Precision dynamical mapping using topological data analysis reveals a hub-like transition state at rest

Spontaneous brain activity at rest is structured in space and time and may subserve multiple functions, but it remains unclear whether transitions between brain states follow an organized plan, whether they proceed continuously or discretely, and whether transitions pass through intermediary states. Conventional resting-state fMRI analyses have emphasized static connectivity, while time-varying analyses face challenges from sampling variability and physiological artifacts. With recent precision mapping efforts that collect hours of data per individual, it is possible to study single-subject dynamics. This study investigates the rules governing transitions among whole-brain configurations at rest, testing whether transitions are continuous versus discrete, whether intermediary states exist, and whether individual-specific differences in dynamic landscapes are present. Using topological data analysis (TDA) with the Mapper algorithm on highly sampled individuals, the authors aim to construct individualized dynamical landscapes to reveal organizing principles of spontaneous brain activity.

Prior time-varying fMRI studies have revealed fast switching between metastable states, intermittent global co-fluctuations, waves, and hierarchical temporal organization, with individual differences linked to behavior. Many approaches rely on sliding windows or HMMs, which can be sensitive to sampling variability, head motion, and require assumptions about state number and exclusivity. Optical imaging-fMRI work supports coupling between hemodynamics and excitatory neural activity, motivating improved analytics to parse neuronal dynamics from artifacts. Open questions include the continuity vs. discreteness of transitions, presence of intermediary states, and individual specificity of state configurations. The authors build on TDA/Mapper, previously used to capture task-evoked dynamics without predefined state numbers or windowing, addressing methodological limitations of earlier approaches.

Datasets: (1) Midnight Scan Club (MSC): 10 healthy adults, ~5 hours resting-state fMRI per individual across ten 30-minute sessions (TR=2.2 s; TE=27 ms; 4×4×4 mm). Data for each participant were split into odd (discovery) and even (replication) sessions (~2.5 h each). Individually defined cortical parcellations (mean 620.8±39.4 parcels) were used. (2) Human Connectome Project (HCP): 100 unrelated participants with four 15-minute resting-state runs over two days; after motion censoring criteria (>20% contaminated frames), n=76 retained. Group parcellation (Gordon 333 parcels) was used. Preprocessing: MSC preprocessing included slice timing correction, intensity normalization, motion correction, atlas registration, distortion correction, CompCor-like nuisance regression (motion, global signal, tissue signals), motion scrubbing (FD and DVARS), band-pass filtering (0.005–0.1 Hz), interpolation across censored frames prior to filtering, and removal of censored frames before analysis. HCP data used minimal preprocessing plus fMRIPrep (bias correction, skull-stripping, segmentation, normalization, BBR co-registration, motion correction), construction of temporal masks (FD>0.2 mm with additional neighboring frames), multiple regression (whole-brain, CSF, WM signals; Volterra-expanded motion regressors), interpolation across censored frames, band-pass filtering (0.009–0.08 Hz), and removal of censored frames. Mapper pipeline: For each participant, session time series were z-scored and concatenated (MSC: odd or even sessions; HCP: all runs). Mapper steps: (1) Nonlinear filter via neighborhood embedding using geodesic distances between whole-brain activation volumes, embedding into d=2 to preserve intrinsic geometry. (2) Overlapping binning in embedded space (MSC resolution ~30 bins; HCP ~14 bins; ~70% overlap). (3) Partial clustering within each bin using original high-dimensional data to form nodes (clusters of similar TRs). (4) Connect nodes across bins if they share any TRs, yielding a shape graph. Nodes represent clusters of time frames; edges reflect shared TRs. Graph analyses and annotations: Nodal degree distributions were computed and compared to two null models: phase-randomized surrogates and multivariate AR(1) surrogates, preserving linear properties. Hubs were identified by high degree (cut-off derived from null comparisons; ~>20) and high centrality (top 1% closeness centrality). Graphs were annotated with meta-information: RSN activations derived from individual (MSC) or group (HCP) network assignments. For each node, RSN mean signals were z-scored; RSN activation defined as >0.5 SD above mean, summarized per-node (pie charts). A variance-based annotation computed the standard deviation across mean RSN activations per node to reveal gradients (high variance indicates RSN-dominant nodes; low variance indicates uniform RSN activation). Temporal transitions: RSN/hub labels were propagated from nodes to constituent TRs. Discrete-time, finite-state, time-homogeneous Markov chains were estimated per participant and split from empirical transition counts between states, excluding transitions spanning censored frames and scan stitching. Transition probability matrices and corresponding graphs were analyzed. Subject specificity and reliability were assessed by correlating RSN co-localization matrices and transition matrices within versus between participants. Robustness: Parameter perturbation varied Mapper resolution and overlap (R: 25–35; G: 65–75%) to test stability of topological properties (degree distributions). Split-half validation (MSC odd vs. even) and independent replication (HCP cohort) were performed.

• Degree distributions in Mapper graphs from real data exhibited heavy (fat) tails compared to both null models, indicating presence of highly connected nodes. MSC split-halves showed significant excess of high-degree (>20) nodes versus nulls (odd: F(2,27)=6.27, p=0.0058; even: F(2,27)=14.49, p=5.32×10^-5).
• Hubs (high degree and top 1% closeness centrality) were consistently present across participants and both MSC splits; not associated with head motion or global signal differences (ps>0.05). Parameter perturbation showed stability of topological properties.
• RSN annotation revealed central hubs had uniformly distributed RSN activations (no dominant RSN), whereas peripheral nodes were dominated by one or more RSNs. The specific combination of RSNs dominating the periphery was subject-specific but stable across sessions.
• RSN co-localization (similarity) matrices were highly similar within individuals across odd/even sessions compared to between participants (F(1,198)=39.36, p=2.18×10^-9), demonstrating subject-specific and reliable topographies. Degree distributions and hub proportions were also more similar within than between participants (degree distribution similarity: F(1,18)=5.31, p=0.034; hub proportion: F(1,18)=1.73, p=0.2).
• A variance-based annotation uncovered a smooth topographic gradient: variance across RSN mean activations was high at periphery and decreased toward central hubs. Hubs had significantly lower SD than non-hub nodes (odd: F(1,18)=141.84, p=5.70×10^-10; even: F(1,18)=222.20, p≈1.49×10^-?—both highly significant), indicating uniform RSN representation.
• Temporal Markov analysis showed the hub state was the most likely destination from any RSN-dominant state; transition probability matrices were more similar within than between participants (F(1,398)=63, p=2.13×10^-14). Hub occurrences were inversely related to RSN dominance amplitude at the TR level (predominantly negative correlations), consistent with a transitional role.
• Replication in HCP: Real data degree distributions again showed fat tails versus nulls (F(2,225)=288.11, p=8.88×10^-63); hubs identified in individuals. RSN-based topography and variance gradient replicated, and Markov chains again showed the hub as the most sought-after destination from other states.
• Group-averaged RSN co-localization suggested greater synchrony among unimodal sensorimotor networks than higher-order networks, although individual patterns deviated idiosyncratically, underscoring precision dynamics.

The findings address key questions about intrinsic brain dynamics: transitions at rest are organized around a central, frequently visited transition state (hub) with uniform RSN expression, serving as an intermediary between RSN-dominant configurations. Traversal across the landscape follows a continuous gradient from high-variance peripheral states to low-variance central hubs, supporting a continuous (rather than discrete-only) conceptualization. The landscape exhibits coarse bistability (low-amplitude hub vs. high-amplitude peripheral states), aligning with prior HMM and edge co-fluctuation work, yet reveals finer, subject-specific idiosyncrasies enabled by precision data and individualized analyses. Comparisons to prior literature suggest hubs may correspond to global attractor-like states with muted connectivity profiles and potentially lower metabolic cost, facilitating efficient switching between network-dominant states. Subject-specific RSN co-localization and transition probabilities were reliable, highlighting potential utility in precision medicine. Methodologically, the TDA/Mapper framework avoids windowing assumptions and state number constraints, mitigating artifacts and enabling direct, frame-wise exploration of whole-brain activation dynamics.

This work introduces a precision dynamics approach using TDA/Mapper to map individualized landscapes of resting brain activity. Four robust observations emerged: (1) centrally located hub nodes—uniform across RSNs—act as transition states frequently visited during rest; (2) transitions follow a smooth, continuous topographic gradient from RSN-dominant periphery to uniform hubs; (3) transition probabilities and RSN co-localization are subject-specific and reliable; and (4) peripheral landscapes are dominated by subject-specific RSN combinations. Findings were validated via split-halves and replicated in an independent cohort. These contributions refine conceptual models of resting dynamics and suggest applications for individualized characterization of neural function. Future directions include testing shorter scans, integrating activation- and connectivity-based dynamics, incorporating subcortical and cerebellar structures, probing the functional role of hub states across consciousness states, and examining brain–behavior associations in large cohorts.

• Data requirements: Robust individual-level mapping used long scan durations (~2.5–5 h per person; ~1 h in replication). Applicability to typical 10–20 min scans remains to be established.
• Scope of signals: Analyses focused on cortical activation; subcortical and cerebellar contributions were not included.
• Modality integration: The approach emphasized activation-based dynamics without direct integration of frame-wise connectivity fluctuations; combining these may capture complementary information.
• Interpretational uncertainty: The functional purpose of hub states (e.g., recovery/washout) is hypothesized but untested; effects across other consciousness states (sleep, anesthesia) are unknown.
• Sample size for phenotypic associations: Limited MSC (n=10) and moderate HCP subsample (n=76 after censoring) precluded robust trait-behavior analyses; larger datasets are needed.
• Parameter choices: Although Mapper outputs were robust across parameter perturbations, specific thresholds (e.g., RSN activation z>0.5; hub centrality cutoffs) may influence details and warrant further evaluation.