Interplay between functional connectivity and scale-free dynamics in intrinsic fMRI networks

Abstract

Studies employing functional connectivity-type analyses have established that spontaneous fluctuations in functional magnetic resonance imaging (fMRI) signals are organized within large-scale brain networks. Meanwhile, fMRI signals have been shown to exhibit 1/f-type power spectra – a hallmark of scale-free dynamics. We studied the interplay between functional connectivity and scale-free dynamics in fMRI signals, utilizing the fractal connectivity framework – a multivariate extension of the univariate fractional Gaussian noise model, which relies on a wavelet formulation for robust parameter estimation. We applied this framework to fMRI data acquired from healthy young adults at rest and performing a visual detection task. First, we found that scale-invariance existed beyond univariate dynamics, being present also in bivariate cross-temporal dynamics. Second, we observed that frequencies within the scale-free range do not contribute evenly to inter-regional connectivity, with a systematically stronger contribution of the lowest frequencies, both at rest and during task. Third, in addition to a decrease of the Hurst exponent and inter-regional correlations, task performance modified cross-temporal dynamics, inducing a larger contribution of the highest frequencies within the scale-free range to global correlation. Lastly, we found that across individuals, a weaker task modulation of the frequency contribution to inter-regional connectivity was associated with better task performance manifesting as shorter and less variable reaction times. These findings bring together two related fields that have hitherto been studied separately – resting-state networks and scale-free dynamics, and show that scale-free dynamics of human brain activity manifest in cross-regional interactions as well.

Functional connectivity arises from a slow rhythmic mechanism

“…Salvador et al (33) separate BOLD into three frequency bands (0-0.08 Hz, 0.08-0.17 Hz, and 0.17-0.25 Hz) and show that correlation is strongest at the lowest-frequency band, consistent with a 1/f spectrum. Ciuciu et al (32) also argue that BOLD coherence is 1/ f. In contrast, Wu et al (41) show that correlation first increases as frequency decreases and then plateaus at 0.04-0.06 Hz. Achard et al (36) show that wavelet correlation, which is similar to coherence, peaks around 0.03-0.06 Hz and drops at lower frequencies.…”

“…S7). This bias is surprisingly strong, yet few studies remove or otherwise compensate for it (32,35). In addition, Zhang et al (40) show that artifacts, such as head motion and systemic physiological fluctuations in pulsation, can mask the frequency structure of the "true" correlation.…”

“…This assumes that the dynamics of interregional oxygen correlation match the dynamics of local fluctuations. Indeed, three studies report that BOLD correlations vary inversely with frequency (1/f), much like local oxygen (32)(33)(34). However, Sasai et al (35), Achard et al (36), and Cordes et al (37) report instead that oxygen correlation peaks around 0.04-0.06 Hz, with less correlation at lower frequencies-a band-limited pattern that is distinctly different from 1/f (38)(39)(40).…”

Spatially regularized wavelet leader scale-free analysis of fMRI data

“…Due to hemodynamic filtering, these arrhythmic dynamics lie below 0.2 Hz in fMRI data. Indeed, scale-free temporal dynamics were observed across several modalities, both at rest or during Work supported by ANR-16-CE33-0020 MultiFracs, France task performance, and under various conditions or pathologies [1][2][3][4][5][6][7][8][9][10][11][12]. It has also been documented that scale-free dynamics are functionally associated with neural excitability [3,13] and negatively correlates with power fluctuation in alpha-band (8−12 Hz) [14], hence explaining the modulation of scaling exponents with task engagement or pathologies.…”

“…Wavelet tranforms permit a theoretically well-grounded and practically robust assessment of scale-free dynamics and estimation of the corresponding scaling or Hurst exponent (cf. e.g., [15] for the methodology and [9,10] for applications to fMRI data). More recently, it has however been shown that the use of wavelet leaders, a non-linear non-local transformation of wavelet coefficients, permits to better account for the richness and variety of scalefree dynamics actually observed in data, and yields estimation procedures for H with better performance (used here, cf.…”