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

Microvascular Research 97 (2015) 6–12

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Transitions in skin blood flow fractal scaling: The importance of fluctuation amplitude in microcirculation Hamza Esen ⁎, Necmi Ata, Ferhan Esen Department of Biophysics, Faculty of Medicine, Eskişehir Osmangazi University, 26480 Eskişehir, Turkey

a r t i c l e

i n f o

Article history: Accepted 30 July 2014 Available online 18 September 2014 Keywords: Forearm skin Blood flow Fluctuation amplitude Transition in fractal scaling Essential hypertension

a b s t r a c t 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). © 2014 Elsevier Inc. All rights reserved.

Introduction Because of the rhythmic pulsation of the heart, the most obvious feature of blood flow in the arterial side of circulation is that it is pulsatile. However, the pressure pulse producing this pulsatile nature of blood flow is the leading hemodynamic risk factor for cardio-vascular system (Nichols and O'Rourke, 2005; Safar and Struijker-Boudier, 2010; Thorin and Thorin-Trescases, 2009). Pressure and flow waves generated during ventricular systole are partially reflected from the vasculature and these reflections can increase pulse pressure and augments mechanical stress on cardiovascular system (Nichols and O'Rourke, 2005; Penny et al., 2008). In addition, increased interaction of macro- and microvascular systems due to wave reflections between them may accelerate the progressive stiffening of the vascular wall that normally occurs with advancing age (Feihl et al., 2009; Thorin and Thorin-Trescases, 2009). Therefore, one of the most important functions of arterial tree is to dampen (cushioning function) the pressure oscillations and to generate continuous blood flow in microvascular beds (Nichols and O'Rourke, 2005). Although the microcirculation was once considered as a segment of the vascular tree in which pulsations have almost completely disappeared, spectral analysis of cutaneous microvascular blood flow has demonstrated that the cardiac signals, source of pulsatility, exist in these vascular beds (Braćić and Stefanovska, 1998). To calculate the ⁎ Corresponding author. Fax: +90 222 239 37 72. E-mail address: [email protected] (H. Esen).

http://dx.doi.org/10.1016/j.mvr.2014.07.014 0026-2862/© 2014 Elsevier Inc. All rights reserved.

pulsatility of microvascular blood flow, relative contribution of its control mechanisms to power spectral density (PSD) function of laser Doppler flow (LDF) signal from cutaneous vascular beds can be used. Recently, Esen et al. (2013) used a pulsatility ratio (R = central PSD/local PSD) for the assessment of microvascular function and they have been shown that R is useful for diagnostics in patients with essential hypertension (EHT). Although lower pulsatility ratio (R ≤ 1) has been commonly found from baseline LDF signal in healthy young (Y) subjects, R has been increased to 3 in middle aged (MA) group and to 9 in EHT patients. In addition it has been shown that vasodilatation increases the R in Y and MA subjects but not in patients with EHT. Therefore, Esen et al. (2013) suggested that pulsatility begins to play a role in controlling the baseline blood flow when R ≥ 1 the local mechanisms lose their control in favor of central mechanisms in microvascular beds. On the other hand, increase in pulsatility due to pathology such as EHT can lower the response of microvascular beds to vasodilator stimuli. However, the level of pulsatility that causes pathology in the microvascular beds is not clearly determined. Recently, fractal analyses have been used to investigate the nonlinear/ nonstationary nature of LDF time series from cutaneous vascular beds (Carolan-Rees et al., 2002; Esen and Esen, 2006; Esen et al., 2009, 2011, 2014; Humeau et al., 2010; Liao et al., 2011). One of the techniques that can cope with nonstationarity of a signal is the detrended fluctuation analysis (DFA). DFA of LDF signals reveals three distinct scaling regions (cardiac, cardio-respiratory and local) indicating individual and/or collective behavior of the microvascular control systems (Esen and Esen, 2006). Scaling exponent (α: slope of

H. Esen et al. / Microvascular Research 97 (2015) 6–12

the straight line in each region) indicates the correlation property of LDF signal for the corresponding time interval. Uncorrelated signals in the cardiac and positively correlated signals in cardio-respiratory and local regions are the common features found in fractal analysis of baseline LDF signals. Transitions from uncorrelated to positive in cardiac and from positive to negative correlation in cardio-respiratory regions are other common features that have been found during vasodilatation (Esen and Esen, 2006; Esen et al., 2009, 2011). This paper is motivated by these previous experimental findings. The appearance of both transitions with vasodilatation suggests that the increase in pulsatility of blood flow can be the cause of these transitions. In this study, we will focus on finding a potential link between pulsatility (peak to peak fluctuation amplitude, AF) and scaling exponents of LDF signals. Furthermore, the importance of pulsatility in aging and disease or in understanding a control mechanism may be quantified with finding a threshold for pulse amplitude, above which the scaling exponents change abruptly. Materials and methods Subjects Fifty nine normotensive healthy subjects (25 Y, 34 MA) and 34 EHT patients participated voluntarily in this study. EHT patients had a history of blood pressure without any apparent underlying cause. Their blood pressure was controlled (below 140/90 mm Hg) with the antihypertensive agents. EHT subjects with diabetes, hypercholesterolemia, hyperhomocysteinemia, chronic renal failure, peripheral vascular disease, coronary artery disease and heart failure were excluded from the study. All subjects were non-obese (body mass index b 30 kg/m2), non-smokers and physically active but none of them were involved in a regular exercise program. The study protocol was approved by the ethics committee of the university hospital and conducted according to the principles of the Declaration of Helsinki 2008. Subject characteristics are summarized in Table 1. Instrumentation A data acquisition system (Biopac Systems, Inc. USA) equipped with a laser Doppler flowmeter (780 nm, 1 mW) was used to record the forearm cutaneous blood flow. Analog signal of the LDF instrument was sampled at 1 kHz. To record the blood perfusion in the center of a locally heated area of the skin, the fibers of the LDF probe (480 μm diameter) were placed in the center of a heating probe. The heating unit (Moor Instruments Ltd. UK) was able to control the temperature of the probe with ± 0.3 °C accuracy. This combined probe was fixed to the volar region of the forearm with a double sided adhesive tape. Measurement of basal and evoked skin blood flow Cutaneous blood flow of the subjects lying in supine position was studied on the volar site of the forearm. The studies were performed in a quiet room at 23 ± 2 °C. All subjects were asked to refrain from consuming alcohol and caffeine containing drinks a day before the

Table 1 Characteristics of the subjects. Characteristic

n Age (years) Systolic BP (mm Hg) Diastolic BP (mm Hg) Heart rate (beats/min)

Control groups Y

MA

EHT

25 21 ± 3 115 ± 5 75 ± 5 78 ± 4

34 50 ± 7 120 ± 5 70 ± 10 75 ± 8

34 44 ± 4 135 ± 5 75 ± 15 71 ± 6

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measurements. Each subject had a 30 min rest before the test. After a 15 min baseline skin blood flow recording, a constant local heat (42 °C) was applied (Minson et al., 2001). The temperature of the local heating unit was increased at a rate of 0.1 °C per second to a temperature of 42 °C and was held constant at 42 °C for at least 35 min. The recording of LDF signal was continued to observe the plateau region in response to local heating. Normalization of LDF signals The values of baseline and vasodilatation LDF signals are not absolute and even in the same subject may have substantial variability due to varying orientation and distribution of the arterioles beneath the probe. Therefore, appropriate data normalization is required prior to subsequent statistical analysis. Several different approaches are commonly used based on assumptions about the characteristics of the data. Since LDF signals have a baseline (minimum) and a plateau region of the vasodilatation (maximum), min–max normalization was used by scaling their average values so that they fall within a range 0 to 1. In general, local heating evokes an initial dilator response that peaks in a few minutes, falls a little and then followed by a secondary dilatation that has a plateau after ~25 min of heat application. The LDF signal in this plateau region (saturation level of the response to local heating) was used for our analyses. The following equation was used to implement a unity-based normalization; LD F ¼

ðLDFÞi −ðLDFÞB ðLDFÞS −ðLDFÞB

where: (LDF)i is the each data point i, (LDF)B is the average value of baseline signal, (LDF)S is the average value of saturation signal during vasodilatation and LDF is the normalized data point between 0 and 1. Fluctuation amplitude (AF) Since there is a constant DC component that is equal to the mean value of a normalized signal, deviations were measured from these average reference signals. The fluctuation amplitude of a LDF signal is defined as the difference between its maximum and minimum values. Two LDF signals, baseline and vasodilatation (plateau region), were used for these measurements and we calculated two amplitude values for each subject. Detrended fluctuation analysis (DFA) The fractal nature of the irregular and nonstationary LDF signal can be obtained by DFA, a method for determining the scaling behavior of data in the presence of possible trends. Complete details of the methodology are published elsewhere (Peng et al., 1994). In brief, the original LDF time series is integrated and then divided into boxes of equal length, n. To find the local trend in each box of length n, a least-squares line is fitted to the data. The root mean square deviation between integrated series and its trend in each box is then calculated and denoted by F(n). This computation is repeated over all box sizes (time scales). A linear relationship between Ln[F(n)] and Ln(n) indicates the presence of scaling (self similarity): F(n) ~ nα. In other words, fluctuations in small boxes are related to the fluctuations in larger boxes in a power-law fashion. The slope of the line relating Ln[F(n)] to Ln(n) determines the fractal scaling exponent, α. To test whether LDF time series exhibit fractal behavior and to determine their correlation properties, we can apply the DFA algorithm to LDF signal. α = 0.5 for a white noise process. Scaling exponent in the range of 0.5 b α ≤ 1 indicates the presence of positive long range correlations. On the other hand 0 b α b 0.5 indicates the presence of negative long range correlations. α = 1 for a flicker noise type of fluctuation in a dynamical system of self organized critical state.

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α = 1.5 for Brownian motion like dynamics and α N 1.5 describes deterministic long-range correlations (Eke et al., 2000, 2002). Data and statistical analysis The DFA analyses were performed on the LDF signals (response to local heating and baseline) by using software, which is written with the tools of Labview (National Instruments Corp. USA). The baseline period of ~11 min before the local heating and the last 11 min of the response to local heating (saturation level) were used for DFA to find the baseline and evoked scaling exponents, respectively. The data which was originally sampled at 1 kHz was resampled at 200 Hz and the signal length of N = 217 data points was used for the fractal analysis performed in this study. The length of data and the sampling rate were adequate for reliable calculation of the fractal scaling exponent (Eke et al., 2002). In general, DFA of LDF signal yields three scaling regions with two crossovers. Based on the DFA of original and high-pass filtered LDF signals, three scaling regions/frequency intervals corresponding to the “linear” parts of each DFA curve were defined (Esen and Esen, 2006). For convenience, these scaling regions are called with the name of contributing physiological systems: cardiac, cardio-respiratory and local (Esen and Esen, 2006). For each region of every DFA graph, linear regression analysis was used to find the best fit line. Squared correlation coefficient (r2) and the p value for the best fit line were used to quantify the degree of linear association between Ln[F(n)] and Ln(n). The slopes (scaling exponents) of these best fit lines can be used to evaluate the vascular and/or microvascular functions (Esen et al., 2009, 2011, 2014) and thus will be the focus of this study. To find a relation between scaling exponents and fluctuation amplitudes, we plotted the data (α's against AF's), scrutinized the plots and we have used curve fitting algorithms of the statistical software: GraphPad Prism 6.01 software (GraphPad Software, Inc. La Jolla, CA USA). Results Comparison of the pulsatility of LDF time series Looking at the pulsatility (the value of peak to peak fluctuation amplitude, AF) patterns of normalized LDF time series (Figs. 1A, 2A and 3A), significantly small fluctuations (AF b 0.5) were found in baseline (B) LDF signal compared to the fluctuation (AF N 0.5) in vasodilatation (T) signal in response to thermal hyperemia in healthy Y and MA subjects but not in EHT patients. Although group average of pulsatility was not significantly different (p N 0.05) compared to MA subjects (Fig. 4), AF was b0.5 in some T signals in Y individuals (Fig. 1A). On the other hand, the pulsatility was higher (p b 0.0001) in EHT patients than in Y and MA subjects for both signals: baseline and vasodilatation (Figs. 3A and 4). Comparison of scaling behaviors Although 3 scaling exponents were commonly obtained in healthy Y subjects, we found only 2 scaling exponents (Fig. 1B) in some individuals. Interestingly, local and cardio-respiratory regions were fused together in these subjects and the slope of fused regions was αCR ≈ αL ≈ 1. Examples may include fractal scaling of baseline and/or vasodilatation signals but only vasodilatation example was given here (Fig. 1B). Furthermore, the slope (αC ≈ 1.5) of the cardiac region was not significantly changed during vasodilatation (p N 0.05) in this example. However, we should note that the fluctuation amplitude of vasodilatation signal (Fig. 1A) was small (AF b 0.5), transition to positive correlation was not observed (Fig. 1B) and signal remained uncorrelated in cardiac region in this example. Similarly, transition from positive (α N 0.5) to negative (α b 0.5) correlation

Fig. 1. Skin blood flow signal for a healthy Y subject (1A) and fractal analysis plots (1B) of its two parts: baseline (○) and response to local heating (●). Note that the fusion of local and cardiorespiratory regions in the DFA graph of vasodilatation signal. Instead of individually distinct two scaling exponents, one scaling exponent (αCR = αL ~ 1) describes scaling behavior in both regions. Dependence of cardiac (αC), local (αL) and cardiorespiratory (αCR) scaling exponents on the fluctuation amplitude of LDF signal in Y group (1C). BPU: blood perfusion unit.

was not observed in the cardio-respiratory region (Fig. 1B) in spite of the increased fluctuation amplitude of LDF signal during vasodilatation (Fig. 1A). Typical examples of DFA graphs displaying 3 scaling regions for baseline and vasodilatation signals were given in Fig. 2B for a healthy MA subject. Slope of its cardiac region was changed from 1.54 (uncorrelated) to 1.71 (positive correlation) during vasodilatation. In addition, scaling exponent of cardio-respiratory region was also changed from 0.73 (positive correlation) to 0.24 (negative correlation). However, slope (αL ≈ 1) of local region was not changed upon vasodilatation. Pulsatility of baseline and vasodilatation LDF signals was higher in EHT patients than in Y and MA groups (Figs. 3A and 4) but scaling exponents were not changed in response to vasodilatation in EHT patients (Figs. 3B and 5). Transitions in scaling exponents with pulsatility Scaling exponents calculated from the LDF signals were plotted versus their fluctuation amplitudes in Figs. 1C and 2C, and these graphs

H. Esen et al. / Microvascular Research 97 (2015) 6–12

Fig. 2. Skin blood flow signal for a healthy MA subject (2A) and fractal analysis plots (2B) of its two parts: baseline (○) and response to local heating (●). Dependence of cardiac (αC), local (αL) and cardio-respiratory (αCR) scaling exponents on the fluctuation amplitude of LDF signal in MA group (2C). BPU: blood perfusion unit.

show that there are transitions in cardiac and cardio-respiratory scaling exponents. To quantify these changes in scaling exponents with fluctuation amplitude, we used segmented linear regression with two segments separated by a breakpoint. These figures also illustrate the regression lines fitting to the data. The values of calculated parameters from these analyses are given in Table 2. Examination of this table indicates that there is an abrupt change at approximately same fluctuation amplitude (A Fo ≈ 0.7) in cardiac and cardio-respiratory scaling exponents in Y and MA groups. The lower confidence limits for the amplitudes at breakpoints were also approximately the same (AFl ≈ 0.5) for all curves (Table 2). Because slopes of the regression lines fitting to the data above 0.5 were not significantly different from zero and the scaling exponents did not change with the value of the fluctuation amplitude, AFl = 0.5 was accepted as a reliable value for transitions in scaling exponents. In addition, intercepts for cardiac and cardio-respiratory scaling exponents were αC ≈ 1.5, and αCR ≈ 1, respectively. However, we did not find transition in the local scaling exponent and the intercept of best fitting line to the local data was αL ≈ 1. In contrast to the findings in Y and MA groups, transitions in cardiac and cardio-respiratory scaling exponents disappeared in EHT patients (Fig. 3C).

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Fig. 3. Skin blood flow signal for a patient with EHT (3A) and fractal analysis plots (3B) of its two parts: baseline (○) and response to local heating (●). Dependence of cardiac (αC), local (αL) and cardio-respiratory (αCR) scaling exponents on the fluctuation amplitude of LDF signal in EHT patients (3C). Transitions seen in the fractal scaling of LDF signal from healthy subjects disappeared in EHT patients. BPU: blood perfusion unit.

from uncorrelated (αC ≈ 1.5) to positive correlation (2 N αC N 1.5) in the cardiac and from positive (1 N αC N 0.5) to negative correlation (0.5 N αC N 0) in the cardio-respiratory regions with increasing pulsatility of the LDF signals in healthy subjects but not in EHT patients. Furthermore, both transitions have occurred at the same pulsatility level (AF ≈ 0.5) of LDF signals. Another important finding of the present

Discussion We studied how the pulsatility seen in skin blood flow could affect the fractal dynamics in this biological system. We found transitions

Fig. 4. Values of peak to peak skin blood flow fluctuation amplitudes (AF) in baseline (B) and vasodilatation (induced by local heating, T) signals in the studied groups: Y, MA and EHT. Pulsatility was higher in EHT patients than in Y and MA groups.

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H. Esen et al. / Microvascular Research 97 (2015) 6–12

Fig. 5. Scatter of the scaling exponents (α) data calculated from baseline (B) and from vasodilatation signals induced by local heating (T) in the studied groups: Y (black), MA (gray) and EHT (light gray). Scaling exponents were significantly different (ANOVA p b 0.0001) in EHT patients compared to Y and MA groups. Bars indicate minimum and maximum values.

study was the fusion of two regions (cardio-respiratory and local) together in a healthy Y subject. Fluctuation amplitude of vasodilatation signal was negligibly small in this subject and we found two scaling exponents (αC ≈ 1.5: Brownian noise and αCR = αL ≈ 1: long range order) instead of three in determining the correlation properties of LDF signal. Taking clues from these experimental results we can describe certain aspects of fractal scaling of the LDF signal in health and breakdown of its correlation properties with aging and disease. Fractal scaling of LDF signals in young subjects One of the important observations of present study is that 2 scaling exponents (αCR = αL ≈ 1 and αC ≈ 1.5) describe the fractal properties of LDF signal when AF b 0.5 (Fig. 1B). Scaling exponent (slope of the line fitting to the DFA data in any scaling region) indicates the correlation properties of the corresponding component(s) of examined signal (Esen and Esen, 2006) and αC ≈ 1.5 corresponds to a cardiac signal behaving as a regular Brownian motion: random and uncorrelated noise (Eke et al., 2000, 2002). Since the most important function of the small arteries and arterioles is to dampen (cushioning function) the pressure/flow oscillations that results from ventricular ejections, attenuated pulsatility (AF b 0.5) and break-down of correlation (αC ≈ 1.5) by cushioning function can be considered as the evidence of good vascular health. Indeed, variations that resemble the periodic nature of cardiac pulsations in the blood flow are negligibly small in this healthy Y subject compared to the healthy groups. In this case, respiratory and local signals corresponding to the value of scaling exponent αCR = αL ≈ 1 determine the correlation properties, long range order, of the LDF signal. Consequently, one may conclude that the fluctuation in blood flow from healthy microvascular beds is controlled mainly by local mechanisms for AF b 0.5 and αC ≈ 1.5 at supine rest. Unifying of local and cardio-respiratory regions is not limited to a vasodilatation signal induced by local heating. These regions were also

Table 2 Summary of segmental linear regression analysis (breakpoint amplitudes, 95% confidence interval of the AFo and goodness of fit, R2) in Y and MA groups. Item

Y

Scaling exponents AFo (breakpoint) 95% AFo R2

αC 0.672 0.470–0.875 0.656

MA αCR 0.647 0.467–0.828 0.680

αC 0.723 0.499–0.947 0.658

αCR 0.710 0.496–0.924 0.628

unified, but for baseline LDF signal in other healthy Y subject. Therefore, we should answer why cardio-respiratory region fuses together with the local region or when it becomes a distinct scaling region in the fractal scaling of LDF signal. It has been shown that all local control mechanisms are arranged along a straight line according to their frequency in the healthy young subjects (Esen and Esen, 2006). Because the slope of this straight line is ≈ 1 and indicates that there is a long range order in the signal (Eke et al., 2000, 2002), this order of the control mechanisms on such a straight line has been suggested as a marker of cooperation and/or integration between the contributing mechanisms (Esen and Esen, 2006). If this cooperation is lost due to a pathology in any mechanism, and an individual mechanism exhibits its intrinsic behavior independently, then one may expect that the line will be broken. For example, endothelial dysfunction causes a break on this local line and the slope of the broken segment corresponding to endothelial dysfunction is b 1 (Esen et al., 2009). Therefore, the unified region (in which local and cardio-respiratory regions are fused together) indicates cooperation/integration between respiratory and local mechanisms that produces a long range order (αCR = αL ≈ 1) in the signal (for A F b 0.5 and α C = 1.5). It is very well known that respiratory system produces pressure difference for the venous return and contributes to increase in blood flow in the microvascular beds. Hence, pressure drop due to respiratory activity can induce myogenic response in arterioles. However, myogenic response is best suited for protecting the microvascular beds against increases, rather than reductions, in pressure (Davis, 2012). Consequently, fluctuation amplitude induced by respiratory activity should be very small compared with the fluctuation amplitude induced by local mechanisms or respiratory activity to be so timed as to cooperate with local mechanisms. On the other hand, if respiratory system exhibits its intrinsic behavior independently or fluctuations induced by respiratory activity are higher than the fluctuations produced by local mechanisms then αCR may indicate the presence of correlation caused by the periodic nature of respiration, when AF b 0.5 and αC ≈ 1.5. Our calculations support above suggestion, because αCR N 0.5 and cardio-respiratory region was a distinct scaling region for baseline LDF signal (Figs. 1B and 2B). Consequently, baseline LDF signal from healthy vascular beds reveals a kind of complex variability associated with Brownian noise (αC ≈ 1.5) and two correlations (αL ≈ 1 and 0.5 b αCR b 1), along with two distinct classes of nonlinear interactions: local and respiratory. Transitions in fractal scaling with healthy vascular aging Vascular aging, which begins in childhood, is obvious in the elderly but is apparent in most human adults (Nichols and O'Rourke, 2005). With increasing age, elastic arteries progressively stiffen as well as dilate. Since the elastic arteries serve predominantly as a cushioning reservoir, stiffening of vascular wall with age causes decrease in its ability to accommodate sudden changes in pressure. Therefore, we studied the change in pulsatility during local vasodilatation at supine rest to evaluate the cushioning function of microvascular beds. We previously stated that AF and αC were b 0.5 and ≈1.5, respectively for appropriately cushioned B and T signals (Figs. 1A and B). In contrast, we found transition in the αC from 1.5 to ~1.75 when AF N 0.5 (Figs. 1C and 2C). Since αC ~ 1.75 corresponds to deterministic correlation (Eke et al., 2000, 2002) that might be caused by the periodic nature of cardiac activity, pulsatile character of the LDF signal should be increased. This increased pulsatility in microvascular beds can be explained by reduced cushioning function due to increased vascular wall rigidity in arterial/arteriolar beds with age (Prewitt et al., 2002; Thorin and Thorin-Trescases, 2009). Our results (Figs. 2A and B) confirming these suggestions imply attenuated cushioning function in small arteries and/or arterioles compared with the results of Y subject (Figs. 1A and B). However, these vessels are still healthy so that their response to the pulsatile blood flow is seen in both regions: cardiac and cardio-respiratory (Figs. 2B and C).

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In addition to the transition in cardiac region, transition from positive (αCR = 0.73) to negatively correlated (αCR = 0.24) behavior in cardio-respiratory region (Figs. 1C, 2C and 5) can also be used to interpret the intrinsic dynamics of the myogenic system. The vascular myogenic response refers to the intrinsic ability of a blood vessel to constrict to an increase or dilate to a decrease in intraluminal pressure (Davis, 2012; Davis and Hill, 1999). In cardio-respiratory region, cardiac, respiratory and myogenic frequencies are in order along a straight line (Esen and Esen, 2006). Because cardiac component can dominate over respiratory signal during vasodilatation (Esen et al., 2013) and compete with intrinsic myogenic activity, it is reasonable to consider that the correlation property of this region would be negative. Indeed, increases in blood flow with elevated cardiac pressure are followed by subsequent decreases due to the myogenic constriction in the arterioles. In this case, traces produced by cardiac, respiratory and myogenic components of LDF signal that correspond to values of α less than 0.5 have a tendency to turn back upon themselves; increases in the values are more likely followed by subsequent decreases, and vice versa (Eke et al., 2002). This property is known as negative correlation (antipersistence). Therefore, transition from positive (0.5 b αCR b 1) to negative (0 b αCR b 0.5) correlation in cardio-respiratory scaling exponent indicates the evidence of intact myogenic system, when AF N 0.5 and 1.5 b αC b 2. Our results indicate the existence of attenuated but intact myogenic response in microvascular beds to increased pulsatility during healthy vascular aging. Disappearance of transitions in fractal scaling with pathology: EHT Essential hypertension (EHT) is a disorder displaying functional and structural changes in the microcirculation (Feihl et al., 2009; Lindstedt et al., 2006; Pries and Secomb, 2002). Increase in blood pressure triggers vascular smooth muscle contraction and if pressure remains for a long time, arterioles undergo inward eutrophic remodeling that thickens the vascular wall and can eventually compromise vessel elasticity (Prewitt et al., 2002; Pries and Secomb, 2002). Chronic elevation in blood pressure also causes aging of endothelial cells prematurely and reduces endothelium dependent vasodilatation (Tang and Vanhoutte, 2010). Thus, reduced and/or impaired myogenic response and endothelial activity are expected to cause diminished transitions in the fractal scaling of LDF signals from healthy Y and MA subjects in both regions: cardiac and cardio-respiratory. Indeed, pulsatility was always high in EHT patients compared to Y and MA subjects (Fig. 4). In addition, we did not observe any transition in fractal scaling depending on the pulsatility of LDF signals in EHT patients (Fig. 3C). These results were also in agreement with the finding of our previous studies (Esen et al., 2011, 2014). This study has a number of limitations that are important to note. First, although lower confidence limit of AFo has been selected to reliably determine the vascular function by transitions in fractal scaling, local heating may attenuate cutaneous vasoconstriction (Wingo et al., 2009) and the amplitude calculated from the vasodilatation signals in response to local heating may be greater than its actual value. Further studies evaluating the effect of elevated local temperature on AF may provide valuable information, but we currently have no reason to believe that AFl = 0.5 had a great error, because it is also approximately equal to the upper limit of fluctuation amplitudes of baseline LDF signals, which are free from the effect of local heating. Second, since α is related to the PSD of spectral analysis (Heneghan and McDarby, 2000) and is equivalent to a frequency weighted spectral ratio of the conventional frequency bands used in heart rate variability (HRV) analysis (Willson et al, 2002), one may consider that the α found from a LDF signal has not a clear meaning as an indicator of unique physiological control system. However, DFA of a LDF signal uses segment size that is related to the oscillation frequency. Therefore, the frequency band(s) of each scaling region and its physiological interpretation in the framework of frequency analysis has been clearly determined

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(Esen and Esen, 2006). Since only the fundamental frequency of cardiac signal and its harmonics prevails in the scaling region denoted by αC, this region corresponds to a unique physiological function: cardiac. This is in agreement with the finding of Baumert et al. (2006) that shows 3 distinct scaling regions, which correspond to the well known 3 frequency bands in the power spectra of HRV. If their 2 regions are fused together, scaling exponent of the unified region may depend on their weighted spectral ratio as calculated by Willson et al. (2002). For example, other 2 regions in the DFA of a LDF signal include more than one frequency band; each of them corresponds to a different control mechanism. Further studies evaluating the contribution of these mechanisms to the related scaling exponent may provide valuable information. Therefore, scaling properties should be discussed with caution. For example, we have taken cardiac signals into account by using the values of AF and αC in describing the scaling properties of cardio-respiratory region. If cardiac signals were negligibly small (AF b 0.5 and α C ≈ 1.5) cardio-respiratory region is fused with local region. In contrast, we observed transition in αCR for AF N 0.5. Third, we defined AF without removing the effect of other sources on cardiac signal. Thus, the AF used in this study cannot be attributed to the cardiac pulsatility only, but reflects real data. In addition, because of our inability to measure the pressure in microvasculature, we could not give a definition of AF indicating the pulsatility in pressure. However, experimental findings of the present study indicate that the pulsatility analysis in flow signal was quite useful in determining the microvascular function. Although morphological assessment may reflect current severity of vascular damage, functional assessment may provide further information for the management of risk factors of the vascular damage. Fractal analysis of LDF signal has the potential to contribute to the existing tools and certain aspects of vascular function are associated with transitions in scaling exponents. Our results have shown that the transitions in the scaling exponents are produced by a same property, pulsatility of LDF signal. Therefore, transitions in scaling exponents can be used to assess the mechanisms responsible from pulsatility. The small pulsatility (AF b 0.5) with no transition (αC ≈ 1.5) and αCR = αL ≈ 1 in response to vasodilatation suggests healthy vascular beds. Pulsatility (AF N 0.5) with transitions (from αC ≈ 1.5 to αC ≈ 1.75 and from 1 N αCR N 0.5 to 0.5 N αCR N 0) in response to vasodilatation also suggests healthy vascular beds with intact myogenic mechanisms, but a reduced cushioning function. High pulsatility with no transitions in response to vasodilatation suggests impairment in cushioning function and myogenic mechanisms of vascular beds. References Baumert, M., Brechtel, L.M., Lock, J., Voss, A., About, D., 2006. Scaling graphs of heart rate time series in athletes demonstrating the VLF, LF and HF regions. Physiol. Meas. 27, N35–N39. Braćić, M., Stefanovska, A., 1998. Wavelet-based analysis of human blood-flow dynamics. Bull. Math. Biol. 60, 919–935. Carolan-Rees, G., Tweddel, A.C., Naka, K.K., Griffith, T.M., 2002. Fractal dimension of laser Doppler flowmetry time series. Med. Eng. Phys. 24, 71–76. Davis, M.J., 2012. Physiological role(s) of the vascular myogenic response. Microcirculation 19, 99–114. Davis, M.J., Hill, M.A., 1999. Signalling mechanisms underlying the vascular myogenic response. Physiol. Rev. 79, 387–423. Eke, A., Hermán, P., Bassingthwaighte, J.B., Raymond, G.M., Percival, D.B., Cannon, M., et al., 2000. Physiological time series: distinguishing fractal noises from motions. Pflugers Arch. Eur. J. hysiol. 439, 403–415. Eke, A., Hermán, P., Kocsis, L., Kozak, L.R., 2002. Fractal characterization of complexity in temporal physiological signals. Physiol. Meas. 23, R1–R38. Esen, F., Esen, H., 2006. Detrended fluctuation analysis of laser Doppler flowmetry time series: the effect of extrinsic and intrinsic factors on the fractal scaling of microvascular blood flow. Physiol. Meas. 27, 1241–1253. Esen, F., Sönmez, Aydın, G., Esen, H., 2009. Detrended fluctuation analysis of laser Doppler flowmetry time series. Microvasc. Res. 78, 314–318. Esen, F., Çağlar, S., Ata, N., Ulus, T., Birdane, A., Esen, H., 2011. Fractal scaling of laser Doppler flowmetry time series in patients with essential hypertension. Microvasc. Res. 82, 291–295. Esen, F., Çağlar, S., Ata, N., Esen, H., 2013. Investigation of cardiac pulsations in the cutaneous circulation in patients with essential hypertension. Turk. Klin. J. Med. Sci. 33 (2), 344–352.

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