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Dynamic fluctuations coincide with periods of high and low modularity in resting-state functional brain networks
Richard F. Betzel, Makoto Fukushima, Ye He, Xi-Nian Zuo, Olaf Sporns
TL;DR
The paper asks how long-timescale static connectivity constrains shorter-timescale resting-state functional connectivity and how to identify fluctuations beyond those expectations. It introduces a conditional, surrogate-based approach and finds that unexpected connection excursions cluster during highly modular network states. The study also reports a scan-length limitation.
Problem
Short-timescale functional connectivity fluctuations are difficult to interpret because static connectivity statistically constrains their expected range.
Method
The paper uses conditional dynamic functional connectivity to compare observed fluctuations with surrogate-derived expectations conditioned on static connectivity.
Results
Unexpectedly strong or weak connections cluster in time, and these events coincide with highly modular functional network topologies.
Takeaways & Limitations
The approach detects dynamic functional connections that fluctuate more or less than expected from their long-time averages.
Takeaways & Limitations
The results are limited in part by the length of the fMRI scan sessions.
Abstract
from arXiv · showhide
We investigate the relationship of resting-state fMRI functional connectivity estimated over long periods of time with time-varying functional connectivity estimated over shorter time intervals. We show that using Pearson's correlation to estimate functional connectivity implies that the range of fluctuations of functional connections over short time scales is subject to statistical constraints imposed by their connectivity strength over longer scales. We present a method for estimating time-varying functional connectivity that is designed to mitigate this issue and allows us to identify episodes where functional connections are unexpectedly strong or weak. We apply this method to data recorded from $N=80$ participants, and show that the number of unexpectedly strong/weak connections fluctuates over time, and that these variations coincide with intermittent periods of high and low modularity in time-varying functional connectivity. We also find that during periods of relative quiescence regions associated with default mode network tend to join communities with attentional, control, and primary sensory systems. In contrast, during periods where many connections are unexpectedly strong/weak, default mode regions dissociate and form distinct modules. Finally, we go on to show that, while all functional connections can at times manifest stronger (more positively correlated) or weaker (more negatively correlated) than expected, a small number of connections, mostly within the visual and somatomotor networks, do so a disproportional number of times. Our statistical approach allows the detection of functional connections that fluctuate more or less than expected based on their long-time averages and may be of use in future studies characterizing the spatio-temporal patterns of time-varying functional connectivity
Introduction
Resting-state functional connectivity is commonly estimated with Pearson correlations over long scans, but shorter-timescale fluctuations and their interpretation remain methodologically challenging. The paper proposes conditioning dynamic fluctuations on static connectivity and relates unexpected excursions to changing network modularity.
- Functional brain networks represent pairwise statistical dependencies among regional BOLD time series, typically summarized in a static correlation matrix.
- Dynamic functional connectivity estimates shorter-timescale changes by dividing scans into windows and calculating a correlation matrix for each window.
- The methodological challenge is determining whether observed dynamic fluctuations are statistically meaningful and neurobiologically functional.
- Static connectivity constrains the expected range of dynamic fluctuations, motivating a method that identifies connections unexpectedly stronger or weaker than expected.
- In data from N = 80 participants, unexpectedly strong or weak connections fluctuated over time and coincided with intermittent periods of high and low modularity.
- During relative quiescence, default mode regions joined attentional, control, and primary sensory communities, whereas many unexpected fluctuations accompanied distinct default mode modules.
Methods
The study analyzes resting-state fMRI data from 80 healthy adults and estimates static and dynamic functional connectivity using overlapping, exponentially weighted windows.
- Each participant completed three resting-state fMRI scans differing in repetition time, voxel size, and duration.
- The analyzed sample comprised 80 healthy adults aged 18–30 years from the NKI-Rockland Lifespan Sample.
- Static functional connectivity was estimated over each full scan from pairwise correlations of zero-mean, unit-variance regional BOLD time series.
- Dynamic connectivity used overlapping windows of approximately 100 seconds, corresponding to L = 156 time points at a sampling frequency of 1/0.645 Hz.
- The window length was selected to capture a full cycle of the slowest retained frequency component, whose high-pass cutoff was 0.01 Hz.
- Within each window, cross-correlations exponentially discounted distant observations so recent events received greater weight.
Conditional dynamic functional connectivity
Pearson correlation creates static-connectivity-dependent constraints on short-timescale fluctuations. The paper’s conditional dynamic functional connectivity measures whether observed fluctuations are expected given each pair’s static connectivity.
- A strong static correlation constrains the corresponding dynamic connection to a narrow fluctuation range, whereas weak static correlation permits larger positive or negative excursions.
- Dynamic fluctuations should therefore be interpreted as expected or unexpected relative to the corresponding static connectivity, rather than by magnitude alone.
- Conditional dynamic functional connectivity is the probability of observing a dynamic connection magnitude given the static connectivity of the same region pair.
- The null distribution of expected fluctuations was approximated from amplitude-adjusted phase-randomized surrogate BOLD time series preserving amplitude distributions and approximate power spectra.
- Repeated surrogate analyses produced connection-specific fluctuation distributions, against which original dynamic connections were assigned percentiles.
- Alternative null distributions could be estimated with bivariate ARMA models instead of phase-randomized surrogates.
Characterizing conditional dynamic functional connectivity
The analysis counts unexpectedly strong and weak dynamic connections over time and across subjects, contextualizing these excursions against surrogate-derived expectations while preserving temporal dependence from overlapping windows.
- At each time point, excursions counted dynamic connections classified as unexpectedly strong or weak after thresholding the connectivity matrices.
- Total excursions were defined as E(t) = E+(t)+E−(t), combining unexpectedly strong and unexpectedly weak connections.
- Observed excursion counts were compared with counts from 1000 surrogate datasets and focused on time points at or above the 97.5th percentile.
- This percentile procedure tests whether dynamic connections are significantly stronger or weaker than their corresponding static connections.
- The stronger/weaker classification is relative to static connectivity: stronger means more positive than expected, while weaker means more negative than expected.
- Randomly permuting excursion times was rejected because overlapping windows create temporal dependence, with adjacent windows sharing L − 1 observations.
- The global excursion matrix counted how often each connection participated in excursions across all subjects, separating stronger and weaker counts.
Community detection
The study applies modularity maximization to dynamic functional-connectivity matrices, then uses repeated Louvain solutions and their similarity to characterize community structure and landscape degeneracy.
- Community detection: The modularity matrix is defined as B(t) = W(t) − P(t), where P(t) supplies expected connection weights.The modularity objective rewards positive within-community connections and penalizes negative within-community connections under this formulation.
- Community detection: Dynamic functional-connectivity matrices are analyzed with a Louvain-like algorithm that maximizes modularity repeatedly and returns brain partitions with quality scores.The algorithm is run 100 times for each matrix, producing community assignments and partition-quality scores.
- Community detection: Because Louvain uses a greedy heuristic and samples near-optimal partitions in a potentially biased way, partition variability is not a complete direct measure of degeneracy.The analysis embraces run-to-run variability rather than replacing it with a consensus partition.
- Community detection: The modularity landscape contains possible community divisions scored by Q, with multiple near-optimal solutions interpreted as a degenerate landscape.The Louvain heuristic searches for increasingly fit partitions, but can return different solutions when near-optimal alternatives coexist.
Results
Conditional dynamic connectivity identifies unexpected connection excursions whose abundance varies over time and coincides with more modular network configurations during mass excursions.
- Results: Resting-state connectivity alternated between periods with unexpectedly strong or weak connections and periods with fewer such excursions.This temporal alternation formed the basis for comparing network modularity across excursion states.
- Results: 6.7 ± 0.8% of dynamic functional connections were classified as unexpectedly strong or weak excursions across participants.The analysis used conditional dynamic functional connectivity in N = 80 individuals.
- Results: Mass excursions produced networks with higher average modularity than time points with fewer excursions in 74 of 80 participants at p < 0.01.The median p-value among those participants was approximately 10^-19.
- Results: The higher modularity during mass excursions was partly associated with correlations favoring extreme values near ±1.These extreme correlations can support highly modular network configurations.
Event count is correlated with low-degeneracy of modularity landscapes
Event counts were related to partition similarity and community number, while motion showed no consistent group-level relationship but could confound excursion counts in some participants.
- Event count is correlated with low-degeneracy of modularity landscapes: Partition similarity was positively correlated with event count, with median r = 0.19 and interquartile range [0.09, 0.32].Partition similarity was used as an indicator related to modularity-landscape degeneracy, where higher similarity indicates lower degeneracy.
- Event count is correlated with low-degeneracy of modularity landscapes: Group-level motion correlations with excursion counts were r = 0.044 and r = 0.041 for L1 and L2 frame-wise displacement norms.The analysis found no consistent group-level relationship between motion estimates and excursion counts.
- Event count is correlated with low-degeneracy of modularity landscapes: At the individual level, 21 of 80 participants showed positive and 23 of 80 showed negative motion correlations at Bonferroni-corrected p = 0.01.The directions were not consistent, so motion may act as a potential confound for a subset of participants.
- Event count is correlated with low-degeneracy of modularity landscapes: The number of detected communities was significantly and negatively correlated with excursion count in most participants.This result links more excursions with fewer detected communities in the reported analysis.
- Event count is correlated with low-degeneracy of modularity landscapes: Default mode regions joined attention, sensory, and control systems during non-mass excursions but dissociated from them during mass excursions.The most frequently changing regions included posterior cingulate, dorsal and medial prefrontal cortex, and inferior parietal lobule.
- Event count is correlated with low-degeneracy of modularity landscapes: All connections participated in at least one excursion, but a small number participated disproportionately often.Frequently excursion-prone connections were concentrated in visual and somatomotor systems, including homotopic pairs.
- Event count is correlated with low-degeneracy of modularity landscapes: Short connection length was not sufficient to explain excursion participation, because many consistently strong or weak connections were long-range.Distance correlations were statistically significant but small in magnitude: r− = 0.14, r+ = 0.035, and r−,+ = −0.092.
Discussion
The discussion argues that dynamic functional-connectivity fluctuations are partly constrained by static connectivity and may not directly reflect neurobiological processes. A proposed measure identifies unexpected fluctuations, which cluster into modular network events and disproportionately involve visual and somatomotor connections.
- Interpretation: Dynamic functional-connectivity fluctuations are partly predicted by static connectivity and may arise as a mathematical consequence of time-series dynamics.This relationship therefore does not necessarily implicate an underlying neurobiological process actively driving the fluctuations.
- Methodological contribution: The proposed measure highlights connections that are unexpectedly strong or weak relative to their static connectivity.It is intended to account for statistical constraints imposed by long-time connectivity estimates.
- Dynamic network organization: Unexpectedly strong or weak connections cluster temporally into mass excursions, during which functional networks adopt highly modular topologies.These events are contrasted with other time periods in the dynamic connectivity record.
- Spatial distribution: Mass excursions involve disproportionately many connections associated with visual and somatomotor systems rather than higher-level association networks.The pattern includes many long-range connections and is not systematically related to participant head motion.
- Limitations: Methodological and interpretational issues remain because the advantage of sliding-window, component, and model-based approaches is unclear.The neurobiological basis of fMRI connectivity fluctuations also remains uncertain, with alternative accounts involving correlated noise or static connectivity configuration.
- Limitations: Whether short-timescale fMRI connectivity fluctuations have a distinct neurobiological basis remains unresolved.Studies using combined EEG-fMRI have reported electrophysiological correlates, but correlated white noise and static connectivity remain alternative interpretations.
Mass excursions
Mass excursions are episodes with many unexpectedly strong or weak connections and higher, more segregated modular organization. Default mode regions dissociate during these episodes, whereas quieter periods show less-defined communities.
- Mass excursions identify episodes in which many functional connections are unexpectedly strong or weak.
- High-modularity excursions contain tightly bound, mutually segregated communities with stronger distinctions between modules.
- Modularity Q increases during mass excursions, although stronger positive weights contribute to this increase only when they cluster into communities.
- During periods with few excursions, communities are less modular and less well-defined, consistent with greater exchange across community boundaries.
- During excursions, default mode regions dissociate from other systems and form more distinct modules.
Possible improvements
The proposed conditional approach removes the static-connectivity dependence that constrains dynamic fluctuations and identifies deviations relative to expected connection-specific distributions. Alternative windowing and Fisher transformation offer limited or largely unchanged relief, while multivariate extensions remain possible.
- Conditional dynamic connectivity identifies fluctuations that are unexpectedly strong or weak relative to each connection’s long-time connectivity.
- Pearson correlation makes short-timescale connectivity distributions depend on long-timescale connectivity, even with non-overlapping windows.
- Fisher transformation approximately equalizes correlation variability, but conditional estimates are essentially unchanged because the transformation is monotonic.
- The current univariate analysis treats connections independently, although their correlative weights are often not independent; multivariate methods are a proposed extension.
- Subtracting time-averaged connectivity before component analysis reveals temporal connection patterns while discounting static baseline levels.
Limitations
The study’s conclusions are constrained by the Pearson-correlation framework, finite scan duration, and unresolved biological interpretation of dynamic connectivity states. The analysis also treats correlated connections independently.
- Static connectivity estimates may not represent true long-term values because sessions contained only 885 observations, approximately 9.37 minutes.
- The study focuses on Pearson correlation, leaving prediction of dynamic connectivity from alternative static measures beyond its scope.
Concluding remarks
The paper introduces a model-free framework for detecting dynamic connectivity deviations relative to long-timescale expectations. Applied to fMRI, it links unexpectedly strong or weak connections to transient high- and low-modularity states.
- Pearson-based dynamic connectivity inherits statistical constraints from longer-timescale connectivity estimates.
- The proposed method identifies when and where dynamic fluctuations are statistically unexpected.
- Dynamic connectivity shows transient periods of high and low modularity driven by over- or under-expression of unexpected connections.
- The approach has practical significance as a model-free method for characterizing spatiotemporal dynamic connectivity patterns.