10	−2.69
	−35	38	−13	−2.65
	−47	23	−7	−2.32
	−46	37	−6	−2.34
Right inferior frontal gyrus, orbital part	42	41	−11	−2.70
Left rolandic operculum	−46	−14	13	2.86
	−48	−16	14	3.42
Right rolandic operculum	58	−14	14	2.56
	50	−7	12	2.31
	49	−5	16	2.30
Left superior frontal gyrus, medial	−4	53	38	−2.51
	−6	33	55	−2.53
	−5	50	20	−2.91
	−6	44	48	−2.70
Right superior frontal gyrus, medial	10	34	57	−2.65
	7	39	41	−2.36
Left superior frontal gyrus, medial orbital	−4	55	−10	−2.51
Right superior frontal gyrus, medial orbital	6	51	−8	−2.38
Left insula	−35	−19	10	2.72
Right insula	40	−4	10	3.74
	36	−18	13	3.89
Left anterior cingulate and paracingulate gyri	−6	35	−5	−2.71
Right median cingulate and paracingulate gyri	8	−42	34	−3.31
Left posterior cingulate gyrus	−6	−46	19	−2.57
	−4	−42	29	−3.11
Right posterior cingulate gyrus	7	−43	20	−2.34
Left hippocampus	−21	−11	−19	−2.51
Right calcarine fissure and surrounding cortex	16	−57	12	2.84
	19	−63	10	2.52
Right lingual gyrus	21	−48	−7	2.94
Left middle occipital gyrus	−24	−94	8	−2.39
	−32	−73	35	−2.63
Right fusiform gyrus	29	−64	−10	2.33
Left postcentral gyrus	−20	−39	74	2.61
	−61	−17	21	3.01
	−36	−38	59	2.56
	−21	−34	68	3.37
	−56	−13	20	2.71
	−30	−31	65	3.86
	−27	−40	64	3.38
	−31	−25	64	2.95
Right postcentral gyrus	30	−34	67	3.33
	24	−34	63	3.04
	14	−36	74	2.40
	37	−36	62	2.60
	26	−26	67	2.81
	19	−27	73	2.68
Left inferior parietal, but supramarginal and angular gyri	−31	−65	43	−2.44
Right inferior parietal, but supramarginal and angular gyri	47	−51	47	−2.68
Left angular gyrus	−38	−64	43	−3.24
	−43	−63	39	−3.64
	−50	−56	31	−2.62
	−45	−66	32	−3.06
Right angular gyrus	46	−59	44	−2.50
	54	−52	31	−2.66
Right precuneus	9	−61	41	−2.90
Left paracentral lobule	−11	−20	76	2.79
	−7	−20	63	2.40
Left caudate nucleus	−7	14	−5	−2.60
Right caudate nucleus	15	21	−1	−3.19
	9	12	1	−3.38
Right lenticular nucleus, putamen	31	−10	1	2.47
Left superior temporal gyrus	−53	−18	3	2.43
Right superior temporal gyrus	57	−27	13	2.94
Left temporal pole: superior temporal gyrus	−34	18	−28	−2.93
Left middle temporal gyrus	−61	−27	−10	−4.12
	−61	−42	−1	−3.79
	−53	−3	−27	−3.31
	−59	−18	−11	−3.25
	−57	−47	−7	−4.26
	−62	−34	−3	−4.30
	−61	−37	−12	−4.62
	−59	−16	−19	−2.92
	−52	2	−24	−2.36
Right middle temporal gyrus	63	−35	−3	−3.66
	64	−24	−8	−3.07
	62	−14	−13	−2.83
	63	−14	−20	−3.59
	63	−28	−11	−3.85
	57	−3	−25	−3.13
Left temporal pole: middle temporal gyrus	−48	13	−31	−2.95
Left inferior temporal gyrus	−57	−50	−15	−2.67
	−58	−41	−18	−3.99
	−47	−15	−30	−2.96
	−51	−54	−19	−2.54
	−45	−39	−22	−2.39
	−56	−23	−24	−4.14
Right inferior temporal gyrus	60	−20	−26	−3.21
	63	−29	−21	−2.92
	61	−39	−9	−2.61

The testing order of three groups was set as Sz, Rel, and HV. The negative z score indicates the nodal efficiencies were ranked in the order Sz > Rel > HV; the positive z score indicates the nodal efficiencies were ranked in the order Sz < Rel < HV. The statistical criterion for between-group differences was set at P < 0.05 (J-T trend test, FDR corrected).

Correlational Analysis of Network Metrics and Clinical Variables.

The network metrics were moderately correlated with each other (Table S3). Over all participants in the study, connectivity strength was negatively correlated with physical (Euclidean) distance of functional connections (r = −0.30) and with three topological measures of network integration: global efficiency (r = −0.40), resilience to targeted attack (r = −0.65), and the power law exponent of a truncated power law degree distribution (r = −0.58). In other words, low strength connections tended to traverse long distances and to be important for both (i) the emergence of high-degree hubs, conferring vulnerability to targeted attack, and (ii) short characteristic path length or high global efficiency. On the other hand, connectivity strength was positively correlated with clustering coefficient (r = 0.69) and the exponential cutoff parameter of the degree distribution (r = 0.56), meaning that high strength connections tended to be important both for a more homogeneous degree distribution and for more clustered or segregated topology. Repeating this correlational analysis group by group, we found that the same relationships between connectivity strength, resilience, and power law degree distribution parameter were consistently and significantly expressed in each group. The relationship between strength and distance was not significant in any individual group, which may reflect the fact that functional connectivity strength decays as a nonlinear function of distance and correlation is a measure of linear association (16). The normal relationship between strength and global efficiency was not expressed by Sz or Rel; see Table S3 for details.

Table S3.

Pearson’s correlation coefficient between topological metrics and clinical variables in each group separately and for all subjects

Variables	Correlation coefficient/P value	Clustering coefficient	Global efficiency	Small worldness	Degree distr. (alpha)	Degree distr. (beta)	Connectivity distance	Target attack	Random failure	PANSS-P	PANSS-N	PANSS-G	PANSS-Total	Chlorpromazine equivalent (value after an outlier exclusion)
Sz (n = 25, df = 23)
Connectivity strength	r	0.645	−0.287	0.35	−0.582	0.514	−0.306	−0.909	−0.295	0.068	0.138	0.168	0.144	−0.173
	P	0.001	0.164	0.086	0.002	0.009	0.136	<0.001	0.152	0.747	0.509	0.421	0.491	0.43
Clustering coefficient	r		−0.771	−0.041	−0.575	0.513	−0.205	−0.596	−0.53	−0.055	0.007	−0.024	−0.023	0.176
	P		<0.001	0.845	0.003	0.009	0.326	0.002	0.006	0.794	0.972	0.911	0.912	0.422
Global efficiency	r			0.651	0.611	−0.744	−0.164	0.385	0.866	0.124	0.151	0.149	0.158	−0.533 (−0.281)
	P			<0.001	0.001	<0.001	0.434	0.057	<0.001	0.555	0.472	0.477	0.452	0.009 (0.205)
Small worldness	r				0.255	−0.531	−0.422	−0.118	0.725	0.155	0.292	0.247	0.262	−0.641 (−0.321)
	P				0.218	0.006	0.036	0.576	<0.001	0.46	0.157	0.234	0.206	0.001 (0.145)
Degree distr. (alpha)	r					−0.886	−0.262	0.753	0.737	0.016	0.068	0.200	0.115	−0.208
	P					<0.001	0.206	<0.001	<0.001	0.939	0.748	0.338	0.584	0.342
Degree distr. (beta)	r						0.280	−0.706	−0.902	0.023	−0.088	−0.107	−0.072	0.32
	P						0.175	<0.001	<0.001	0.915	0.675	0.611	0.731	0.136
Connectivity distance	r							0.099	−0.295	−0.141	−0.214	−0.466	−0.321	0.366
	P							0.638	0.152	0.501	0.304	0.019	0.118	0.086
Targeted attack	r								0.498	−0.045	−0.066	−0.08	−0.072	0.017
	P								0.011	0.832	0.754	0.703	0.731	0.94
Random failure	r									0.133	0.151	0.194	0.179	−0.464
	P									0.525	0.472	0.352	0.391	0.026
Rel (n = 25, df = 23)
Connectivity strength	r	0.531	−0.321	−0.077	−0.424	0.459	−0.290	−0.810	−0.467
	P	0.006	0.117	0.714	0.035	0.021	0.160	<0.001	0.019
Clustering coefficient	r		−0.755	−0.375	−0.580	0.619	−0.222	−0.546	−0.630
	P		<0.001	0.065	0.002	0.001	0.285	0.005	0.001
Global efficiency	r			0.875	0.709	−0.852	0.215	0.310	0.895
	P			<0.001	<0.001	<0.001	0.302	0.132	<0.001
Small worldness	r				0.618	−0.777	0.181	0.102	0.823
	P				0.001	<0.001	0.387	0.627	<0.001
Degree distr. (alpha)	r					−0.931	0.221	0.638	0.791
	P					<0.001	0.289	0.001	<0.001
Degree distr. (beta)	r						−0.257	−0.611	−0.934
	P						0.215	0.001	<0.001
Connectivity distance	r							0.308	0.253
	P							0.135	0.223
Targeted attack	r								0.494
	P								0.012
HV (n = 29, df = 27)
Connectivity strength	r	0.787	−0.501	0.029	−0.694	0.643	−0.173	−0.191	0.199
	P	<0.001	0.006	0.880	<0.001	<0.001	0.370	0.320	0.300
Clustering coefficient	r		−0.719	−0.041	−0.680	0.570	−0.190	−0.087	0.234
	P		<0.001	0.831	<0.001	0.001	0.324	0.653	0.222
Global efficiency	r			0.666	0.795	−0.772	0.452	0.011	−0.090
	P			<0.001	<0.001	<0.001	0.014	0.956	0.642
Small worldness	r				0.453	−0.514	0.548	−0.131	0.046
	P				0.014	0.004	0.002	0.497	0.812
Degree distr. (alpha)	r					−0.946	0.407	0.191	−0.021
	P					<0.001	0.028	0.322	0.915
Degree distr. (beta)	r						−0.429	−0.293	−0.068
	P						0.020	0.122	0.728
Connectivity distance	r							0.007	−0.049
	P							0.972	0.802
Targeted attack	r								0.618
	P								<0.001
All subjects (n = 79, df = 77)
Connectivity strength	r	0.686	−0.397	0.070	−0.577	0.561	−0.302	−0.651	−0.263
	P	<0.001	<0.001	0.539	<0.001	<0.001	0.007	0.000	0.019
Clustering coefficient	r		−0.755	−0.177	−0.613	0.584	−0.261	−0.460	−0.400
	P		<0.001	0.118	<0.001	<0.001	0.020	<0.001	<0.001
Global efficiency	r			0.754	0.691	−0.793	0.169	0.277	0.656
	P			<0.001	<0.001	<0.001	0.137	<0.001	<0.001
Small worldness	r				0.453	−0.621	0.050	−0.027	0.583
	P				<0.001	<0.001	0.663	0.810	<0.001
Degree distr. (alpha)	r					-0.923	0.079	0.566	0.579
	P					<0.001	0.487	<0.001	<0.001
Degree distr. (beta)	r						−0.117	−0.560	−0.685
	P						0.306	<0.001	<0.001
Connectivity distance	r							0.157	−0.002
	P							0.167	0.987
Targeted attack	r								0.559
	P								<0.001

The age was regressed out before correlation. The degree of freedom for correlational analysis may be overestimated because the age was regressed, and the Sz and Rel were related. Italic boldfaced values indicate significant correlation (P < 0.05); P, P values; r, correlation coefficient. For PNASS entries: P, positive; N, negative; G, general psychopathology.

In the Sz group only, we explored the relationships between all network metrics and questionnaire measures of psychotic symptom severity [the Positive and Negative Syndrome Scale (PANSS) global and subscale scores] and a measure of current antipsychotic drug exposure (chlorpromazine equivalent dose, milligrams per day). The global psychotic symptom score was negatively correlated with connection distance (r = −0.47); there were no other significant associations between clinical variables and network measures. Antipsychotic drug exposure was negatively correlated with both global efficiency (r = −0.53) and small worldness (r = −0.64), but these effects were not significant after exclusion of a single outlier with very high antipsychotic drug exposure; see Table S3 and Fig. S4 for details.

Fig. S4.

The relationships between network metrics and clinical variables in the Sz group. (A) The connectivity distance was negatively correlated with PANSS general psychopathology. (B) Significant correlations between chlorpromazine exposure and (Bottom) small worldness or (Top) global efficiency were found; however, after excluding a single Sz with a very high level of antipsychotic drug exposure (marked by x), there was no significant correlation between network metrics and treatment.

Discussion

It is encouraging that many of these graph theoretical results on an independent Chinese sample are consistent with prior functional network studies of schizophrenia in US or European populations, suggesting that these are internationally replicable diagnostic markers. The global and nodal topological changes of increased global efficiency and decreased clustering coefficient are consistent with prior reports of “subtle randomization” of brain networks in schizophrenia (5–8). Randomization is also consistent with the degree distribution being less fat tailed, and the distance distribution being more weighted toward long-distance connections, in schizophrenia (6).

In this context, it is empirically more novel, although conceptually not surprising, that schizophrenia should also be associated with greater than normal resilience of functional networks to targeted attack. Random graphs, as shown in Fig. 3, maintain high levels of global efficiency even after a large percentage of nodes have been deleted, whether randomly or by targeted attack on the higher-degree hubs. Complex networks, like the brain, the Internet, and many other nonrandom systems, are more vulnerable to targeted attack because they have more heterogeneous degree distributions than a random graph, and the deletion of high-degree hubs consequently has a more serious effect on the global integrity of the network (17). Thus, it is predictable that functional networks in schizophrenia, being topologically more random than normal, and with a less heterogeneous degree distribution, should be more resilient to targeted attack, as we have shown.

We interpret this result by supposing that topological resilience may be advantageous, to some extent, simply because it protects the integrity of the network from pathological attack. It seems increasingly clear from neuroimaging studies of brain network topology in neurological and psychiatric disorders that “lesions” of gray matter measured by MRI tend to be concentrated in high-degree hub regions of the brain (18, 19). This pattern of results is compatible with the hypothesis that hubs are preferentially vulnerable to pathogenesis and/or that damaged hubs are especially likely to be symptomatic. There is also evidence from pathogenic modeling of neurodegenerative processes on imaging networks that Alzheimer’s disease and related disorders can be understood to progress by propagation between nodes, which will naturally expose the hubs of the brain to the degenerative process at a relatively early stage in its propagation through the connectome (20, 21).

Given this prior evidence that brain disorders preferentially target high-degree hub nodes, it seems reasonable to expect that brain networks with greater resilience to computational attack on their hubs might in real life confer some survival advantage in the face of pathological attack. This advantage might exert a positive selection pressure on genes favoring network randomization, which might in turn explain the persistence in the population of alleles that, at “high dose” or in adverse combinations, are associated with increased incidence of a disabling neurodevelopmental disorder like schizophrenia. However, it is possible that there is some other factor that drives emergence of this systems-level endophenotype, and its hypothetically greater resilience to pathological attack is immaterial to its selection. One testable hypothesis generated by these reflections is that the first-degree relatives of patients with schizophrenia might have reduced incidence or severity of brain disorders, such as Alzheimer’s disease, that are associated with gray matter volume deficits in structural network hubs.

A conceptually related previously unidentified result of this study is that it is the first, to our knowledge, to demonstrate that topological abnormalities of functional networks are also evident in the nonpsychotic, first-degree relatives of patients. Compared with HV, we have shown that Rel had significantly reduced clustering coefficient, increased efficiency, less fat-tailed degree distributions, and greater resilience to targeted attack. In other words, fMRI networks in Rel also demonstrated an abnormal shift to greater randomization of network topology. These results suggest that fMRI network randomization is a marker of genetic or shared environmental risk for disorder, rather than simply a marker of schizophrenia per se. Equally, the abnormal topological profile in the fMRI networks of Rel discounts possible interpretations of the abnormalities in the Sz group in terms of their exposure to antipsychotic medication or other factors specifically related to a clinical diagnosis of schizophrenia. Given the high heritability of functional connectivity and functional network markers (22, 23), and the high heritability of schizophrenia, it is plausible that the abnormalities of network randomization demonstrated here represent the effects of genetic variants conferring risk for schizophrenia. However, it would require a twin study to rule out the alternative possible interpretation that network randomization is indicative of shared environmental effects.

Two questions in particular arise when thinking about these putative network endophenotypes of schizophrenia. First, what is different about the network configuration of patients compared with their relatives that could explain why the relatives are not psychotic? We do not have a complete answer to this question, but it is notable that Rel did not converge in all respects on the pattern of network abnormalities described in Sz. For example, Sz had significantly reduced small worldness, and greater proportion of long-distance connections, whereas Rel were not significantly different from normal on these measures. On many other topological measures (such as efficiency and resilience to targeted attack), it was also notable that the average scores of Rel were intermediate between the scores of Sz and HV. In short, the randomization endophenotype may be more topologically extreme and/or more biologically expensive in patients compared with their first-degree relatives.

A second key question concerns the potentially beneficial aspects of network randomization. It has been shown that higher-IQ individuals tend to have more-efficient structural and functional networks (24, 25), that more-difficult cognitive tasks demand more-integrated or efficient functional network topology (26, 27), and that a pharmacological challenge (acute nicotine replacement in abstinent cigarette smokers) that enhanced attention also increased efficiency and connection distance of fMRI networks (28). These observations are consistent with earlier theoretical claims that higher-order conscious processing depends on access to a “global workspace” rather than a segregated, modular architecture (29–31). This would imply that the greater efficiency of more random network organization in patients with schizophrenia should be associated with superior performance on higher-order cognitive tasks. However, in fact, this is not the case for schizophrenia, which is typically associated with moderate to severe impairments in executive function and working memory. The normal link between greater network efficiency and superior cognitive performance seems to be disrupted in schizophrenia, for reasons that are not yet known.

There are several limitations to this work. Sz were receiving antipsychotic drugs that can affect functional connectivity and network topology (32, 33). However, this cannot explain the network abnormalities in Rel, as they were unmedicated (except one who was taking antidepressants). A more fundamental limitation is that the edges of fMRI networks represent above-threshold correlations between time series, but the underlying biological substrate of this functional connectivity is not well characterized. We used Euclidean distance between nodes as a simple measure of the physical distance of edges in the functional brain graphs. Because functional connectivity does not securely imply a direct anatomical connection (34), and because anatomical connections are typically not linear, the Euclidean distance will generally be an underestimate of the true anatomical (axonal) distance between functionally connected areas of the brain. We have assumed that this bias applies consistently between groups and therefore does not substantively distort the rank order of different groups in terms of connection distance. Developments in human diffusion-weighted imaging may provide more-accurate estimates of the anatomical connection distance subtending functional connectivity in future. The construction of brain graphs from any modality of neuroimaging data entails multiple methodological choices about preprocessing and analysis that could influence the pattern of results. We have addressed this issue by testing that key results are robust to contemporary standards for correction of head motion (35–37) and to reasonable variation in other analysis steps, including choice of parcellation, wavelet scale, and connection density.

Methods

Sample.

We recruited three groups of participants: patients with schizophrenia, Sz (n = 35); the first-degree relatives of patients with schizophrenia, Rel (n = 39); and healthy volunteers, HV (n = 36). Sz and Rel were recruited from the Psychiatric Outpatient Department of Lo-Sheng Sanatorium and Hospital in Taipei, Taiwan. Sz were diagnosed according to the Diagnostic and Statistical Manual of Mental Disorders-IV criteria (38) for schizophrenia, and completed PANSS (39) for evaluation of psychotic symptom severity. Rel and HV were cognitively normal with no history of neurological or psychiatric disorders, and had no cognitive complaints, confirmed by Mini-International Neuropsychiatric Interview (40). After elimination of subjects due to uncontrolled head motion and to optimize matching of the remaining groups for age and sex, the final sample included 25 Sz, 25 Rel, and 29 HV subjects; see SI Text, Table S4, and Fig. S5 for details. There were no significant differences between groups in terms of sex, age, handedness (41), or mean or maximum head displacement. All Sz were medicated: 9 Sz were taking typical antipsychotics, of which 2 were also taking antidepressants; 14 Sz were taking atypical antipsychotics, of which 2 were also taking antidepressants; and 2 Sz were taking antidepressants only. The average antipsychotic dose was 408 mg/d in chlorpromazine equivalents. One Rel had a history of mild depressive disorder and was taking antidepressants. The remaining participants were not taking any medication at the time of study. The study was approved by the Institutional Review Board of Taichung Veterans General Hospital, Taichung, Taiwan. All participants gave informed consent in writing. Further details on sample recruitment and assessment are provided in SI Text.

Table S4.

Demographic and clinical characteristics of final sample

Characteristics	Sz (n = 25)	Rel (n = 25)	HV (n = 29)	ANOVA test/χ2 test
				F/χ2	P
Sex (F/M)	16/9	17/8	19/10	0.09	P = 0.956
Age, y	36.6 (13.8)	46.7 (17.3)	38.3 (13.5)	3.08	P = 0.052
Duration of illness, y	9.28 ± 8.15	—	—	—	—
Chlorpromazine equivalent dose	408 ± 432	—	—	—	—
PANSS symptoms
Total	58.9 (19.8)	—	—	—	—
Positive	13.6 (5.8)	—	—	—	—
Negative	15.0 (7.6)	—	—	—	—
General psychopathology	30.4 (8.4)	—	—	—	—
Executive function (WCST)
Perseverative errors, %	25.5 (17.9)	22.5 (17.1)	12.0 (7.5)	6.225	P = 0.003
Categories	3.4 (3.0)	4.5 (3.2)	5.5 (1.4)	4.501	P = 0.016
Conceptual level responses	62.1 (25.2)	62.9 (33.2)	61.8 (12.4)	0.003	P = 0.988
Wechsler Digit Span Forward Test	12.9 (2.5)	12.1 (2.3)	14.3 (1.8)	8.298	P = 0.001
Wechsler Digit Span Backward Test	7.1 (3.1)	6.8 (1.6)	9.7 (2.9)	11.633	P < 0.001

Scores are shown with mean (SD). WCST, Wisconsin Card Sorting Test.

Fig. S5.

Flowchart of head motion estimation and subject exclusion for Sz, Rel, and HV. (i) In total, 110 participants were enrolled in this study. (ii) After fMRI motion correction, the participants were discarded if any of the six head motion parameters estimated during movement correction was greater than 2 mm translation or 2 degrees rotation. (iii) Images having FD > 0.5 mm and also having DVARS > 3% baseline signal were flagged, and participants who had >10% frames marked were excluded. The movement/connectivity correlation versus Euclidean distance was examined at group level. (iv) Sz and Rel in these two groups were paired to ensure each Sz was matched with at least one of their Rel, and vice versa. Rel and HV were also examined to match the sex and age between all three groups.

Magnetic Resonance Imaging.

Resting-state fMRI data were acquired using a 3T MR system (Siemens Magnetom Tim Trio) at National Yang-Ming University, Taipei, Taiwan, using a gradient echo-planar imaging sequence sensitive to blood oxygenation level-dependent contrast; see SI Text for detailed imaging protocols.

fMRI Preprocessing.

The preprocessing procedures for the fMRI datasets in native space included slice-timing correction; motion correction to the first volume with rigid-body alignment; obliquity transform to the structural MR image; spatial smoothing within functional mask with a 6-mm at full-width at half-maximum Gaussian kernel; intensity normalization to a whole brain median of 1,000 (35, 37); wavelet despike (removing signal transients related to small amplitude (<1 mm) head movements) (37); and multiple regression of motion parameters and their first derivatives, and the global average white matter (WM) and cerebrospinal fluid (CSF) signals, from the fMRI time series data. The effects of transient micromovements on functional connectivity were carefully assessed and controlled in individuals and groups; see refs. 35–37 and SI Text. Preprocessed data were spatially normalized to Montreal Neurological Institute (MNI) stereotactic standard space by an affine transformation and interpolated to 3.4-mm cubic voxels. The gray matter areas were parcellated into 638 regions of approximately similar size (26), and gray matter regions were excluded if the signal quality in regions was not satisfactory in all participants, resulting in a set of 585 motion-corrected, regional mean fMRI time series for each participant; see SI Text and Fig. S6 for details. Preprocessing, spatial normalization, and parcellation procedures were implemented with Analysis of Functional NeuroImages (AFNI) (42) and FMRIB Software Library (FSL v5.02, fsl.fmrib.ox.ac.uk/fsl/fslwiki/). The BrainWavelet Toolbox was used for correction of transient head movements (37) (www.brainwavelet.org).

Fig. S6.

The excluded 53 brain regions. The fMRI signal did not satisfy the criteria for signal quality (mean tSNR > 80) in all participants, mostly in orbitofrontal and inferior temporal areas that are frequently compromised by susceptibility artifact.

Functional Connectivity Estimation.

We used the maximal overlap discrete wavelet transform with a Daubechies 4 wavelet to decompose each fMRI time series into four scales or frequency intervals: scale 1, 0.10–0.20 Hz; scale 2, 0.05–0.10 Hz; scale 3, 0.025–0.05 Hz; and scale 4, 0.0125–0.025 Hz. We estimated the pairwise wavelet correlations between the wavelet coefficients at each scale for each of 183,921 possible pairs of regions.

Graph Theoretical Analysis of Network Connections.

The absolute wavelet correlation matrices were used to construct binary undirected graphs. The minimum spanning tree that connected all 585 regional nodes with 584 edges was first defined, and then additional edges were added in decreasing order of wavelet correlation to construct a series of graphs for each individual with connection density in the range 1–100% in increments of 1% (5, 6). The following global topological parameters were estimated for each graph at each connection density: global efficiency, a measure of network integration; clustering coefficient, a measure of network segregation; and small worldness, the ratio of normalized clustering to normalized efficiency. The degree, clustering, and efficiency were also estimated for each regional node. All of these metrics have been frequently used in prior graph theoretical studies of fMRI data (43–47) and are described in more detail in SI Text. They were estimated using MATLAB code in the Brain Connectivity Toolbox (see ref. 47; www.brain-connectivity-toolbox.net).

Degree Distribution, Network Connection Distance, and Resilience.

The probability distribution of degree (K) over all nodes in the network (the degree distribution) was best fit to an exponentially truncated power law $P\left(K\right)=K^{\alpha -1}{e}^{K/\beta }$, which has two parameters, the power law exponent, $\alpha$, and the exponential cutoff, $\beta$ (16); see SI Text for details. The connection distance was simply defined as the Euclidean distance between the centroids of each pair of regional nodes connected by an edge in MNI stereotactic standard space (6, 16). To test the resilience of each network, we simulated attacks on the network by removal of nodes either in descending order of their degree (targeted attack on hubs) or in random order (random failure). We thus incrementally increased the percentage of deleted nodes from 0 to 100% in increments of 1%, and recalculated the global efficiency of the remaining network after deletion of each node (17). The area under the curve of normalized global efficiency (scaled to maximum) versus the percentage of deleted nodes was defined as a summary measure of the resilience of a network (48).

Nodal Topology.

Efficiency and clustering were estimated for each regional node in the series of networks with connection density in the range 1–24%, in increments of 1%. To explore the relationship between abnormal nodal topology in patients and normative nodal topology, the difference of nodal topology between Sz and HV groups at each node was correlated with the corresponding nodal topology metric in the HV group only (49).

Statistical Analysis and Hypothesis Testing.

To assess the ordered between-group differences in the measures of functional connectivity and functional network organization, we used the J-T test (50) to test the hypotheses that metrics were ranked in the order Sz > Rel > HV or HV > Rel > Sz. If this test indicated significant differences between the medians of all three groups, we conducted additional pairwise t tests to compare network metrics between Sz versus HV groups and Rel versus HV groups. Two significance levels of stringency were set for statistical testing: uncorrected P < 0.05 and FDR correction at the 5% level (51).

SI Text

Recruitment and Assessment Details.

Patients were diagnosed according to the Diagnostic and Statistical Manual of Mental Disorders-IV criteria (38) for schizophrenia, and underwent structured clinical assessments to reconfirm the diagnosis and evaluate psychiatric comorbidity. Patients also completed the PANSS (39) for evaluation of psychotic symptom severity. Patients’ relatives and healthy volunteers were cognitively normal with no history of neurological or psychiatric disorders, and had no cognitive complaints, confirmed by Mini-International Neuropsychiatric Interview (40). All participants also completed the Wisconsin Card Sorting Test (53) (one failed to complete), and the Wechsler Digit Span Forward and Backward tests.

Exclusion criteria included history of substance abuse, mental retardation, systemic medical or neurological disorder, brain trauma, unstable psychotic symptoms, or psychotropic medication adjustment within 3 mo preceding the study.

Participants.

We recruited three groups of participants: patients with schizophrenia, Sz (n = 35); the first-degree relatives of patients with schizophrenia, Rel (n = 39); and healthy volunteers, HV (n = 36). Sz and Rel were recruited from the Psychiatric Outpatient Department of Lo-Sheng Sanatorium and Hospital in Taipei, Taiwan. Diagnosis of schizophrenia was made according to standardized criteria by a structured interview. Rel were screened for a past or current history of psychotic symptoms by structured interview. HV were recruited by advertisement from the local community and had no known personal or family history of psychiatric disorder. After elimination of subjects due to uncontrolled head motion and to optimize matching of the remaining groups for age and sex, the final sample included 25 Sz, 25 Rel, and 29 HV subjects; see Table S4, and Fig. S5 for details. There were no significant differences between groups in terms of sex, age, handedness, or mean or maximum head displacement.

All subjects in the final dataset were right-handed, except one Rel was left-handed, as determined by the Edinburgh Handedness Inventory (41). All patients were medicated: 9 Sz were taking typical antipsychotics, of which 2 were also taking antidepressants; 14 Sz were taking atypical antipsychotics, of which 2 were also taking antidepressants; and 2 Sz were taking antidepressants only. The average antipsychotic dose was 408 mg/d in chlorpromazine equivalents. One Rel had a history of mild depressive disorder and was taking antidepressants. The remaining participants were not taking any medication at the time of study.

The study was approved by the Institutional Review Board of Taichung Veterans General Hospital, Taichung, Taiwan. All participants gave informed consent in writing.

Magnetic Resonance Imaging.

MRI data were acquired using a 3T MR system (Siemens Magnetom Tim Trio) at National Yang-Ming University, Taipei, Taiwan, equipped with a high-resolution 12-channel head array coil. To minimize head motion, each subject’s head was immobilized with cushions inside the coil during scanning. An anatomical T1-weighted image was acquired with sagittal 3D magnetization-prepared rapid gradient echo sequence: repetition time (TR) = 3,500 ms, echo time (TE) = 3.5 ms, voxel size = 1 × 1 × 1 mm³. Resting-state fMRI data were acquired while subjects were lying quietly and with their eyes closed in the scanner, using a gradient echo-planar imaging sequence sensitive to blood oxygenation level dependent contrast: TR = 2,500 ms, TE = 27 ms, flip angle = 90°, FOV = 220 × 220 mm², thickness = 3.4 mm without gap, matrix size = 64 × 64, voxel size = 3.44 × 3.44 × 3.4 mm³, 200 volumes. An additional diffusion-weighted MRI dataset was acquired, but these data are not reported here. Total scan time for each subject was ∼35 min 19 s.

Functional MRI Preprocessing.

The core image preprocessing included the following steps, implemented by the corresponding AFNI, FSL, or BrainWavelet functions italicized in parentheses. Slice timing correction was applied with seventh-order heptic Lagrange polynomial interpolation (3dTShift). Motion correction parameters were estimated with 6 degrees of freedom by rigid-body alignment of the image at each time point to the first image in the series (3dvolreg). Obliquity transformation parameters were estimated for the first fMRI image relative to structural MRI images (3dWarp). Functional-to-structural image coregistration parameters were estimated using a gray matter mask by 12 degrees of freedom affine alignment with the local Pearson correlation cost functional (fast, 3dAllineate). The transformation parameters for motion correction, obliquity transformation, and structural coregistration were then applied in one step to each fMRI image in the individual series (3dAllineate). Each image in the realigned series was spatially smoothed with a 2D Gaussian kernel (6 mm at full width at half maximum) within the brain mask, generated from the first fMRI image (bet, 3dBlurInMask). A within-run intensity normalization to a whole-brain median of 1,000 was computed (3dBrickStat, 3dcalc). A wavelet despike for functional time series was applied (WaveletDespike) (37). The nuisance variables, including six estimated motion parameters (translations and rotations in 3D) and their first derivatives, and the global average WM and CSF, were regressed out by a general linear model (3dBandpass). The averaged WM and CSF signals were obtained by averaging the time series in corresponding tissue masks that were thresholded at 80% tissue probability (fast, 3dmaskave). The spatial normalization parameters for transformation from native space to MNI stereotactic standard space were estimated by registering the structural images to the MNI152 T1 template image, and the parameters were then applied to the functional images previously coregistered to the individual structural MRI data with fixed 3.4-mm cubic voxel size (@auto_tlrc, adwarp).

Head Movement Correction and Subject Exclusion Criteria.

Scans were excluded from further analysis if any of the six head motion parameters estimated during movement correction were greater than 2 mm translation or 2 degrees rotation. To ensure adequate correction of artifactual signal changes due to excessive head motion, we additionally implemented the modified methods originally described by Power et al. (35).

After fMRI preprocessing and band-pass filtering (0.02 Hz < f < 0.1 Hz), images having framewise displacement > 0.5 mm (FD, the sum of the derivatives of translation and arc length displacement converted from rotation with radius of 50 mm) and also having DVARS > 3% baseline signal (DVARS denotes the 10 × percentage signal change of frame-to-frame differences in fMRI signal) were flagged. We also flagged frames occurring one frame before and two frames after the frames with high FD and DVARS. The marked frames were then “scrubbed” (or deleted from the time series), and the difference between scrubbed and unscrubbed correlations was estimated (∆R) and plotted against the Euclidean distance between regions.

We also examined the relationship between mean head motion and the distance of interregional connectivity at group level, as proposed by Satterthwaite et al. (36). The connectivity between each pair of brain regions was estimated by Pearson’s correlation coefficients; the mean head motion across all subjects was defined by an average of the FD corresponding to 3D translations. The correlation between functional connectivity and head motion was then estimated and plotted against the Euclidean distance between regional pairs.

Based on the results of these two additional analyses of transient head movement (at individual and group levels), we excluded four Sz, three Rel, and two HV who had >5% frames marked for scrubbing. There was no evidence for residual movement effects in the diagnostic plots of ΔR versus Euclidean distance (35) or movement/connectivity correlation versus Euclidean distance (36) for this reduced sample. All results were identical after including mean FD as a covariate in statistical analysis.

In total, therefore, we excluded eight Sz and six Rel to pair the patients and relatives in these two groups, ensuring that each Sz was matched with at least one of their Rel, and vice versa. Finally, we excluded seven HV to match the mean sex and age between all three groups, and to ensure that there were no significant differences in terms of mean FD or maximum displacement due to head motion. See Fig. S5 for more details on each step.

Gray Matter Regions for Network Construction.

The gray matter areas were initially defined using automated anatomical labeling (54) and then subdivided into 638 finer regions with similar size (26, 55); no regional parcel crossed the midline between hemispheres or lobar boundaries within hemispheres. Voxel-wise temporal signal-to-noise ratio (tSNR) was estimated after motion correction and smoothing (56, 57), and averaged over voxels for each gray matter region. Only the regions with tSNR larger than 80 were included for network construction (8, 56, 57). Thus, 53 regions were excluded from consideration, mostly in orbitofrontal and inferior temporal areas that are frequently compromised by susceptibility artifact (Fig. S6), resulting in a total of 585 regions.

Graph Properties.

This study used several metrics to estimate the topological properties of functional networks. Clustering coefficient, efficiency, and degree were estimated at each regional node. The degree distribution was used to summarize nodal degree over the whole brain. Nodal clustering and efficiency were averaged over nodes to estimate global clustering and efficiency. Small worldness was also estimated at a whole-brain level.

For each node, the clustering coefficient is defined as the ratio of the existing connections to all possible connections of the subgraph that is composed by the nearest neighbors of the node. The clustering coefficient of a given node $i$ in an undirected network can be expressed as

$$C\left(i\right)=\frac{2E_i}{K_i\left(K_i-1\right)}$$ [S1]

where $E_i$ is the number of connections of the subgraph, and $K_i$ is the degree of node $i$. Of note, the clustering coefficient is zero, $C\left(i\right)=0$, if the nodes are isolated or have just one connection ($K_i=0$ or $K_i=1$). The clustering coefficient, C_p, of the whole network was computed by averaging the clustering coefficients over all nodes, i.e.,

$$C_p=\frac{1}{N}{\displaystyle \sum }_{i=1}^{N}C\left(i\right)$$ [S2]

where $N$ is the number of nodes in the network. The clustering coefficient is a measure of local cliquishness or segregated network topology (58).

The global efficiency of a network,$\hspace{0.17em}{E}_{glob}$, is the inverse of the harmonic mean of the shortest path length between each pair of nodes within the network,

$$E_{glob}=\frac{1}{N(N-1)}{\displaystyle \sum }_{i=1}^N{\displaystyle \sum }_{j\ne i}^N\frac{1}{L_{\text{min}}(i,j)}\hspace{0.17em},$$ [S3]

where $L_{\text{min}}(i,j)$ denotes the shortest path length between node $i$ and node $j$. The global efficiency is a measure of integrated network topology (59).

The small worldness, $\sigma$, represents a simple measure of both segregation and integration in a network, compared with a random graph with the same number of nodes and edges,

$$\sigma =\frac{\gamma }{\lambda }=\frac{C_p/C_R}{L_p/L_R},$$ [S4]

where C_R is the clustering coefficient of a random graph, and L_p and L_R are the mean shortest path length of a given graph and a random graph, respectively. Note that the L_p for an unweighted network is equivalent to the inverse of global efficiency. A small-world network, defined as σ > 1, has higher clustering than a random graph and minimum path length approximately the same as a random graph (much shorter than a regular lattice) (60). To estimate C_R and L_R, 100 random graphs were generated by the Erdős–Rényi model and the averaged clustering coefficient and shortest path length over the random networks were computed.

The degree of a node, denoted K_i, is simply the number of edges connecting this node to the rest of the network. The nodal efficiency is defined as the inverse of the mean harmonic shortest path length between the ith node and all other nodes (61),

$$E_{nod\_i}=\frac{1}{N-1}{\displaystyle \sum }_{i\ne j\in G}\frac{1}{L_{min}(i,\hspace{0.17em}j)}.$$ [S5]

All topological measures were calculated using MATLAB code in the Brain Connectivity Toolbox (see ref. 47; www.brain-connectivity-toolbox.net).

Degree Distribution.

The probability distribution of degree over all nodes in the network (the degree distribution) was best fit by nonlinear fitting function in Brainwaver R package (cran.r-project.org) using Akaike’s information criterion to an exponentially truncated power law,

$$P\left(K\right)=K^{\alpha -1}{e}^{K/\beta },$$ [S6]

where K denotes degree and the parameters of this distribution are the power law exponent, α, and the exponential cutoff, β (16).