Monofractal analysis of functional magnetic resonance imaging: An introductory review

Abstract

The following review will aid readers in providing an overview of scale-free dynamics and monofractal analysis, as well as its applications and potential in functional magnetic resonance imaging (fMRI) neuroscience and clinical research. Like natural phenomena such as the growth of a tree or crashing ocean waves, the brain expresses scale-invariant, or fractal, patterns in neural signals that can be measured. While neural phenomena may represent both monofractal and multifractal processes and can be quantified with many different interrelated parameters, this review will focus on monofractal analysis using the Hurst exponent (H). Monofractal analysis of fMRI data is an advanced analysis technique that measures the complexity of brain signaling by quantifying its degree of scale-invariance. As such, the H value of the blood oxygenation level-dependent (BOLD) signal specifies how the degree of correlation in the signal may mediate brain functions. This review presents a brief overview of the theory of fMRI monofractal analysis followed by notable findings in the field. Through highlighting the advantages and challenges of the technique, the article provides insight into how to best conduct fMRI fractal analysis and properly interpret the findings with physiological relevance. Furthermore, we identify the future directions necessary for its progression towards impactful functional neuroscience discoveries and widespread clinical use. Ultimately, this presenting review aims to build a foundation of knowledge among readers to facilitate greater understanding, discussion, and use of this unique yet powerful imaging analysis technique.

Is resting state fMRI better than individual characteristics at predicting cognition?

“…It quantifies three different types of trends: ( i ) values between 0.5 and 1, indicating that the time series is complex and has long-range dependence; ( ii ) values less than 0.5, indicating that the time series is random and has short-range dependence; or ( iii ) a value close to 0.5, indicating that the time series is a random walk with no memory of the past. HE has been shown to be stable and reproducible across different fMRI datasets [83]. In this study, we estimated HE using the rescaled range analysis technique [50].…”

On the Spatial Distribution of Temporal Complexity in Resting State and Task Functional MRI

“…In spite of these technical differences, several simulated and experimental studies supported the hypothesis of a power law distribution for the fMRI power spectrum over the frequency band of 0.01 Hz to 0.1 Hz [ 21 , 52 , 65 , 66 ]. See [ 67 ] for a recent review on this topic.…”

Wavelet-based approach for diagnosing attention deficit hyperactivity disorder (ADHD)

“…A higher H value of a signal indicates that the signal exhibits a more regular and less erratic behavior. In general, defines an anticorrelated signal, is a random noise, and indicates a positively correlated signal (or characterizes a long-memory process) 14 . Methods used to estimate H include Fourier-spectra methods, variance plots, quadratic variations, and zero-level crossings 15 .…”