Multifractality in cerebrovascular dynamics: an approach for mechanisms-related analysis

Павлов, А. Н.; Semyachkina-Glushkovskaya, Oxana; Pavlova, O. N.; Abdurashitov, Arkady S.; Shihalov, G.M.; Rybalova, Elena; Sindeev, Sergey S.

doi:10.1016/j.chaos.2016.06.002

Cited by 7 publications

(3 citation statements)

References 25 publications

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“…A number of physiologic time series were found to be characterized by a distribution of scaling parameters and therefore to belong to a broader class of complex processes known as multifractals. Such multifractal time series appear in the rich variability of healthy physiological networks, including but not restricted to human gait [32], cerebral blood flow (CBF) [77,78] and heart rate variability (HRV) [79][80][81], and changes in scaling behavior [82] reflect certain kinds of pathologies, as discussed in prequel I [2] of this series.…”

Section: Multifractal Time Seriesmentioning

confidence: 98%

The Fractal Tapestry of Life: III Multifractals Entail the Fractional Calculus

West

2022

Fractal Fract

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This is the third essay advocating the use the (non-integer) fractional calculus (FC) to capture the dynamics of complex networks in the twilight of the Newtonian era. Herein, the focus is on drawing a distinction between networks described by monfractal time series extensively discussed in the prequels and how they differ in function from multifractal time series, using physiological phenomena as exemplars. In prequel II, the network effect was introduced to explain how the collective dynamics of a complex network can transform a many-body non-linear dynamical system modeled using the integer calculus (IC) into a single-body fractional stochastic rate equation. Note that these essays are about biomedical phenomena that have historically been improperly modeled using the IC and how fractional calculus (FC) models better explain experimental results. This essay presents the biomedical entailment of the FC, but it is not a mathematical discussion in the sense that we are not concerned with the formal infrastucture, which is cited, but we are concerned with what that infrastructure entails. For example, the health of a physiologic network is characterized by the width of the multifractal spectrum associated with its time series, and which becomes narrower with the onset of certain pathologies. Physiologic time series that have explicitly related pathology to a narrowing of multifractal time series include but are not limited to heart rate variability (HRV), stride rate variability (SRV) and breath rate variability (BRV). The efficiency of the transfer of information due to the interaction between two such complex networks is determined by their relative spectral width, with information being transferred from the network with the broader to that with the narrower width. A fractional-order differential equation, whose order is random, is shown to generate a multifractal time series, thereby providing a FC model of the information exchange between complex networks. This equivalence between random fractional derivatives and multifractality has not received the recognition in the bioapplications literature we believe it warrants.

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Section: Multifractal Time Seriesmentioning

confidence: 98%

The Fractal Tapestry of Life: III Multifractals Entail the Fractional Calculus

West

2022

Fractal Fract

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“…The processes satisfying (1) or some variant of it have received considerable attention in variety of applications like turbulence, finance, climatology, medical imaging, texture classification (see e.g. Mandelbrot et al (1997), Bacry et al (2008), Robert & Vargas (2008), Duchon et al (2012), Lovejoy & Schertzer (2013), Abry et al (2015), Pavlov et al (2016), Kalamaras et al (2017), Laib et al (2018) and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Multifractal processes: Definition, properties and new examples

Grahovac

2020

Chaos, Solitons & Fractals

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We investigate stochastic processes possessing scale invariance properties which we refer to as multifractal processes. The examples of such processes known so far do not go much beyond the original cascade construction of Mandelbrot. We provide a new definition of the multifractal process by generalizing the definition of the selfsimilar process. We establish general properties of these processes and show how existing examples fit into our setting. Finally, we define a new class of examples inspired by the idea of Lamperti transformation. Namely, for any pair of infinitely divisible distribution and a stationary process one can construct a multifractal process. * dgrahova@mathos.hr

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“…A mechanism-related characterization of the complexity is a more perspective topic. 9 This tendency can be traced in recent studies of physiological processes with entropy-based approaches. Entropy is often considered as a complexity measure that is able to characterize the dynamics of biological systems.…”

Section: Introductionmentioning

confidence: 99%

Characterization of cerebral blood flow dynamics with multiscale entropy

Павлов

Abdurashitov

Pavlova

et al. 2017

J. Innov. Opt. Health Sci.

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Based on the laser speckle contrast imaging (LSCI) and the multiscale entropy (MSE), we study in this work the blood°ow dynamics at the levels of cerebral veins and the surrounding network of microcerebral vessels. We discuss how the phenylephrine-related acute peripheral hypertension is re°ected in the cerebral circulation and show that the observed changes are scale-dependent, and they are signi¯cantly more pronounced in microcerebral vessels, while the macrocerebral dynamics does not demonstrate authentic inter-group distinctions. We also consider the permeability of blood-brain barrier (BBB) and study its opening caused by sound exposure. We show that alterations associated with the BBB opening can be revealed by the analysis of blood°ow at the level of macrocerebral vessels.

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Multifractality in cerebrovascular dynamics: an approach for mechanisms-related analysis

Cited by 7 publications

References 25 publications

The Fractal Tapestry of Life: III Multifractals Entail the Fractional Calculus

The Fractal Tapestry of Life: III Multifractals Entail the Fractional Calculus

Multifractal processes: Definition, properties and new examples

Characterization of cerebral blood flow dynamics with multiscale entropy

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