Networks extracted from nonlinear fMRI connectivity exhibit unique spatial variation and enhanced sensitivity to differences between individuals with schizophrenia and controls

Abstract

Functional magnetic resonance imaging (fMRI) studies often estimate brain intrinsic connectivity networks (ICNs) from temporal relationships between hemodynamic signals using approaches such as independent component analysis (ICA). While ICNs are thought to represent functional sources that play important roles in various psychological phenomena, current approaches have been tailored to identify ICNs that mainly reflect linear statistical relationships. However, the elements comprising neural systems often exhibit remarkably complex nonlinear interactions that may be involved in cognitive operations and altered in psychiatric conditions such as schizophrenia. Consequently, there is a need to develop methods capable of effectively capturing ICNs from measures that are sensitive to nonlinear relationships. Here, we advance a novel approach to estimate ICNs from explicitly nonlinear whole-brain functional connectivity (ENL-wFC) by transforming resting-state fMRI (rsfMRI) data into the connectivity domain, allowing us to capture unique information from distance correlation patterns that would be missed by linear whole-brain functional connectivity (LIN-wFC) analysis. Our findings provide evidence that ICNs commonly extracted from linear (LIN) relationships are also reflected in explicitly nonlinear (ENL) connectivity patterns. ENL ICN estimates exhibit higher reliability and stability, highlighting our approach's ability to effectively quantify ICNs from rsfMRI data. Additionally, we observed a consistent spatial gradient pattern between LIN and ENL ICNs with higher ENL weight in core ICN regions, suggesting that ICN function may be subserved by nonlinear processes concentrated within network centers. We also found that a uniquely identified ENL ICN distinguished individuals with schizophrenia from healthy controls while a uniquely identified LIN ICN did not, emphasizing the valuable complementary information that can be gained by incorporating measures that are sensitive to nonlinearity in future analyses. Moreover, the ENL estimates of ICNs associated with auditory, linguistic, sensorimotor, and self-referential processes exhibit heightened sensitivity towards differentiating between individuals with schizophrenia and controls compared to LIN counterparts, demonstrating the translational value of our approach and of the ENL estimates of ICNs that are frequently reported as disrupted in schizophrenia. In summary, our findings underscore the tremendous potential of connectivity domain ICA and nonlinear information in resolving complex brain phenomena and revolutionizing the landscape of clinical FC analysis.

Keywords: distance correlation; functional connectivity (FC); independent component analysis (ICA); intrinsic connectivity network (ICN); nonlinear; schizophrenia (SZ).

Fig. 1.

Schematic of the analysis pipeline. Preprocessed resting-state fMRI (rsfMRI) data is transformed to the connectivity domain using covariance (Cov), as a linear functional connectivity (FC) estimator, and distance correlation (dCorr), which is sensitive to both linear and nonlinear associations between voxel time series, as a nonlinear FC estimator. Explicitly nonlinear whole-brain functional connectivity (ENL-wFC) is obtained by removing the nonlinear whole-brain functional connectivity (NL-wFC) information that is linearly explained by linear whole-brain functional connectivity (LIN-wFC). Group-level spatial independent component analysis (gr-sICA) is implemented in the connectivity domain on LIN-wFC and ENL-wFC to estimate separate sets of intrinsic connectivity networks (LIN and ENL ICNs). Group information-guided ICA (GIG-ICA) is then used to estimate subject-specific ICNs, and statistical analysis is conducted on the subject-level spatial maps.

Fig. 2.

Intrinsic connectivity networks (ICNs) obtained from linear whole-brain functional connectivity (LIN-wFC) and explicitly nonlinear whole-brain functional connectivity (ENL-wFC) group-level spatial independent component analysis (gr-sICA) in the connectivity domain. ICNs are displayed thresholded at Z = 1.96 (p = .05) on the ch2bet template in order of maximum spatial similarity. Common ICNs (maximum similarity > .80) include primary visual (VIS1), primary sensorimotor (MTR1), secondary sensorimotor (MTR2), secondary visual (VIS2), right frontoparietal (rFP), cerebellum (CER), subcortical (SUB), posterior default mode (pDM), temporal (TEMP), and dorsal attention (ATN). ICNs exhibiting maximum similarity between .40 - .80 and unique ICNs (maximum similarity < .40) are also displayed.

Fig. 3.

Scatterplots of nonlinear whole-brain functional connectivity (ENL-wFC) and linear whole-brain functional connectivity (LIN-wFC) group-level spatial independent component analysis (gr-sICA) iterations. Each iteration is plotted according to a colormap reflecting the bilinear mapping between the spatial correlation of the component matched with the unique ENL ICN and that component’s ICASSO quality index (IQ) value. The broken lines demarcate spatial similarity and IQ thresholds of .80. ENL-wFC gr-sICA iterations (A) cluster within the top right quadrant of the plot, indicating that matched components extracted from ENL-wFC analyses generally exhibited suprathreshold spatial similarity and suprathreshold ICASSO IQ values. This pattern is not observed in the LIN-wFC plot (B), which reveals that most LIN-wFC gr-sICA iterations failed to identify the unique ENL ICN.

Fig. 4.

Assessment of intrinsic connectivity network (ICN) spatial variation. Warmer hues indicate ENL > LIN, while cooler hues indicate LIN > ENL. Contours indicate statistical significance (q < .05). Displayed ICNs include subcortical (SUB) (A), cerebellum (CER) (B), primary (VIS1) (C) and secondary (VIS2) (D) visual, temporal (TEMP) (E), primary (MTR1) (F) and secondary (MTR2) (G) sensorimotor, dorsal attention (ATN) (H), posterior default mode (pDM) (I), and right frontoparietal (rFP) (J). Results are overlaid on the ch2bet template with X, Y, and Z coordinates listed relative to the origin in Montreal Neurological Institute (MNI) 152 space. Dual code visualization was adapted from sample scripts provided by Allen et al. (2012).

Fig. 4.

Assessment of intrinsic connectivity network (ICN) spatial variation. Warmer hues indicate ENL > LIN, while cooler hues indicate LIN > ENL. Contours indicate statistical significance (q < .05). Displayed ICNs include subcortical (SUB) (A), cerebellum (CER) (B), primary (VIS1) (C) and secondary (VIS2) (D) visual, temporal (TEMP) (E), primary (MTR1) (F) and secondary (MTR2) (G) sensorimotor, dorsal attention (ATN) (H), posterior default mode (pDM) (I), and right frontoparietal (rFP) (J). Results are overlaid on the ch2bet template with X, Y, and Z coordinates listed relative to the origin in Montreal Neurological Institute (MNI) 152 space. Dual code visualization was adapted from sample scripts provided by Allen et al. (2012).

Fig. 5.

Statistical comparisons between subject-level temporal (TEMP) (A), secondary sensorimotor (MTR2) (B), posterior default mode (pDM) (C), and unique ENL (D) ICN estimates derived from distinct clinical cohorts (HC and SZ). In A-C, results from LIN comparisons are located on the left, while results from ENL comparisons are located on the right. Warmer hues indicate HC > SZ, while cooler hues indicate SZ > HC. Contours indicate statistical significance (q < .05). Results are overlaid on the ch2bet template with X, Y, and Z coordinates listed relative to the origin in MNI 152 space. Dual code visualization was adapted from sample scripts provided by Allen et al. (2012).