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Abstract
Temporal blood oxygen level dependent (BOLD) contrast signals in functional MRI during rest may be characterized by power spectral distribution (PSD) trends of the form 1/fα. Trends with 1/f characteristics comprise fractal properties with repeating oscillation patterns in multiple time scales. Estimates of the fractal properties enable the quantification of phenomena that may otherwise be difficult to measure, such as transient, non-linear changes. In this study it was hypothesized that the fractal metrics of 1/f BOLD signal trends can map changes related to dynamic, multi-scale alterations in cerebral blood flow (CBF) after a transient hyperventilation challenge. Twenty-three normal adults were imaged in a resting-state before and after hyperventilation. Different variables (1/f trend constant α, fractal dimension Df, and, Hurst exponent H) characterizing the trends were measured from BOLD signals. The results show that fractal metrics of the BOLD signal follow the fractional Gaussian noise model, even during the dynamic CBF change that follows hyperventilation. The most dominant effect on the fractal metrics was detected in grey matter, in line with previous hyperventilation vaso-reactivity studies. The α was able to differentiate also blood vessels from grey matter changes. Df was most sensitive to grey matter. H correlated with default mode network areas before hyperventilation but this pattern vanished after hyperventilation due to a global increase in H. In the future, resting-state fMRI combined with fractal metrics of the BOLD signal may be used for analyzing multi-scale alterations of cerebral blood flow.
Highlights
Natural phenomena, from coastline dimensions to organization of brain functional connectivity, incorporate self-similarity; i.e. the proportional characteristics of the observed variables resemble each other in multiple scales (Mandelbrot, 1975; Maxim et al, 2005; van den Heuvel et al, 2008; Wink et al, 2008)
The lowest frequency trends prevail after removing the signal trends suggestive of dynamic changes in blood oxygen level dependent (BOLD) variance throughout the POST-V scan
As the cardiorespiratory challenge that we used was a dynamic change occurring over several minutes after cessation of hyperventilation, it was hypothesized that the variance of the BOLD signal might alter as a function of time, i.e. be fractional Brownian motion (fBm) in nature
Summary
From coastline dimensions to organization of brain functional connectivity, incorporate self-similarity; i.e. the proportional characteristics of the observed variables resemble each other in multiple scales (Mandelbrot, 1975; Maxim et al, 2005; van den Heuvel et al, 2008; Wink et al, 2008). Fractal temporal signals have power spectrum characteristics following a 1/f trend (Herman et al, 2009; Maxim et al, 2005; Sprott et al, 2003). In the absence of cued stimuli, the BOLD signal variations in the brain follow a power spectral distribution (PSD) trend 1/f α, where f is the frequency and α is an index describing the trend (Biswal et al, 1995; Kiviniemi et al, 2000, 2005; Purdon and Weisskoff, 1998; Zarahn et al, 1997). The parameter α ( often referred to as the spectral index β) describes the PSD trend slope on a logarithmic scale
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