Multifractality in the Peripheral Cardiovascular System from Pointwise Hölder Exponents of Laser Doppler Flowmetry Signals

We study the dynamics of skin laser Doppler flowmetry signals giving a peripheral view of the cardiovascular system. The analysis of Hölder exponents reveals that the experimental signals are weakly multifractal for young healthy subjects at rest. We implement the same analysis on data generated by a standard theoretical model of the cardiovascular system based on nonlinear coupled oscillators with linear couplings and fluctuations. We show that the theoretical model, although it captures basic features of the dynamics, is not complex enough to reflect the multifractal irregularities of microvascular mechanisms.     

Cathodal current-induced vasodilation to single application and the amplified response to repeated application in humans rely on aspirin-sensitive mechanisms.

Assumed to rely on an axon reflex, the current-induced vasodilation (CIV) interferes with the microvascular response to iontophoretic drug delivery. Mechanisms resulting in CIV are likely different at the anode and at the cathode. While studies have been conducted to understand anodal CIV, little information is available on cathodal CIV. The present study investigates CIV observed following 0.1-mA cathodal applications on forearms of healthy volunteers and the possible mechanisms involved. Results are expressed in percentage of the cutaneous heat-induced maximal vascular conductance [%MVC (means +/- SE)]. 1) The amplitude of CIV was proportional to the duration of cathodal currents for periods of <1 min: r = 0.99. 2) Two current applications of 10 s, with 10-min interstimulation interval, induced a higher peak value of CIV (79.1 +/- 8.6% MVC) than the one obtained with all-at-once 20-s current application (39.5 +/- 4.3% MVC, P < 0.05). This amplified vascular response due to segmental application was observed for all tested interstimulation intervals (up to 40 min). 3) Two hours and 3 days following pretreatment with 1-g oral aspirin, the CIV observed following cathodal application, as well as the difference of cathodal CIV amplitude between all-at-once and segmented applications, were reduced. These findings suggest a role of prostaglandins, not only released from endothelial or smooth muscle cells, as direct vasodilator and/or as a sensitizer. Thus aspirin pretreatment could be used to decrease CIV resulting from all-at-once and repeated cathodal application and facilitate the study of the specific vascular effect induced by the drug delivered.     

Early vasodilator response to anodal current application in human is not impaired by cyclooxygenase-2 blockade

It is generally acknowledged that cutaneous vasodilatation in response to monopolar galvanic current application would result from an axon reflex in primary afferent fibers and the neurogenic inflammation resulting from neuropeptide release. Previous studies suggested participation of prostaglandin (PG) in anodal current-induced cutaneous vasodilatation. Thus the inducible cyclooxygenase (COX) isoform (COX-2), assumed to play a key role in inflammation, should be involved in the synthesis of the PG that is released. Skin blood flow (SkBF) variations induced by 5 min of 0.1-mA monopolar anodal current application were evaluated with laser-Doppler flowmetry on the forearm of healthy volunteers treated with indomethacin (COX-1 and COX-2 inhibitor), celecoxib (COX-2 inhibitor), or placebo. SkBF was indexed as cutaneous vascular conductance (CVC), expressed as percentage of heat-induced maximal CVC (%MVC). Urinalyses were performed to test celecoxib treatment efficiency. No difference was found in CVC values at rest: 14.3 +/- 4.0, 11.9 +/- 3.2, and 10.9 +/- 2.0% MVC after indomethacin, celecoxib, and placebo treatment, respectively. At 10 min after the onset of anodal current application, CVC values were 22.2 +/- 4.9% MVC (not significantly different from rest) with indomethacin, 85.7 +/- 15.3% MVC (P < 0.001 vs. rest) with celecoxib, and 70.4 +/- 13.1% MVC (P < 0.001 vs. rest) with placebo. Celecoxib significantly depressed the urinary prostacyclin metabolite 6-keto-PGF(1alpha) (P < 0.05 vs. placebo). Indomethacin, but not celecoxib, significantly inhibited the anodal current-induced vasodilatation. Thus, although they are assumed to result from an axon reflex in primary afferent fibers and neurogenic inflammation, these results suggest that the early anodal current-induced vasodilatation is mainly dependent on COX-1-induced PG synthesis.     

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Platelet inhibition by low-dose aspirin but not by clopidogrel reduces the axon-reflex current-induced vasodilation in humans

We previously showed a prolonged inhibition of current-induced vasodilation (CIV) after a single oral high dose of aspirin. In this study, we tested the hypothesis of platelet involvement in CIV. Nine healthy volunteers took 75 mg aspirin/day, 98 mg of clopidogrel bisulfate/day, or placebo for 4 days. CIV was induced by two consecutive 1-min anodal current applications (0.08 mA/cm(2)) through deionized water with a 10-min interval. CIV was measured with laser Doppler flowmetry and expressed as a percentage of baseline cutaneous vascular conductance: %C(b). In a second experiment in 10 volunteers, aspirin and placebo were given as in experiment 1, but a 26-h delay from the last aspirin intake elapsed before ACh iontophoresis and postocclusive hyperemia were studied in parallel to CIV. In experiment 1, the means +/- SE amplitude of CIV was 822 +/- 314, 313 +/- 144, and 746 +/- 397%C(b) with placebo, aspirin (P < 0.05 from placebo and clopidogrel), and clopidogrel (NS from placebo), respectively. In experiment 2, CIV impairment with aspirin was confirmed: CIV amplitudes were 300 +/- 99, and 916 +/- 528%C(b) under aspirin and placebo, respectively (P < 0.05), whereas vasodilation to ACh iontophoresis (322 +/- 74 and 365 +/- 104%C(b)) and peak postocclusive hyperemia (491 +/- 137 and 661 +/- 248%C(b)) were not different between aspirin and placebo, respectively. Low-dose aspirin, even 26 h after oral administration, impairs CIV, while ACh-mediated vasodilation and postocclusive hyperemia are preserved. If platelets are involved in the neurovascular mechanism triggered by galvanic current application in humans, it is likely to occur through the cyclooxygenase but not the ADP pathway.     

Multifractality in the peripheral cardiovascular system from pointwise holder exponents of laser Doppler flowmetry signals

We study the dynamics of skin laser Doppler flowmetry signals giving a peripheral view of the cardiovascular system. The analysis of Hölder exponents reveals that the experimental signals are weakly multifractal for young healthy subjects at rest. We implement the same analysis on data generated by a standard theoretical model of the cardiovascular system based on nonlinear coupled oscillators with linear couplings and fluctuations. We show that the theoretical model, although it captures basic features of the dynamics, is not complex enough to reflect the multifractal irregularities of microvascular mechanisms.In clinical and physiological investigations, the cardiovascular system dynamics can be considered from a central or from a peripheral point of view. Heart-beat interval sequences, reflecting a central view of the human cardiovascular system, have been analyzed and the results have shown that they display multifractal properties for healthy subjects (1). A peripheral view of the cardiovascular system dynamics is possible by studying microvascular blood flow signals given by the laser Doppler flowmetry technique (2). These signals have complex dynamics, with fractal structures and chaos (3,4). However, are these data, reflecting the underlying mechanisms acting at the microscopic level of the human physiology, as irregular as those giving a central view point of the system dynamics? Is a single fractal exponent sufficient to characterize them? Moreover, a set of nonlinear coupled oscillators has recently been proposed as a standard theoretical model of the cardiovascular system (5–8). Is the dynamics of the corresponding simulated data close to the one of real cardiovascular signals?Herein we report that skin laser Doppler flowmetry signals display multifractal properties on young healthy subjects at rest. By estimating Hölder exponents of signals recorded on the finger, we show that the dynamics of peripheral signals can be irregular, as central data are. We also conclude that the use of a standard theoretical model of the cardiovascular system, based on five nonlinear coupled oscillators with linear couplings and fluctuations, is not complex enough to model the multifractal properties of the cardiovascular system. To our knowledge, it is the first time that multifractality of experimental and simulated laser Doppler flowmetry signals is studied.The rapid changes in a time series are called singularities and a characterization of their strength is obtained with the Hölder exponents (9). When a broad range of exponents is found, signals are considered as multifractal. A narrow range implies monofractality. One of the most widely used monofractal signal models is the fractional Brownian motion. In opposition, multifractal signals are more complex and inhomogeneous. The multifractal formalism has been established to account for the statistical scaling properties of time series observed in various physical situations. A singularity spectrum D(h) of a signal is the function that gives, for a fixed h, the Hausdorff dimension of the set of points x where the Hölder exponent h(x) is equal to h. The Hölder exponent h(x₀) of a function f at the point x₀ is the highest h value so that f is Lipschitz at x₀. There exists a constant C and a polynomial P_n(x) of order n so that for all x in a neighborhood of x₀ we have (10,11)(1)The Hölder exponent measures the degree of irregularity of f at the point x₀.We analyze experimental skin laser Doppler flowmetry signals reflecting microvascular blood flow. The signals are recorded with a frequency sampling of 20 Hz on the finger of seven young healthy people between 20 and 35 years old (12). A laser Doppler flowmetry signal is shown in Fig. 1. For each recording, 15,601 pointwise Hölder exponents are taken into account. They are computed with a parametric generalized quadratic variation based estimation method (13). Open in a separate windowFIGURE 1Skin laser Doppler flowmetry signal recorded on a young healthy subject at rest.For the skin laser Doppler flowmetry signals, we find a minimum Hölder exponent of 0.56, a maximum of 0.71, a mean value of 0.63, and a standard deviation of 0.03 (average values over seven signals). The difference between the minimum and maximum Hölder exponents is therefore of 0.15. An example of Hölder exponent time series is shown in Fig. 2. To compare the results with known mono and multifractal data, we generate a fractional Brownian motion (monofractal signal) and a multifractional Brownian motion (multifractal signal) (14). For each data, 15,601 pointwise Hölder exponents are taken into account. Open in a separate windowFIGURE 2Hölder exponents for a skin laser Doppler flowmetry signal recorded on a young healthy subject at rest.

TABLE 1

Value for the minimum, maximum, range, mean, and standard deviation of the Hölder exponents computed for skin laser Doppler flowmetry (LDF) signals (average value computed over seven signals), for a monofractal signal (fBm), and for a multifractal signal (mBm)

Prolonged aspirin inhibition of anodal vasodilation is not due to the trafficking delay of neural mediators

We previously reported that forearm vasodilation to a delivered all-at-once over 5 min or a 1-min repeated monopolar anodal 0.10-mA current application is aspirin sensitive and that a single high-dose aspirin exerts a long-lived effect in the former case. We hypothesized that 1) in the latter case, the effect of aspirin would also be long lived and 2) the time required to resupply nerve endings with unblocked cyclooxygenase through axonal transport could explain this phenomenon. We studied the time course for the recovery of vasodilation to repeated current application after placebo or 1-g aspirin treatment. We then searched for a difference at a proximal vs. distal site in the recovery of the response. Aspirin abolished current-induced vasodilation at 2 h, 10 h, and 3 days, with a progressive recovery thereafter, but no difference between distal and proximal site was observed for the recovery of the response. This suggests that, although neural cyclooxygenase could participate in the response, the time course of aspirin inhibition of current-induced cutaneous vasodilation is not due to the time required through neural transport to resupply nerve endings with unblocked proteins.