Multifractal analysis of heart rate variability and laser Doppler flowmetry fluctuations:comparison of results from different numerical methods

Complexity synchronization in living matter: a mini review

Fractal time series have been argued to be ubiquitous in human physiology and some of the implications of that ubiquity are quite remarkable. One consequence of the omnipresent fractality is complexity synchronization (CS) observed in the interactions among simultaneously recorded physiologic time series discussed herein. This new kind of synchronization has been revealed in the interaction triad of organ-networks (ONs) consisting of the mutually interacting time series generated by the brain (electroencephalograms, EEGs), heart (electrocardiograms, ECGs), and lungs (Respiration). The scaled time series from each member of the triad look nothing like one another and yet they bear a deeply recorded synchronization invisible to the naked eye. The theory of scaling statistics is used to explain the source of the CS observed in the information exchange among these multifractal time series. The multifractal dimension (MFD) of each time series is a measure of the time-dependent complexity of that time series, and it is the matching of the MFD time series that provides the synchronization referred to as CS. The CS is one manifestation of the hypothesis given by a "Law of Multifractal Dimension Synchronization" (LMFDS) which is supported by data. Therefore, the review aspects of this paper are chosen to make the extended range of the LMFDS hypothesis sufficiently reasonable to warrant further empirical testing.

Complexity Synchronization of Organ Networks

The transdisciplinary nature of science as a whole became evident as the necessity for the complex nature of phenomena to explain social and life science, along with the physical sciences, blossomed into complexity theory and most recently into complexitysynchronization. This science motif is based on the scaling arising from the 1/f-variability in complex dynamic networks and the need for a network of networks to exchange information internally during intra-network dynamics and externally during inter-network dynamics. The measure of complexity adopted herein is the multifractal dimension of the crucial event time series generated by an organ network, and the difference in the multifractal dimensions of two organ networks quantifies the relative complexity between interacting complex networks. Information flows from dynamic networks at a higher level of complexity to those at lower levels of complexity, as summarized in the 'complexity matching effect', and the flow is maximally efficient when the complexities are equal. Herein, we use the scaling of empirical datasets from the brain, cardiovascular and respiratory networks to support the hypothesis that complexity synchronization occurs between scaling indices or equivalently with the matching of the time dependencies of the networks' multifractal dimensions.

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

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.

Camera-Based, Non-Contact, Vital-Signs Monitoring Technology May Provide a Way for the Early Prevention of SIDS in Infants

Sudden infant death syndrome (SIDS) is the unexplained death, usually during sleep, of a baby younger than 1-year-old. Even though researchers have discovered some factors that may put babies at extra risk, SIDS remains unpredictable up until now. One hypothesis is that impaired cardiovascular control may play a role in the underlying mechanism of SIDS. A reduction of heart rate variability (HRV) and progressive decrease in heart rate (HR) have been observed in infants who have later succumbed to SIDS. Many clues indicated the heart could be the final weakness in SIDS. Therefore, continuous monitoring of the dynamic changes within the heart may provide a possible preventive strategy of SIDS. Camera-based photoplethysmography was recently demonstrated as a contactless method to determine HR and HRV. This perspective presents a hypothesis that a camera-based, non-contact, vital-sign monitoring technology, which can indicate abnormal changes or a sudden loss of vital signs in a timely manner, may enable a crucial and low-cost means for the early prevention of SIDS in newborn infants.

n-Order and maximum fuzzy similarity entropy for discrimination of signals of different complexity: Application to fetal heart rate signals

This paper presents two new concepts for discrimination of signals of different complexity. The first focused initially on solving the problem of setting entropy descriptors by varying the pattern size instead of the tolerance. This led to the search for the optimal pattern size that maximized the similarity entropy. The second paradigm was based on the n-order similarity entropy that encompasses the 1-order similarity entropy. To improve the statistical stability, n-order fuzzy similarity entropy was proposed. Fractional Brownian motion was simulated to validate the different methods proposed, and fetal heart rate signals were used to discriminate normal from abnormal fetuses. In all cases, it was found that it was possible to discriminate time series of different complexity such as fractional Brownian motion and fetal heart rate signals. The best levels of performance in terms of sensitivity (90%) and specificity (90%) were obtained with the n-order fuzzy similarity entropy. However, it was shown that the optimal pattern size and the maximum similarity measurement were related to intrinsic features of the time series.

Transitions in skin blood flow fractal scaling: the importance of fluctuation amplitude in microcirculation

Detrended fluctuation analysis (DFA) of laser Doppler flowmetry (LDF) time series from volar skin reveals three scaling regions: cardiac, cardio-respiratory and local. Scaling exponents, slopes (αC, αCR and αL) of the straight lines, in these regions indicate correlation properties of LDF signal. Transitions from uncorrelated to positive in cardiac (αC) and positive to negative correlations in the cardio-respiratory (αCR) exponent have been observed for vasodilatation signals in response to local heating. However, positive correlation in local region (αL) did not change with vasodilatation. We studied whether the transitions in scaling exponents are correlated with the increase in peak to peak fluctuation amplitude (AF) of LDF signal. LDF signals were normalized to unity using average values of their pulsatile parts: baseline and saturation signals. If AF of normalized LDF signal is ≥0.5, we observed transitions in αC and in αCR but not in αL, in healthy subjects. It is suggested that the transition from positive to negative correlation in αCR with increasing amplitude may be explained by intact arteriolar myogenic activity in healthy young (Y) and middle aged (MA) subjects. In contrast, we did not observe transition in αCR suggesting impaired myogenic activity in patients with essential hypertension (EHT).

Coarse-grained multifractality analysis based on structure function measurements to discriminate healthy from distressed foetuses

This paper proposes a combined coarse-grained multifractal method to discriminate between distressed and normal foetuses. The coarse-graining operation was performed by means of a coarse-grained procedure and the multifractal operation was based on a structure function. The proposed method was evaluated by one hundred recordings including eighty normal foetuses and twenty distressed foetuses. We found that it was possible to discriminate between distressed and normal foetuses using the Hurst exponent, singularity, and Holder spectra.

Study of time reversibility/irreversibility of cardiovascular data: theoretical results and application to laser Doppler flowmetry and heart rate variability signals

Time irreversibility can be qualitatively defined as the degree of a signal for temporal asymmetry. Recently, a time irreversibility characterization method based on entropies of positive and negative increments has been proposed for experimental signals and applied to heart rate variability (HRV) data (central cardiovascular system (CVS)). The results led to interesting information as a time asymmetry index was found different for young subjects and elderly people or heart disease patients. Nevertheless, similar analyses have not yet been conducted on laser Doppler flowmetry (LDF) signals (peripheral CVS). We first propose to further investigate the above-mentioned characterization method. Then, LDF signals, LDF signals reduced to samples acquired during ECG R peaks (LDF_R(ECG) signals) and HRV recorded simultaneously in healthy subjects are processed. Entropies of positive and negative increments for LDF signals show a nonmonotonic pattern: oscillations--more or less pronounced, depending on subjects--are found with a period matching the one of cardiac activity. However, such oscillations are not found with LDF_R(ECG) nor with HRV. Moreover, the asymmetry index for LDF is markedly different from the ones of LDF_R(ECG) and HRV. The cardiac activity may therefore play a dominant role in the time irreversibility properties of LDF signals.

Oscillatory dynamics of vasoconstriction and vasodilation identified by time-localized phase coherence

We apply wavelet-based time-localized phase coherence to investigate the relationship between blood flow and skin temperature, and between blood flow and instantaneous heart rate (IHR), during vasoconstriction and vasodilation provoked by local cooling or heating of the skin. A temperature-controlled metal plate (approximately 10 cm2) placed on the volar side of the left arm was used to provide the heating and cooling. Beneath the plate, the blood flow was measured by laser Doppler flowmetry and the adjacent skin temperature by a thermistor. Two 1 h datasets were collected from each of the ten subjects. In each case a 30 min basal recording was followed by a step change in plate temperature, to either 24 °C or 42 °C. The IHR was derived from simultaneously recorded ECG. We confirm the changes in the energy and frequency of blood flow oscillations during cooling and heating reported earlier. That is, during cooling, there was a significant decrease in the average frequency of myogenic blood flow oscillations (p < 0.05) and the myogenic spectral peak became more prominent. During heating, there was a significant (p < 0.05) general increase in spectral energy, associated with vasodilation, except in the myogenic interval. Weak phase coherence between temperature and blood flow was observed for unperturbed skin, but it increased in all frequency intervals as a result of heating. It was not significantly affected by cooling. We also show that significant (p < 0.05) phase coherence exists between blood flow and IHR in the respiratory and myogenic frequency intervals. Cooling did not affect this phase coherence in any of the frequency intervals, whereas heating enhanced the phase coherence in the respiratory and myogenic intervals. This can be explained by the reduction in vascular resistance produced by heating, a process where myogenic mechanisms play a key role. We conclude that the mechanisms of vasodilation and vasoconstriction, in response to temperature change, are oscillatory in nature and are independent of central sources of variability.