Higher-order connectomics of human brain function reveals local topological signatures of task decoding, individual identification, and behavior

The study investigates whether reconstructed higher-order interactions (involving three or more brain regions) provide advantages over traditional pairwise functional connectivity for fMRI data analysis. Context is set by the connectome framework, where functional connectivity typically assumes pairwise interactions between regions. Emerging evidence suggests higher-order interactions are crucial for capturing complex spatiotemporal brain dynamics at micro- and macro-scales. Because non-invasive human neuroimaging cannot directly measure true higher-order interactions, the authors aim to infer higher-order patterns from fMRI signals and test their utility across task decoding, individual identification (fingerprinting), and brain–behavior associations.

The paper reviews advances beyond pairwise models, including edge-centric approaches and methods rooted in information theory and computational topology. Prior information-theoretic work showed higher-order dependencies can differentiate states of consciousness and detect aging effects, and temporal HOI statistics improved machine learning classification (e.g., financial crises, disease spreading) over pairwise measures. Edge-centric representations in fMRI revealed overlapping communities and fine-timescale dynamic connectivity, but benefits of HOIs in fMRI remain underexplored. Related topology-based analyses have identified cliques, cavities, and homological scaffolds in brain networks. Multivariate information theoretic methods (e.g., partial information decomposition) distinguish redundancy and synergy, revealing synergistic cores (precuneus, prefrontal, cingulate). These strands motivate assessing HOI advantages over FC and eFC.

Data: 100 unrelated HCP subjects (Release Q3; 54 females, 46 males; mean age 29.1 ± 3.7). Resting-state runs (REST1, REST2) across two days with LR/RL phase encoding; tasks include gambling, relational, social, working memory, motor, language, emotion. Minimally preprocessed data with GLM regression (detrending, motion and derivatives, white matter/CSF signals and derivatives, global signal regression and derivative), bandpass 0.01–0.15 Hz, and parcellation into Schaefer 100 cortical regions plus 16 subcortical and 3 cerebellar nodes (total N=119), followed by z-scoring. Higher-order temporal construction: (i) z-score each BOLD time series. (ii) Compute k-order co-fluctuation time series as element-wise products of k+1 z-scored signals, then z-score for comparability; assign sign via parity rule to emphasize perfectly coherent group interactions (all positive or all negative mapped positive; discordant mapped negative). For k up to 2, edges (k=1) and triangles (k=2) are considered, yielding binomial(N,k+1) time series per order. (iii) At each time t, encode all k-order co-fluctuations into a weighted simplicial complex K^t with simplex weights equal to the corresponding co-fluctuation magnitude. (iv) Apply computational topology to derive indicators: global (hyper-coherence: fraction of violating coherent triangles with weight exceeding their edge weights; hyper-complexity: sliced Wasserstein distance to empty H1 persistence diagram) and local (list/weights of violating triangles; homological scaffold weighting edges by frequency of participation in 1D cycles). Task decoding: Concatenate first 300 volumes of rest data with seven tasks (excluding rest blocks). For local observables (BOLD, edge time series, triangle time series, scaffold signals), compute time–time Pearson correlation matrices (recurrence plots), binarize at the 95th percentile, detect communities via Louvain, and quantify alignment with true task/rest blocks via element-centric similarity (ECS). Fingerprinting: From the four temporal methods, derive static connectivity: node FC, eFC (correlations between edge time series), average violating triangle weights, and average scaffold weights. Compute inter-session similarity (REST1 vs REST2) for each subject; build identifiability matrix and differential identifiability (Idiff = mean self-similarity minus mean others-similarity). Evaluate whole-brain and local (connections involving at least one node from each of seven canonical networks: visual, somatomotor, dorsal attention, ventral attention, limbic, frontoparietal, default mode, subcortical). Brain–behavior association: Perform PLSC between static connectivity features (FC, eFC, triangles, scaffold) and ten HCP cognitive domains (episodic memory, executive function, fluid intelligence, language, processing speed, impulsivity/self-regulation, spatial orientation, sustained visual attention, verbal episodic memory, working memory). For domains with multiple raw measures, extract first principal component. Assess significance via permutation testing (1000 permutations; p<0.05), reliability via bootstrapping (1000 resamples; absolute standard score >2), and compute percentage covariance explained by significant components. Robustness via repeated bootstrap subsampling (80 of 100 subjects, 100 repetitions). Analyses repeated for whole-brain connectivity and within-network connectivity.

- Global indicators: Hyper-coherence and hyper-complexity show similar values across tasks with no significant differences (pairwise t-tests p>0.1), indicating poor task decoding utility at whole-brain level. - Task decoding (local): Recurrence plots from violating triangles and homological scaffolds discriminate task blocks markedly better than lower-order BOLD and edge signals, with higher ECS values for higher-order methods; temporal separability of tasks decreases moving from higher- to lower-order measures. - Fingerprinting: Whole-brain identifiability scores are similar across methods. Restricting to connections involving specific functional networks, triangles consistently yield higher differential identifiability across nearly all seven networks, while scaffold scores remain below ~9%. Triangle-based patterns highlight variability in interactions between unimodal (visual, somatosensory) and transmodal (DMN, frontoparietal) areas across subjects. - Brain–behavior association: Whole-brain connectivity yields ~10–20% covariance explained for all methods. Focusing within functional subsystems, higher-order methods (triangles, scaffold) show sharply increased covariance explained versus FC/eFC; triangles reach ~80% covariance explained in somatosensory areas. Cognitive saliences differ across methods and networks, indicating complementary cognitive dimensions captured beyond FC. - Comparative insights: Violating triangle activity resembles redundancy patterns, while scaffold aligns with synergistic contributions observed in multivariate information-theoretic analyses.

Findings demonstrate that local higher-order indicators capture nuanced, spatially specific dynamics of brain function better than global or pairwise measures. While global higher-order metrics do not outperform pairwise approaches, local HOIs enhance temporal task decoding, individual identification especially within transmodal and unimodal subsystems, and brain–behavior associations with markedly higher explained covariance in specific networks. Results support the view that pairwise FC often reflects redundancy-dominated patterns, whereas higher-order synergies are more behaviorally relevant. The homological scaffold corresponds to synergistic cores (e.g., precuneus, prefrontal, cingulate), and violating triangles correspond to redundancy, aligning with multivariate information theory findings. The approach’s instantaneous, topology-based framework offers a refined window on distributed and centralized task processing and dynamic recruitment of functional groups.

The study establishes that local higher-order topological measures derived from fMRI time series outperform traditional pairwise methods in three applications: task decoding, functional brain fingerprinting, and brain–behavior association. Despite global indicators’ limited discriminative power, local HOIs reveal informative, coherent structures driving human brain dynamics. Contributions include a temporal, simplicial-complex-based framework, evidence of improved subject identifiability in functional subsystems, and substantially stronger behavioral associations (up to ~80% covariance explained). Future work should reduce computational complexity by reconstructing subsets of k-order interactions, extend beyond triangles to higher k where feasible, and integrate causal and geometric techniques (e.g., Takens’ embeddings, spectral decompositions) to further elucidate temporal dependencies and the circuitry linking HOIs to behavior.

Primary limitation is computational cost: computing co-fluctuation patterns up to order k has O(N^k) time complexity, with current processing around 5 minutes per HCP subject on a high-end workstation. Analyses were limited to k≤2 (triangles). Global higher-order indicators did not improve task decoding over pairwise methods. As with fMRI-based approaches, HOIs are inferred rather than directly measured, and choices like thresholding and filtration may influence results. Future work should target efficient subset reconstruction of k-order interactions and explore complementary causal/geometric methods.