Fractal analysis of spontaneous fluctuations of the BOLD signal in rat brain

Abstract

Analysis of task-evoked fMRI data ignores low frequency fluctuations (LFF) of the resting-state the BOLD signal, yet LFF of the spontaneous BOLD signal is crucial for analysis of resting-state connectivity maps. We characterized the LFF of resting-state BOLD signal at 11.7T in α-chloralose and domitor anesthetized rat brain and modeled the spontaneous signal as a scale-free (i.e., fractal) distribution of amplitude power (∣A∣2) across a frequency range (f) compatible with an ∣A(f)∣2 ∝ 1/fβ model where β is the scaling exponent (or spectral index). We compared β values from somatosensory forelimb area (S1FL), cingulate cortex (CG), and caudate putamen (CPu). With α-chloralose, S1FL and CG β values dropped from ~0.7 at in vivo to ~0.1 at post mortem (p<0.0002), whereas CPu β values dropped from ~0.3 at in vivo to ~0.1 at post mortem (p<0.002). With domitor, cortical (S1FL, CG) β values were slightly higher than with α-chloralose, while subcortical (CPu) β values were similar with α-chloralose. Although cortical and subcortical β values with both anesthetics were significantly different in vivo (p<0.002), at post mortem β values in these regions were not significantly different and approached zero (i.e., range of −0.1 to 0.2). Since a water phantom devoid of susceptibility gradients had a β value of zero (i.e., random), we conclude that deoxyhemoglobin present in voxels post-sacrifice still impacts tissue water diffusion. These results suggest that in the anesthetized rat brain the LFF of BOLD signal at 11.7T follow a general 1/fβ model of fractality where β is a variable responding to physiology. We describe typical experimental pitfalls which may elude detection of fractality in the resting-state BOLD signal.

Fractal Analysis of Brain Blood Oxygenation Level Dependent (BOLD) Signals from Children with Mild Traumatic Brain Injury (mTBI)

“…The log-log representation of the power spectrum Fig 1b contained multiple characteristic regions, which could be a sign of multi-modality [12]. However, for the purpose of our study, we selected a frequency range from 0.08–0.16 Hz where power-law scaling behavior was consistently observed across all voxels and subjects.…”

“…Fractals are infinitely complex patterns that are self-similar across different scales and their estimated dimension is a measure of the complexity of the system [15]. Complexity of the BOLD signal has been previously used as a descriptor of the neural activity based on hemodynamics and metabolic response [12, 16]. The brain, when healthy, is best described as a complex system and thus could display regional changes in the fractal dimension (FD) of the rs-BOLD signal as a result of a mTBI.…”

Quantitative basis for neuroimaging of cortical laminae with calibrated functional MRI

“…All procedures were performed in accordance with approved protocols as previously described (10,19,57,58). Briefly, rats were anesthetized with α-chloralose and prepared for fMRI and electrophysiology studies (57).…”

Role of Ongoing, Intrinsic Activity of Neuronal Populations for Quantitative Neuroimaging of Functional Magnetic Resonance Imaging–Based Networks

“…Since the cross-correlation method assumes a seed region and assesses the functional connectivity of that region with other areas, future R-fMRI data analysis should consider nonseeded approaches such as independent component analysis and fractal analysis (Herman et al, 2011;Hutchison et al, 2010). Independent component analysis was developed for linear representation of mixed data (Bell and Sejnowski, 1995), with the aim of identifying non-gaussian independent components that underlie unique neural networks.…”

“…In contrast, fractal analysis, which is a scale-free examination of fluctuating data (Mandelbrot and van Ness, 1968), calculates a fractal parameter independently for each BOLD signal time series (i.e., from each voxel). Thus, a fractal parameter map itself can be used to define subtle changes across brain states (Wang et al, 2011) and/or regional variations (Herman et al, 2011). Since the fractal parameter captures the unique behavior of the fluctuating signal that is governed by physiological processes (see Eke et al, 2002 for details on fractal analysis), it could potentially be used for network identification without experimental bias of visual inspection.…”