Fractal Analysis of BOLD Time Series in a Network Associated With Waiting Impulsivity

Abstract

Fractal phenomena can be found in numerous scientific areas including neuroscience. Fractals are structures, in which the whole has the same shape as its parts. A specific structure known as pink noise (also called fractal or 1/f noise) is one key fractal manifestation, exhibits both stability and adaptability, and can be addressed via the Hurst exponent (H). FMRI studies using H on regional fMRI time courses used fractality as an important characteristic to unravel neural networks from artificial noise. In this fMRI-study, we examined 103 healthy male students at rest and while performing the 5-choice serial reaction time task. We addressed fractality in a network associated with waiting impulsivity using the adaptive fractal analysis (AFA) approach to determine H. We revealed the fractal nature of the impulsivity network. Furthermore, fractality was influenced by individual impulsivity in terms of decreasing fractality with higher impulsivity in regions of top-down control (left middle frontal gyrus) as well as reward processing (nucleus accumbens and anterior cingulate cortex). We conclude that fractality as determined via H is a promising marker to quantify deviations in network functions at an early stage and, thus, to be able to inform preventive interventions before the manifestation of a disorder.

Keywords: Hurst Exponent; biomarker; fMRI; frontal cortex; impulse control disorders; nucleus accumbens.

Figure 1

The 1/f noise pattern in a power spectrum (Equation 1) of an exemplary time course is shown on logarithmic scales while the scale invariance relation (Equation 3) is indicated by the slope H. Please note, that the relationship between β and H is according to Equation (2) β = 2H − 1. For demonstration, the example of a representative individual time course of the right MFG during task has been used.

Figure 2

Structure of an experimental trial.

Figure 3

Power frequency spectrum of the original time course (black dots), as well as of the resulting low (yellow line) and high frequency (red line) components. Please note the overlap between the black dots (original time course) and the yellow line (LFC) in low frequencies (left part of the x-axis) and between the black dots and the red line (HFC) in high frequencies (right part of the x-axis). The same time course of the right MFG during task of a representative subject has been used.

Figure 4

Overlap between low frequency course (LFC) and the original time course. LFC fits well the data without overfitting leaving out unnecessary information for the fractal analysis. In this figure, the same time course of the right MFG during task of a representative subject has been used.

Figure 5

Log-log diffusion plots of the power spectrum density (PSD) of the low and high frequency components (LFC, HFC): whereas the HFC (red dots) fails to fulfill the criteria of a fractal structure expressed by Equation 1, the PSD of the LFC (yellow dots) is clearly inversely proportional to frequency hinting toward a fractal nature. The data presented is the same time course of the right MFG during task of a representative subject.

Figure 6

The impulsivity network is presented in terms of significantly activated brain regions across all subjects while performing the 5-choice serial reaction time task. PFC, prefrontal cortex; ACC, anterior cingulate cortex; Nacc, nucleus accumbens.