Temporal fluctuations in regional red blood cell flux in the rat brain cortex is a fractal process

Model-based evaluation of the microhemodynamic effects of PEGylated HBOC molecules in the rat brain cortex: a laser speckle imaging study

Hemoglobin-based oxygen carriers (HBOCs) were developed with the aim of substituting transfusions in emergency events. However, they exhibit adverse events, such as nitric oxide (NO) scavenging, vasoactivity, enhanced platelet aggregation, presently hampering their clinical application. The impact of two prototypical PEGylated HBOCs, Euro-PEG-Hb and PEG-HbO₂, endowed by different oxygen affinities and hydrodynamic volumes, was assessed on the cerebrocortical parenchymal microhemodynamics, and extravasation through the blood-brain-barrier (BBB) by laser speckle contrast imaging (LSCI) method and near-infrared (NIR) imaging, respectively. By evaluating voxel-wise cerebrocortical red blood cell velocity, non-invasively for its mean kernel-wise value ( v ¯ RBC ), and model-derived kernel-wise predictions for microregional tissue hematocrit, ^TH_t, and fractional change in hematocrit-corrected vascular resistance, R', as measures of potential adverse effects (enhanced platelet aggregation and vasoactivity, respectively) we found i) no significant difference between tested HBOCs in the systemic and microregional parameters, and in the relative spatial dispersion of ^TH_t, and R' as additional measures of HBOC-related adverse effects, and ii) no extravasation through BBB by Euro-PEG-Hb. We conclude that Euro-PEG-Hb does not exhibit adverse effects in the brain microcirculation that could be directly attributed to NO scavenging.

Pitfalls in Fractal Time Series Analysis: fMRI BOLD as an Exemplary Case

This article will be positioned on our previous work demonstrating the importance of adhering to a carefully selected set of criteria when choosing the suitable method from those available ensuring its adequate performance when applied to real temporal signals, such as fMRI BOLD, to evaluate one important facet of their behavior, fractality. Earlier, we have reviewed on a range of monofractal tools and evaluated their performance. Given the advance in the fractal field, in this article we will discuss the most widely used implementations of multifractal analyses, too. Our recommended flowchart for the fractal characterization of spontaneous, low frequency fluctuations in fMRI BOLD will be used as the framework for this article to make certain that it will provide a hands-on experience for the reader in handling the perplexed issues of fractal analysis. The reason why this particular signal modality and its fractal analysis has been chosen was due to its high impact on today’s neuroscience given it had powerfully emerged as a new way of interpreting the complex functioning of the brain (see “intrinsic activity”). The reader will first be presented with the basic concepts of mono and multifractal time series analyses, followed by some of the most relevant implementations, characterization by numerical approaches. The notion of the dichotomy of fractional Gaussian noise and fractional Brownian motion signal classes and their impact on fractal time series analyses will be thoroughly discussed as the central theme of our application strategy. Sources of pitfalls and way how to avoid them will be identified followed by a demonstration on fractal studies of fMRI BOLD taken from the literature and that of our own in an attempt to consolidate the best practice in fractal analysis of empirical fMRI BOLD signals mapped throughout the brain as an exemplary case of potentially wide interest.

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

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/f(β) 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/f(β) 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 characterization of complexity in dynamic signals: application to cerebral hemodynamics

We introduce the concept of spatial and temporal complexity with emphasis on how its fractal characterization for 1D, 2D or 3D hemodynamic brain signals can be carried out. Using high-resolution experimental data sets acquired in animal and human brain by noninvasive methods - such as laser Doppler flowmetry, laser speckle, near infrared, or functional magnetic resonance imaging - the spatiotemporal complexity of cerebral hemodynamics is demonstrated. It is characterized by spontaneous, seemingly random (that is disorderly) fluctuation of the hemodynamic signals. Fractal analysis, however, proved that these fluctuations are correlated according to the special order of self-similarity. The degree of correlation can be assessed quantitatively either in the temporal or the frequency domain respectively by the Hurst exponent (H) and the spectral index (beta). The values of H for parenchymal regions of white and gray matter of the rat brain cortex are distinctly different. In human studies, the values of beta were instrumental in identifying age-related stiffening of cerebral vasculature and their potential vulnerability in watershed areas of the brain cortex such as in borderline regions between frontal and temporal lobes. Biological complexity seems to be present within a restricted range of H or beta values which may have medical significance because outlying values can indicate a state of pathology.

Spatial and temporal heterogeneity of regional pulmonary blood flow in piglets

Regional pulmonary blood flow (PBF) in adult animals varies over space and time, following a fractal pattern. We hypothesized that PBF would follow a fractal pattern in young animals. Five, two-week old piglets were sedated and mechanically ventilated. After stabilization, fluorescent microspheres were injected via the right atrium at baseline and then again at 5, 20, 20.5, 40 and 60 min. The lungs were subsequently excised, dried, inflated, and cored into 0.12-cm3 pieces (mean n=561+/-106 per animal) with the spatial coordinates recorded for each piece. Regional PBF was spatially and temporally heterogeneous with a spatial coefficient of variation of 43.3+/-7.9% and a temporal coefficient of variation of 14.3+/-0.4%. PBF followed a fractal pattern with a fractal dimension of 1.20+/-0.06 at 20 min, remaining stable throughout the experiment. PBF decreased with distance from the hilum but did not follow a lobar pattern. Temporal heterogeneity did not significantly increase with time but low flow regions demonstrated the greatest temporal variability throughout the study. Hence, PBF in young piglets was characterized both spatial and temporal heterogeneity.

Nonlinear analysis of blood cell flux fluctuations in the rat brain cortex during stepwise hypotension challenge

Blood flow through a region of interest in the brain cortex (cerebral blood flow (CBF)) as measured by laser-Doppler flowmetry (LDF) shows a complex temporal pattern, which can be either merely random or a manifestation of segmental chaotic dynamics of vasomotion-induced flowmotion in the arterial tree, a deterministic phenomenon; or that of a fractal, self-similar correlation order that emerges from the set of segmental perfusion events on statistical ground. Fractal content (F%) was determined by coarse-graining spectral analysis and their self-similar exponent, H, estimated by bridge-detrended Scaled Windowed Variance (bdSWV) method and a variant of the power Spectral Density method ((low)PSD(w,e)). Chaotic dynamics were assessed by computing the correlation dimension (D(corr)) and the largest Lyapunov exponent (lambda(max)) on unfiltered raw and surrogate datasets. In 10 Sprague-Dawley rats anesthetized by halothane, CBF was measured through the thinned calvarium by the LDF method. Blood pressure (BP) was reduced from 100 to 40 mm Hg in steps of 20 mm Hg maintained for 2 mins by the lower body negative pressure method. Fractal and chaotic patterns coexisted in tissue perfusion. CBF did not show autoregulation. At every BP step, F% remained high (72% to 88%) and was independent of BP. Laser-Doppler flowmetry signals proved to be nonstationary fractional Brownian motions. Their H's by bdSWV and (low)PSD(w,e) (0.29+/-0.006 and 0.25+/-0.012, respectively) were independent of BP. Neither D(corr) nor lambda(max) varied with hypotension. Their values were characteristic of a chaotic system, but surrogate data analysis rendered some of them inconclusive. Hence, CBF fluctuations can be regarded as a robust phenomenon that is not abolished even by sustained hypotension at 40 mm Hg.

Fractal characterization of complexity in temporal physiological signals

This review first gives an overview on the concept of fractal geometry with definitions and explanations of the most fundamental properties of fractal structures and processes like self-similarity, power law scaling relationship, scale invariance, scaling range and fractal dimensions. Having laid down the grounds of the basics in terminology and mathematical formalism, the authors systematically introduce the concept and methods of monofractal time series analysis. They argue that fractal time series analysis cannot be done in a conscious, reliable manner without having a model capable of capturing the essential features of physiological signals with regard to their fractal analysis. They advocate the use of a simple, yet adequate, dichotomous model of fractional Gaussian noise (fGn) and fractional Brownian motion (fBm). They demonstrate the importance of incorporating a step of signal classification according to the fGn/fBm model prior to fractal analysis by showing that missing out on signal class can result in completely meaningless fractal estimates. Limitation and precision of various fractal tools are thoroughly described and discussed using results of numerical experiments on ideal monofractal signals. Steps of a reliable fractal analysis are explained. Finally, the main applications of fractal time series analysis in biomedical research are reviewed and critically evaluated.