Infra-slow scale-free dynamics modulate the connection of neural and behavioral variability during attention

The study addresses how infra-slow brain dynamics (0.01–0.1 Hz), particularly scale-free properties quantified by the power-law exponent (PLE), and neural variability measures (SD and SE), modulate behavioral variability during sustained attention. Prior work has focused on faster EEG/MEG bands, leaving a gap in understanding infra-slow BOLD fluctuations and their role in behavior. The methodological challenge is linking long infra-slow timescales to shorter trial-based cognitive events. The authors hypothesize that SD, SE, and PLE reflect layered facets of neural dynamics, with PLE acting as a background constraint that shapes the relationship between neural variability and behavioral fluctuations, consistent with the Dynamic Layer Model of the Brain.

Infra-slow BOLD fluctuations have been linked to neural activity through correlations with infra-slow LFP/EEG and large-scale network dynamics. Studies show infra-slow oscillations regulate integration and segregation of neuronal communities and can be modulated by basal forebrain activation. Behavioral and neural dynamics align at multiple timescales: steady-state low-frequency brain responses in fMRI (e.g., 0.0625–0.125 Hz) match stimulus timing, and n-back performance tracks BOLD activity at stimulus frequency. Attention networks (VIS, SMN, DAN, VAN, FPN, DMN) are central to sustained attention, with evidence for DMN/FPN involvement and GradCPT-related changes. Scale-free dynamics (PLE) are higher in association cortex (DMN) and lower in sensory cortex, and have been related to aging, consciousness, task performance, and rest-task modulation. Neural variability (SD) and complexity (SE) have been associated with cognition, aging, and clinical conditions. The gap: mechanisms by which infra-slow scale-free dynamics mediate neural-behavioral variability during attention remain unclear.

Participants: 49 healthy adults (24 males, 25 females; 21.15 ± 2.10 years) from Sichuan Normal University; screened for psychiatric conditions; abstained from alcohol/caffeine 24 h prior; ethics approved. Design: Two fMRI sessions—rest (eyes open, fixation, 8 min) and Gradual-onset Continuous Performance Task (GradCPT; 8 min, 400 trials). Task: 10 urban and 10 mountain grayscale images; urban targets (90%), mountain non-targets (10%); gradual transparency transitions lasting 1200 ms; keypress for urban, withhold for mountain. Behavioral recording: reaction times (RT) measured from image transition onset; algorithmic reassignment of ambiguous/multiple responses; cubic spline interpolation for error trials; primary behavioral metric was RT SD (variability), with mean RT and errors reported in supplements. Imaging: Siemens 3T Connectome-Skyra, gradient-echo EPI; TR=800 ms, TE=38 ms, flip angle=52°, FOV=208×180 mm, 72 slices, 2 mm thickness, 2×2×2 mm voxels. Preprocessing: fMRIPrep v23.0.2; outputs in fsaverage5 CIFTI; discard first 4 time points; regress 6 motion parameters, frame-wise displacement, white matter, CSF; extract time series for Yeo 7 networks (VIS, SMN, DAN, VAN, Limbic, FPN, DMN); ideal bandpass filter 0.01–0.1 Hz. Task confounds control: GLM with HRF-convolved regressors for correct omissions, commission errors, omission errors; correct commissions not regressed; analyses repeated on residuals (task-regressed). Measures: BOLD SD computed with MATLAB std; SE (Sample Entropy) with m=2, r=0.5×SD, SE=−ln(A/B), code available online; PLE computed from PSD log-log slope via linear regression confined to 0.01–0.1 Hz, code available online. Mediation: CANLAB toolbox; bootstrapping 10,000 iterations; models testing PLE mediation between BOLD SD/SE and RT SD, and PLE mediation between BOLD SE and BOLD SD. Simulation: 1000 samples of colored noise using MATLAB dsp.ColoredNoise across PLE values −2 to 2; compute SD and SE to examine PLE-dependent SD–SE relationship. Statistics: Paired t-tests for rest vs task differences; Pearson correlations between RT SD and BOLD SD/SE/PLE per network; correlations among BOLD measures; polynomial regression (second-order) where nonlinearity observed; FDR correction (Benjamini–Hochberg) across 21 tests (7 networks × 3 measures); significance at two-sided p<0.05.

Rest–task modulation: Significant differences (paired t-tests, n=49, FDR-corrected p<0.05) concentrated in unimodal and attention-related networks (VIS, SMN, DAN, VAN). SD and PLE decreased from rest to task in these networks, while SE increased. In DMN, SD increased modestly; SE and PLE showed different/non-significant patterns. Representative t-values (Fig. 3): SD—VIS T=3.23**, SMN T=3.00**, DAN T=4.08**, VAN T=4.00**, DMN T=2.85**; SE—VIS T=−2.92**, SMN T=−2.97**, DAN T=−6.06**, VAN T=−4.27**; PLE—VIS T=3.34**, SMN T=5.41**, DAN T=5.52**, VAN T=6.44** (Limbic/FPN/DMN largely non-significant). Brain–behavior correlations (task state, Pearson, n=49, FDR-corrected): RT SD positively correlated with BOLD SD in VIS (R=0.40**), SMN (R=0.44**), DAN (R=0.33**), VAN (R=0.39**), FPN (R=0.30*), DMN (R=0.38**); SE showed negative correlations with RT SD in VIS (R=0.42**), SMN (R=0.36**), DAN (R=0.34**), VAN (R=0.36**); PLE correlated positively with RT SD only in VIS (R=0.47***), and nominally in SMN (R=0.30*), others non-significant. Correlations with mean RT and error counts did not survive multiple comparison correction. Mediation: In VIS, PLE partially mediated the relationship between BOLD SD and RT SD in task data, and fully mediated in task-regressed data; PLE did not significantly mediate between BOLD SE and RT SD. Inter-measure relations: SE negatively correlated with both SD and PLE across networks; SD–PLE relation showed nonlinearity (second-order polynomial) in VIS/SMN with inflection around PLE≈0 (transition from blue to pink noise). Simulation: SD–SE correlation ~0 for blue noise (PLE=−1) and white noise (PLE=0); strong negative correlation approaching R=−0.91*** at pink noise (PLE=1), mirroring empirical patterns. Overall, evidence supports a hierarchical, layered mechanism where scale-free dynamics (PLE) operate as neural background modulating the linkage between neural variability (SD, SE) and behavioral variability.

Findings demonstrate that infra-slow brain dynamics contribute to behavioral variability during sustained attention and that SD, SE, and PLE play distinct roles. Unimodal networks (VIS, SMN, DAN, VAN) show convergent rest–task modulation across measures, while transmodal networks (DMN, FPN, Limbic) diverge, with SD more sensitive to task-related changes in DMN. Brain–behavior relations are network-specific: SD and SE track performance variability across attention-related networks; PLE relates to behavior primarily in VIS, indicating its role in processing visual inputs. PLE functions as a background index mediating neural-to-behavioral variability and the SD–SE relationship, particularly under pink-noise regimes. This supports a layered organization: scale-free dynamics (input encoding and temporal background), information complexity/entropy (temporal integration), and variability (output scaffolding) collectively bridge stimulus dynamics, neural activity, and behavior, aligning with the Dynamic Layer Model and spatiotemporal neuroscience perspective.

The study establishes a direct link between infra-slow BOLD dynamics and behavioral variability in sustained attention, revealing a layered organization of neural measures: PLE as a global background constraint, SE as complexity/integration, and SD as variability reflecting output dynamics. Scale-free dynamics modulate how neural variability connects to behavioral variability, with strongest SD–SE coupling under pink-noise conditions. These results advance understanding of infra-slow fMRI activity in cognition and underscore the importance of neural timescales and their spatiotemporal structure. Future work should test these mechanisms in naturalistic paradigms across multiple timescales, incorporate oscillatory components alongside fractal properties, explore parameter spaces for entropy measures, and extend analyses beyond 0.1 Hz to capture broader frequency-dependent brain–behavior dynamics.

The GradCPT paradigm is highly controlled and may not capture the richness of naturalistic, multi-timescale inputs; future studies should use complex stimuli (e.g., music, movies). Analyses focused on fractal background (PLE) and did not examine oscillatory components in the infra-slow range, which may be behaviorally informative. SE was computed with fixed parameters (m=2, r=0.5×SD); results may vary with different settings, especially m. Frequency range was limited to 0.01–0.1 Hz; important information may reside at higher frequencies. Methodological concerns include potential thermal noise effects on SE and the need to further validate non-linear relationships and mediation across broader contexts.