The suppression of scale-free fMRI brain dynamics across three different sources of effort: aging, task novelty and task difficulty

Abstract

There is growing evidence that fluctuations in brain activity may exhibit scale-free ("fractal") dynamics. Scale-free signals follow a spectral-power curve of the form P(f ) ∝ f(-β), where spectral power decreases in a power-law fashion with increasing frequency. In this study, we demonstrated that fractal scaling of BOLD fMRI signal is consistently suppressed for different sources of cognitive effort. Decreases in the Hurst exponent (H), which quantifies scale-free signal, was related to three different sources of cognitive effort/task engagement: 1) task difficulty, 2) task novelty, and 3) aging effects. These results were consistently observed across multiple datasets and task paradigms. We also demonstrated that estimates of H are robust across a range of time-window sizes. H was also compared to alternative metrics of BOLD variability (SDBOLD) and global connectivity (Gconn), with effort-related decreases in H producing similar decreases in SDBOLD and Gconn. These results indicate a potential global brain phenomenon that unites research from different fields and indicates that fractal scaling may be a highly sensitive metric for indexing cognitive effort/task engagement.

Figure 1

Plots depicting (A) the central hypothesis of the paper, and (B) fractal scaling examples in fMRI. (A) schematic illustrating the key hypothesis of this paper: effort is inversely related to fractal scaling. For low task effort, the brain is in a highly scale-free “ground” state (depicted by the black disk). Numerous factors increase cognitive effort (and decrease H), including task complexity, task novelty, and aging. This is analogous to the “potential energy wells” that are often employed in physics diagrams. (B) BOLD timecourse for two subjects from the Verbal Working Memory Task (VWMT), based on an 8-voxel seed in the posterior cingulate, with Hurst exponents of H = 0.72 (moderately fractal) and H = 0.94 (highly fractal). We observe smooth, highly autocorrelated time-series for the more fractal red curve.

Figure 2. Representative Hurst exponent (H) scaling plots for selected brain regions.

(A) average Hurst exponent map for Sustained Attention to Response Task (SART), averaged over all subjects, with selected regions of interest (ROIs) in the precuneus, precentral gyrus and white matter, as representative regions with high/moderate/low H. (B) average variance F(n) vs. time window size n, as estimated for Detrended Fluctuations Analysis (DFA), along with the slope of a linear fit α. (C) average spectral power P(f ) vs. frequency f, along with the slope of a linear fit β. Results for (B,C) and linear fits are shown in log-log scale. Error bars represent Bootstrapped 95% confidence intervals (95%CIs).

Figure 3. Brain regions showing decreased Hurst exponent (H) going from simple to complex tasks.

Results of a Partial Least Squares analysis are shown for four different tasks obtained from a Multi-Task Assessment battery, reaction time (RT), attentional cueing (ATT), delayed match to sample (DMS) and perceptual matching (PMT). We display results of the first component, which accounts for 44.3% total covariance (significant at p < 0.001, permutation testing). (left) plots task saliences with Bootstrapped 95% CI errorbars, and (right) plots associated significant bootstrap ratio values in the brain at a False Discovery Rate threshold of 0.05, indicating widespread negative change in Hurst exponent, associated with the more complex DMS and PMT conditions. A liberal cluster-size threshold of >3 contiguous voxels was also applied to improve image interpretability.

Figure 4. Brain regions showing decreased Hurst exponent (H) going from run-2 to run-1 of a task (increasing task novelty).

Panels (A,B) show results of pairwise testing of Hurst exponent in run-1 vs. run-2, for TMT = Trail-Making Test (block design) and SART = Sustained Attention to Response Task (fast event-related). (C) Results of a Partial Least Squares analysis of 4 runs of a VWMT = Verbal Working Memory Task (slow event-related). We display results of the first component, which accounts for 54.0% total covariance (significant at p < 0.001, permutation testing), showing decreased Hurst exponent (negative Bootstrap ratios) is associated with later task runs. All Bootstrap ratio maps are corrected for multiple comparisons at FDR = 0.05 threshold; run saliences have 95% CI errorbars. A liberal cluster-size threshold of >3 contiguous voxels was also applied to improve image interpretability.

Figure 5. Brain regions showing decreased Hurst exponent (H) going from older to younger subjects (increasing age).

Panels (A,B) show results of pairwise testing of Hurst exponent in young vs. old, for TMT = Trail-Making Test (block design) and SART = Sustained Attention to Response Task (fast event-related). (C) Results of a Partial Least Squares analysis of Hurst exponent against age for VWMT = Verbal Working Memory Task (slow event-related), showing decreased Hurst exponent (positive Bootstrap ratios) is associated with age. All Bootstrap ratio maps are corrected for multiple comparisons at FDR = 0.05 threshold. A liberal cluster-size threshold of >3 contiguous voxels was also applied to improve image interpretability.

Figure 6. The impact of maximum scaling window size on DFA results.

(A) boxplots plots showing correlations between individual subject H maps obtained for maximum window size n_max = 50 TR, compared to H maps obtained for shorter n_max. (B) plots showing brain regions with significantly reduced H as a function of n_max, for run-1 vs. run-2 (task novelty) and old vs. young (aging). Results are shown for the representative SART dataset.

Figure 7. The relationship between Hurst exponent (H), BOLD variability (SD_BOLD) and global connectivity (Gconn).

(A–C) average brain maps computed across subjects, for H, SD_BOLD and Gconn. Scatterplots (D,E) show median H vs. SD_BOLD of brain voxels, for run-1 vs. run-2 (young subjects only) and old vs. young subject (averaged over runs). Scatterplots (F,G) show median H vs. Gconn of brain voxels, for run-1 vs. run-2 (young subjects only) and old vs. young subject (averaged over runs). Results are shown for the representative SART dataset.