Functional hierarchy underlies preferential connectivity disturbances in schizophrenia

Abstract

Schizophrenia may involve an elevated excitation/inhibition (E/I) ratio in cortical microcircuits. It remains unknown how this regulatory disturbance maps onto neuroimaging findings. To address this issue, we implemented E/I perturbations within a neural model of large-scale functional connectivity, which predicted hyperconnectivity following E/I elevation. To test predictions, we examined resting-state functional MRI in 161 schizophrenia patients and 164 healthy subjects. As predicted, patients exhibited elevated functional connectivity that correlated with symptom levels, and was most prominent in association cortices, such as the fronto-parietal control network. This pattern was absent in patients with bipolar disorder (n = 73). To account for the pattern observed in schizophrenia, we integrated neurobiologically plausible, hierarchical differences in association vs. sensory recurrent neuronal dynamics into our model. This in silico architecture revealed preferential vulnerability of association networks to E/I imbalance, which we verified empirically. Reported effects implicate widespread microcircuit E/I imbalance as a parsimonious mechanism for emergent inhomogeneous dysconnectivity in schizophrenia.

Keywords: computational modeling; functional connectivity; schizophrenia.

Fig. 1.

Functional connectivity increases as a generic effect of elevated E/I ratio. (A) Schematic of computational model used to generate BOLD signals under conditions of increased E/I ratio (i.e., disinhibition). Illustration depicts six nodes for visual simplicity; full model has 66 nodes. (B–E) Mean covariance of each node with all other nodes, yielding GBC, as a function of increasing E-E weight (B), reducing E-I weight (i.e., attenuating feedback inhibition) (C), increasing G (D), or noise amplitude (E). Shading represents the SD of GBC values across four separate simulations with different starting random noise. (F) To test model predictions, GBC was computed from an a priori defined parcellation of empirical fMRI data using identical calculations as for the model (SI Appendix). The bar plot shows mean GBC for SCZ vs. HCS [t(287) = 3.8, P < 2 × 10⁻⁴]. (G) Distribution of GBC values for each group (SCZ, red; HCS, black/gray). Vertical lines represent group mean values, showing a significant rightward shift for SCZ vs. HCS [Cohen’s d = 0.42]. (H) Type I error-corrected voxel-wise GBC map, revealing distributed increases in GBC for SCZ, particularly in prefrontal and thalamic regions (see SI Appendix, Table S3 for full list of regions; see Fig. 2 for network overlap calculation). Error bars mark ±1 SEM; ***P < 0.001; d = Cohen’s d effect size. GBC in the model is in arbitrary units.

Fig. 2.

Quantifying overlap between increased whole-brain connectivity in SCZ and independently defined association regions. (A) Using a priori defined, network-based parcellations (58, 101), we defined areal boundaries for the FPCN, and for the association cortex comprised of the FPCN, DMN, and VAN. (B) After down-sampling images to 10-mm voxels, to attenuate spatial correlations, 37% of areas showing elevated SCZ connectivity (Fig. 1H) overlapped with the FPCN (12.7% of total down-sampled gray matter voxels belong to the FPCN). In contrast, for the outside FPCN region, defined as all cortical gray matter not belonging to FPCN, there was far less overlap with regions of elevated SCZ connectivity (63%) than expected by chance (87.3%). (C) We repeated analyses using all association networks (FPCN, DMN, and VAN), again showing preferential colocalization of elevated SCZ connectivity with association regions. Again, the outside association region was defined as all cortical gray matter not belonging to the association region comprised of the FPCN, DMN, and VAN. An additional control analysis was computed using the combined sensory networks (SI Appendix, Fig. S11). (D) The significance above each bar represents the result from binomial tests computed for B and C and for sensory networks in SI Appendix, Fig. S11, comparing the expected percentage of significant voxels with the observed percentage of total significant voxels lying within each region (inside FPCN, outside FPCN, inside association, outside association, sensory networks). The percent spatial coverage plotted represents the total number of significant voxels in a region, divided by the total number of voxels for that region. The significance between bars marks difference between proportions, comparing spatial coverage within the FPCN (or association cortex) with spatial coverage outside, or comparing spatial coverage in association regions vs. spatial coverage in sensory regions. The dashed line marks the spatial coverage of all gray matter voxels by significant voxels (Fig. 1H). ***P < 0.001. Brain images are for visualization purposes only and have not been down-sampled. All reported statistics are computed on images that have been down-sampled to 10-mm voxels. Results remain unchanged without down-sampling (SI Appendix, Fig. S11).

Fig. 3.

FPCN between-network functional connectivity is preferentially increased in SCZ. Between-network connectivity was computed for the FPCN (Upper Left), DMN (Upper Right), and the sensory networks (Lower, combining somatosensory, auditory, and visual networks), using the average BOLD signal from each network. Bar plots highlight the group difference (patients–HCS) for each between-network connectivity measure: (A) FPCN-DMN connectivity group difference for SCZ–HCS (red) and BD–HCS (orange). (B and C) Distribution of FPCN–DMN connectivity values for each group (SCZ, red; HCS, black/gray; BD, orange), confirming specificity in SCZ. (D) FPCN-sensory connectivity group difference for SCZ–HCS and BD–HCS. (E and F) Distribution of FPCN-sensory connectivity values for each group, confirming specificity in SCZ. (G) DMN-sensory connectivity group difference for SCZ–HCS and BD–HCS. (H and I) Distribution of DMN-sensory connectivity values, revealing no effects in either clinical group. Error bars mark ±1 SE of the difference of means. ***P < 0.001; Cov, covariance; n.s., not significant; d, Cohen’s d effect size. Vertical dashed lines represent group mean values.

Fig. 4.

Preferential network-level connectivity changes emerge from a functional hierarchy. (A) Differentiated model scheme, illustrating association (brown) versus sensory (cyan) nodes in the model with network-specific scalar multiplier values (w_A > w_S) for recurrent local self-excitation (E-E weight). Illustration depicts 8 nodes for visual simplicity, but full model has 66 nodes, divided into 38 association and 28 nonassociation (sensory) nodes based on anatomical connectivity. BOLD signals were extracted from each node of the model. We perturbed E/I ratio by varying four key model parameters: recurrent local self-excitation (E-E weight) within nodes, local recurrent inhibition (E-I weight) within nodes, long-range global coupling (G) between nodes, and local noise amplitude (σ) within all nodes. (B–E). Mean within-network connectivity (mean covariance of each node in a network with all other nodes in the same network, for either association or sensory nodes) (SI Appendix) was computed for the differentiated model (w_A > w_S) as a function of increasing E/I via increasing E-E weight, reducing E-I weight, increasing G, or increasing σ. Within-network connectivity preferentially increased in association nodes as E/I imbalance became more severe. Shading represents the SD of within-network connectivity values as evaluated for four separate simulations with different starting random noise. (F–I) Undifferentiated model results, using homogeneous values of recurrent local excitation (E-E weight) via a uniform scalar multiplier value (w_A = w_S) for E-E weight at all nodes. Here we define association and sensory nodes by their distinct anatomical connectivity (rather than any functional difference in recurrent excitation). In contrast to the differentiated model, anatomical connectivity differences alone could not account for preferential effects in association regions (also see SI Appendix, Fig. S6). Within-network connectivity values are in arbitrary units.

Fig. 5.

Preferential network-level functional connectivity changes in SCZ follow modeling predictions. (A–D) Difference between association (“A”) and sensory network (“S”) within-network connectivity (as shown in Fig. 4), highlighting that within-network connectivity in A grows more steeply than in S as E/I elevation becomes more severe as a function of changing E-E weight, E-I weight, or G, but not σ. Shading represents the SD of values for the difference, A − S, in within-network connectivity evaluated across nodes for four separate simulations with different starting random noise. (E, Upper) Within-network connectivity group difference z-map shown across three major association networks: DMN, FPCN, and VAN (type I error corrected) (SI Appendix). (Lower Left) Group average for SCZ illustrates significantly elevated within-network connectivity in association networks compared with HCS. (Lower Right) Group distributions of mean within-network connectivity in association networks (SCZ, red; HCS, black/gray). (F, Upper) Within-network connectivity group difference z-map shown across three major sensory networks: somatosensory, auditory, and visual (type I error corrected) (SI Appendix). Group averages (Lower Left) and distributions (Lower Right) for SCZ and HCS reveal no significant differences for sensory networks. Error bars mark ±1 SEM; *P < 0.05. n.s., not significant; d, Cohen’s d effect size. Vertical dashed lines represent the group mean values. Within-network connectivity in the model is in arbitrary units. Of note, here we focused our empirical analyses on a subset of carefully movement-matched subjects (n = 130 per group).

Fig. 6.

Preferential network-level variance changes emerge from a functional hierarchy. (A) Model schematic. Illustration depicts eight nodes for simplicity; full model uses 66 nodes. (B–E) Mean BOLD signal variance of association or sensory nodes as a function of increasing E-E weight (B), percent reduction of E-I weight (C), G (D), or σ (E), showing that variance preferentially increases for association nodes as E/I elevation becomes more severe. Shading represents the SD of variance values as evaluated for four separate simulations with different starting random noise. (F–I) Undifferentiated model (w_A = w_S) results, using homogeneous values of local recurrent excitation at all nodes. As before, undifferentiated association and sensory nodes are defined by their distinct anatomical connectivity (rather than any functional difference in recurrent excitation). In contrast to the differentiated model, anatomical connectivity differences alone could not account for observed in vivo effects. BOLD signal variance in the model is in arbitrary units.

Fig. 7.

Preferential network-level variance changes in SCZ follow modeling predictions. (A–D) Difference in variance between the association (“A”) and sensory nodes (“S”) (similar to Fig. 5). (E, Upper) We computed a between-group voxel-wise BOLD signal variance z-map restricted to association network regions (specifically DMN, FPCN, and VAN) (type I error corrected) (SI Appendix). (Lower) Group averages and distributions illustrate elevated variance for association networks in SCZ compared with matched HCS. (F) Analyses for the sensory networks show no significant effects. We focused empirical analyses on a subset of movement-matched subjects, given the possibility that BOLD signal variance is particularly susceptible to head motion (102). Nevertheless, all reported association cortex effects held in the full sample (SI Appendix, Fig. S9 A and B). Error bars mark ± 1 SEM; *P < 0.05. n.s., not significant; d, Cohen’s d effect size. Vertical dashed lines represent the group mean values. Model variance is in arbitrary units.

Fig. 8.

Quantitative model comparison. We used four measures to assess models and empirical data: (i) within-network connectivity in association regions, (ii) within-network connectivity in sensory regions, (iii) BOLD signal variance in association regions, and (iv) BOLD signal variance in sensory regions. (A) Change in measures 3–4 on the x and y axis, respectively. The green and blue dots represent the amount of change in each measure when the models (homogeneous and inhomogeneous) are pushed toward elevated E/I ratio via an 8% reduction in E-I weight relative to the healthy starting values. Of note, other E-I reductions (we simulated from 0% up to 20%) all fall closely along the same vectors for each model regime. Because the magnitudes of the model vectors are in arbitrary units, we focused on quantifying the angle of the model vector formed by elevations in E/I, rather than the magnitude. Specifically, we computed the angle between the model vector and the data vector (φ_h for the homogeneous model, φ_i for the inhomogeneous model). The data vector (red) is computed by subtracting mean values for HCS in each measure from the mean values for SCZ on the same measure, to obtain a change in measure, exactly as done for the model data. The red line represents the direction of the vector formed by the empirical data. Formula box: We projected both model simulations and empirical data into a 4D space analogous to the 2D example in A, using the four dependent measures (x₁–x₄) as axes in the 4D space (x₁ = change in within-network connectivity in association regions, x₂ = change in within-network connectivity in sensory regions, x₃ = change in BOLD signal variance in association regions, and x₄ = change in BOLD signal variance in sensory regions). The angle θ between the model and the empirical data were used to compute the cosine similarity (cos θ) between these vectors, with 1 representing perfect similarity between vectors. (B–E) Cosine similarity values, for the similarity between respective model simulations and empirical data, were computed for both the homogeneous (cos θ_h) and inhomogeneous (cos θ_i) models, as a function of increasing E/I along four parameters: increasing E-E weight (B), reducing E-I weight (C), increasing global coupling (D), or increasing local noise amplitude (E). (F–I) Plots of the difference between models with respect to their cosine similarity to the empirical data (cos θ_i − cos θ_h). The teal line represents the values computed for the models as a function of increasing E/I ratio from baseline. After generating 1,000 random permutations of the node identities (association vs. nonassociation) for both models, we recomputed the difference of cosine similarity to empirical data (cos θ_i − cos θ_h), to estimate the values expected by chance. The brown line represents the mean difference of cosine similarity expected by chance. The 95% confidence interval (yellow shading) around the brown line is barely visible because of minimal spread of the distribution.