Wavelet coherence analysis of spontaneous oscillations in cerebral tissue oxyhemoglobin concentrations and arterial blood pressure in elderly subjects

Microvascular Research 93 (2014) 14–20

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Wavelet coherence analysis of spontaneous oscillations in cerebral tissue oxyhemoglobin concentrations and arterial blood pressure in elderly subjects Ruofei Cui a, Ming Zhang b, Zengyong Li a,⁎, Qing Xin c, Liqian Lu a, Weiei Zhou a, Qingyu Han a, Yuanjin Gao a a b c

Key Laboratory of High Efficiency and Clean Mechanical Manufacture, School of Mechanical Engineering, Shandong University, Jinan, 250061, PR China Interdisciplinary Division of Biomedical Engineering, Faculty of Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong Special Administrative Region P.R. China Hospital of Shandong University, Jinan 250061, PR China

a r t i c l e

i n f o

Article history: Accepted 20 February 2014 Available online 2 March 2014

a b s t r a c t This study aims to assess the relationship between spontaneous oscillations in changes in cerebral tissue oxyhemoglobin concentrations (Delta [HbO2]) and arterial blood pressure (ABP) signals in healthy elderly subjects during the resting state using wavelet coherence analysis. Continuous recordings of near-infrared spectroscopy (NIRS) and ABP signals were obtained from simultaneous measurements in 33 healthy elderly subjects (age: 70.7 ± 7.9 years) and 27 young subjects (age: 25.2 ± 3.7 years) during the resting state. The coherence between Delta [HbO2] and ABP oscillations in six frequency intervals (I, 0.4–2 Hz; II, 0.15–0.4 Hz; III, 0.05–0.15 Hz; IV, 0.02–0.05 Hz, V, 0.005–0.0095 Hz and VI, 0.005–0.0095 Hz) was analyzed using wavelet coherence analysis. In elderly subjects, the Delta [HbO2] and ABP oscillations were significantly wavelet coherent in interval I, and wavelet phase coherent in intervals I, II and IV. The wavelet coherence in interval I was significantly higher (p = 0.040), in elderly subjects than in young subjects whereas that in interval V significantly lower (p = 0.015). In addition, the wavelet phase coherence in interval IV was significantly higher in elderly subjects than in young subjects (p = 0.028). The difference in the wavelet coherence of the elderly subjects and the young subjects indicates an altered cerebral autoregulation caused by aging. This study provides new insight into the dynamics of Delta [HbO2] and ABP oscillations and may be useful in identifying the risk for dynamic cerebral autoregulation processes. © 2014 Elsevier Inc. All rights reserved.

Introduction Aging is associated with marked structural and functional changes in the cerebrovascular and cardiovascular systems (Matteis et al., 1998). Age-related alterations in cerebral vasculature and autoregulatory mechanisms have been subjects of interest in many studies (Li et al., 2013; Mehagnoul-Schipper et al., 2000; Peng et al., 2008; Schroeter et al., 2004). Spontaneous oscillations are generally found in the spectral analysis of changes in cerebral tissue oxyhemoglobin concentrations (Delta [HbO2]) signals measured using near-infrared spectroscopy (NIRS) (Cheng et al., 2012; Li et al., 2010) as well as arterial blood pressure (ABP) signals (Peng et al., 2008; Rowley et al., 2007). The power spectra of Delta [HbO2] and ABP signals exhibit oscillations in various frequency bands. Wavelet analysis via the Morlet wavelet can detect these oscillations with logarithmic frequency resolution (Li et al., 2010, 2012). Different characteristic frequencies of Delta [HbO2] and ABP signals, which indicate possible regulatory mechanisms of the tissue oxygenation signal, have ⁎ Corresponding author at: School of Mechanical Engineering, Shandong University, Jinan 250061, PR China. Fax: +86 531 8839 2863. E-mail address: [email protected] (Z. Li).

http://dx.doi.org/10.1016/j.mvr.2014.02.008 0026-2862/© 2014 Elsevier Inc. All rights reserved.

been identified using wavelet analysis (Li et al., 2010, 2012, 2013) (Table 1). The oscillations in intervals I and II reflect the effects of cardiac and respiratory activities, respectively (Li et al., 2010, 2012; Shiogai et al., 2010). Within the brain, interval IV is closely regulated through tight neurovascular coupling and partial autonomic control (Zhang et al., 2002). The cerebral oscillations in interval III (0.05–0.15 Hz) were suggested to originate locally from intrinsic myogenic activity of smooth muscle cells in resistance vessels and this myogenic mechanism may be partly under autonomic control (Rowley et al., 2007; Shiogai et al., 2010). The oscillations in frequency intervals V and VI were identified and investigated by Stefanovska et al. (1999) and Kvandal et al. (2006), which correspond to nitric oxide (NO)-related endothelial activity and NO-independent endothelial activity, respectively. The bivariate relationship between the spontaneous oscillations in ABP and those in Delta [HbO2] can be used to assess the state of cerebral autoregulation (CA) (Van Beek et al., 2012). CA refers to the capacity of the brain vascular bed to maintain cerebral perfusion despite changes in blood pressure (BP) (Van Beek et al., 2008). The brain has a high metabolic demand and therefore requires adequate nutritional flow. The brain vasculature must respond to changes in arterial blood pressure (ABP) or intracranial pressure to maintain stable cerebral blood flow (CBF) (Van Beek et al., 2008). Thus, cerebral blood vessels have an

R. Cui et al. / Microvascular Research 93 (2014) 14–20 Table 1 Frequency intervals seen in Delta [HbO2] oscillations, and their physiological origins (Li et al., 2010, 2012; Shiogai et al., 2010). Interval

Frequency (Hz)

Physiological origin

I II III IV V VI

0.6–2 0.15–0.6 0.05–0.15 0.02–0.05 0.0095–0.02 0.005–0.0095

Cardiac activity Respiration Myogenic activity Neurogenic activity Endothelial metabolic activity Endothelial activity

15

accordance with the ethical standards specified by the Helsinki Declaration of 1975 (revised in 1983).

Measurement

inherent ability to keep the CBF fluctuation around certain value through myogenic, neurogenic, or metabolic mechanisms (Van Beek et al., 2008; Zhang et al., 2000). A cross-spectrum can be used to determine whether two processes result in oscillations within the same frequency region. The cross spectrum obtained from the Fourier transforms of an entire time series is uninformative, and a true cross spectrum must be estimated by windowing and averaging (Sheppard et al., 2012). The continuous wavelet transform, which enables logarithmic frequency resolution, rather than the windowed Fourier, approach to coherence was used because it offers a more intuitive visualization of the time-frequency behavior (Sheppard et al., 2012). A previous study used wavelet cross-correlation to identify significant differences in the wavelet scale of maximum cross-correlation in patients suffering from autonomic failure upon posture change (Rowley et al., 2007). However, this technique is limited by its inability to determine whether the oscillations at a given frequency are independent or mutually related (Bandrivskyy et al., 2004). The wavelet phase coherence can reveal possible relationships by evaluating the match between the instantaneous phases of two signals (Bandrivskyy et al., 2004; Sheppard et al., 2011). Wavelet coherence (WCO) identifies high common power, whereas wavelet phase coherence (WPCO) finds locally phase locked-behavior. WPCO analysis has been used to analyze relationships between oscillations in skin blood flow, temperature and oxygen saturation within certain frequency ranges (Bandrivskyy et al., 2004; Bernjak et al., 2012). In this study, we investigated the relationship between oscillations in Delta [HbO2] and spontaneous oscillations in ABP at different frequency ranges. Moreover, WCO and WPCO analyses were used to test the hypothesis that oscillations in ABP are transmitted into changes in Delta [HbO2], and that this dynamic relationship is altered in elderly subjects at rest because of aging.

Data for the NIRS and ABP signals were obtained from simultaneous measurements. After the age, height and body mass of the participants were recorded, NIRS measurements were performed on the subjects in a comfortable sitting posture using the tissue saturation An Heng monitor (TSAH-100, developed by Tsinghua University, China). This equipment has been previously described in detail by Li et al. (2010, 2012, 2013). In brief, the TSAH-100 sensor consisted of a two-wavelength LED and two PIN diodes. The LED component served as the source of emitted light at 760 and 850 nm, whereas the PIN diodes served as the detectors. Photons can penetrate the overlying tissues into the cerebral cortex (gray matter) when the distance between the detector and the source is ≥30 mm. Moreover, the penetration depth can reach the maximum value when the distance is 40 mm (Teng et al., 2006). Therefore, the distances between the light source and the two detectors were set to 30 mm (S1) and 40 mm (S2), respectively. The differential signal (S1–S2) in the optical density (OD) was recorded by the two detectors and used to obtain the cortical signal. This configuration was validated by Teng et al. (2006). The forehead of each subject was cleaned using isopropyl alcohol. Afterward, the sensors were carefully fixed using a flexible adhesive fixation pad and an elastic band. A sensor was placed on the left forehead 1.5 cm lateral to the cerebral midline to avoid the sagittal sinus and at least 2 cm above the eyebrow to avoid the frontal sinus. The sensor was carefully secured with a tensor bandage wrapped around the forehead while ensuring no admission of background light. The sampling rate of the NIRS-derived signals was set to 20 Hz. The Delta [HbO2] signal was monitored at the frontal lobe for 15 min using NIRS. The continuous ABP waveform was monitored noninvasively by a transducer attached to the wrist and using an ABP analysis system (FDP-I, Shanghai Science Teaching Co., China) at a sampling of 1000 Hz. This system continuously measure ABP by a sensor located over the subject's radial artery. A special designed device positions the sensor to the best position to monitor the radial artery pulse. The measured ABP data were resampled to 20 Hz. During the ABP recordings, the wrist was held at the heart level. Changes in the mean ABP measured at the heart level were used to estimate changes in cerebral perfusion pressure in the sitting position.

Methods and materials

Data pre-processing

Subjects

Wavelet transform was applied to the NIRS and ABP time series to decompose them into signal and uncorrelated noise components in distinct scales. The wavelet transform was calculated in the 0.005 Hz to 2 Hz frequency intervals. Very slow variations defined as below 0.005 Hz and uncorrelated noise components above 2 Hz were removed. The average Delta [HbO2] and ABP of all recorded segments were subtracted for signal normalization to avoid systematic differences between subjects and groups.

A total of 60 subjects were recruited from Shandong University to participate in this study, among whom 33 were elderly subjects (age: 70.7 ± 7.9 years; Group Elderly) and 27 were young people (age: 25.2 ± 3.7 years; Group Young). Table 1 shows the characteristics of the participants. Excluded from the study were subjects with hypertension; diabetes mellitus; subarachnoid hemorrhage; insufficiency of the heart, lungs, kidneys and liver; smoking or drinking habits, and additional medications (angiotensin-converting enzyme, inhibitors/angiotensin II-receptor blockers, and calcium-channel blockers). A diagnosis of hypertension was made when systolic blood pressure (SBP) ≥ 140 mmHg or diastolic blood pressure (DBP) ≥ 90 mmHg (Jones et al., 2003). A diagnosis of diabetes mellitus was based on clinical assessment or fasting serum glucose level. Prior to the experiment, basic subject information, including age, weight, height, and BP was recorded (Table 2). Informed consent was obtained from all subjects. The experimental procedures were approved by the Human Ethics Committee of Shandong University and were in

Table 2 Characteristics of the participants. Characteristic

Young

Old

P for difference

Age (years) Body mass index (BMI) Female sex Systolic blood pressure (mmHg) Diastolic blood pressure (mmHg)

25.2(3.7) 21.3(2.5) 25.9% 115.3(12.6) 68.7(6.3)

70.7(7.9) 25.0(2.9) 21.2% 124.1(10.5) 71.0(8.1)

0.000** 0.000** 0.674 0.006** 0.046*

Values are presented as means and standard deviations and percentages. P values for differences are calculated using t-test for means and standard deviations, and Chi-square test for percentages, * b 0.05, ** b 0.01.

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R. Cui et al. / Microvascular Research 93 (2014) 14–20

Wavelet transform Wavelet transform is a method that allows the complex transformation of a time series from the time domain to the time-frequency domain. It involves convolving the time series g(u) with a family of generally nonorthogonal basis functions that are generated from the mother wavelet (Bernjak et al., 2012; Stefanovska et al., 1999): 1 W ðs; t Þ ¼ pffiffi s

Z

þ∞ −∞

 Ψ

 u−t g ðuÞdu s

1Þ

where W(s, t) is a wavelet coefficient and Ψ is the Morlet mother wavelet, scaled by the factor s and translated in time by t. The Morlet mother wavelet is a complex sinusoid modulated by the Gaussian function: 2 1 −i2πu −u ffiffiffi  e e 2 ΨðuÞ ¼ p 4 π

2Þ

pffiffiffiffiffiffiffiffi where i ¼ −1. The continuous wavelet transform is a mapping of the function g(u) onto the time-frequency plane. Wavelet scaling enables the detection of oscillations with different frequencies, whereas wavelet translation in time allows the monitoring of spectra evolution over time. The rationale for using the Morlet wavelet is that its Gaussian envelope provides sufficient localization of events in both time and frequency; in time, approximately six to seven periods are used to detect the power of each oscillatory component (Bernjak et al., 2012). Moreover, a direct inverse relationship exists between the scaling factor s and its corresponding frequency: f = 1/s (Bernjak et al., 2012). The wavelet transform was calculated in the frequency interval of 0.005 Hz to 2 Hz. The upper limit of 2 Hz was set to include the heart rate frequency, whereas the lower limit was selected to include possible regulatory mechanisms of the tissue oxygenation signal (Li et al., 2010, 2012; Shiogai et al., 2010). Wavelet coherence Wavelet coherence (WCO) was used to determine the coherence of the wavelet cross-spectrum in the time-frequency domain. For two complex oscillatory time series w1,2(t) with wavelet transform values at frequency f, we use (Sheppard et al., 2012): iφk ð f ;t n Þ

wk ðt n Þ ¼ W k ð f ; t n Þe

3Þ

where k = 1, 2 and n ranges from 1 to N. The wavelet power at this frequency is: Pk ¼

N 1X  w ðt Þw ðt Þ N n¼1 k n k n

#" #)1=2 N N 1X 1X   w1 ðt n Þw2 ðtnÞ w1 ðt n Þw2 ðt m Þ N n¼1 N m¼1

Cφ ð f kÞ ¼

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2  2 cosΔφk;n þ sinΔφk;n :

6Þ

The value of the phase coherence function Cφ(fk) is between 0 and 1. This function quantifies the tendency of the phase difference between the two signals to remain constant at a particular frequency (Bernjak et al., 2012). When two oscillations are unrelated, their phase difference continuously changes with time; thus, their phase coherence approaches zero. Significant coherence was determined during the evaluation of the coherence of two oscillatory time series that may have variable amplitude and frequency. Amplitude-adjusted Fourier transform (AAFT) surrogate signals were generated by shuffling the phases of the original time series to create a new time series with the same means, variances, and autocorrelation functions as the original sequences but without any phase relations (Berrnjak et al., 2012). We then averaged 100 WPCOs from surrogate signals. A WPCO from the original recording was considered statistically significant when it was two standard deviations above the mean surrogate coherence. Statistical analysis The values were expressed as the median (standard deviations) or percentages. The data of each subject were tested for the normality (Kolmogorov–Smirnov test) at the group level and homogeneity of variance (Levene test) to ensure the values fulfilled the assumption required by the parameter analysis. Significant differences between the characteristics of the elderly and of the young subjects were determined using t-test for means and standard deviations and a chi-square test (for percentages). One-way ANOVA, was used to determine the main effects of group (age) on the coherence. Post-hoc analyses of the two groups were performed using Bonferroni comparison tests. A difference with an adjusted p b 0.05 was considered statistically significant. Results

4Þ

The coherence is determined from two complex oscillatory time series w1,2(t) with internal correlations. WCO is defined as follows (Sheppard et al., 2012): (" WCO ¼

instantaneous relative phase for each frequency and time. Phase information can be used to investigate the relationships between oscillations from different signals (Bernjak et al., 2012). Wavelet phase coherence identifies possible relationships by evaluating the match between the instantaneous phases of two signals (Bernjak et al., 2012). The instantaneous phases, named φ1k,n and φ2k,n, are calculated at each time tn and frequency fk for both signals. The relative phase difference is obtained using the formula Δφk,n = φ2k,n − φ1k,n. The sine and cosine components of the phase differences are calculated and averaged in time for the entire length of the signal. The phase coherence function is then defined as (Bernjak et al., 2012):

5Þ

A value of 1 indicates a linear relationship between two time series around time ti on a scale s. A value of zero is obtained for a vanishing correlation. A value above 0.5 typically indicates significant linear relationship at this scale (Rowley et al., 2007). Wavelet phase coherence The wavelet coefficients are complex numbers with the complex Morlet wavelet. These values define the absolute amplitude and

In this study, periodic oscillations in the ABP and Delta [HbO2] signals were identified at six frequency intervals (Fig. 1): I (0.4–2 Hz, II (0.15– 0.4 Hz), III (0.05–0.15 Hz), IV (0.02–0.05 Hz), V (0.0095–0.02 Hz) and VI (0.005–0.0095 Hz. Figs. 2a and b show the WCO of the ABP and Delta [HbO2] signals for an elderly subject and a young subject. The ABP and Delta [HbO2] oscillations showed WCO across a wide spectrum of oscillations (from intervals I to VI). For the elderly subjects, significant WCO was found in interval I (0.4–2 Hz). Fig. 3 shows a comparison of the mean WCO values of the elderly and the young subjects. Significant differences were found between the WCO for the elderly and young subjects in intervals I (p = 0.04) and V (p = 0.015). Fig. 4 shows the WPCO of the ABP and Delta [HbO2] signals of an elderly and a young subject. The WPCO of the ABP and Delta [HbO2] oscillations was significant in intervals I, II and IV in the elderly subjects (Fig. 4a) and in intervals III and VI in the young subjects (Fig. 4b). Fig. 5 shows a comparison of the mean values of the WPCO of the elderly and the young subjects. The phase coherence in interval IV showed significant difference (p = 0.028) between the two groups.

R. Cui et al. / Microvascular Research 93 (2014) 14–20

d

20

10 5 0

150 100 50

-5 -10

250 200

15

ABP(mmHg)

Δ [HbO2](µ mol/L)

a

17

0

100

200

300

400

500

600

700

800

0

900

Time(s)

0

100

200

300

400

500

600

700

800

900

Time(s)

b

e

c

f

Fig. 1. Typical time series of the simultaneous recordings of Δ[HbO2] signal and arterial blood pressure (ABP) signals from one subject; (a)Δ[HbO2] signal, (b) the average wavelet amplitude and (c) corresponding wavelet transform in the time-frequency plane; (d) ABP signal, (e) the average wavelet amplitude and (f) corresponding wavelet transform in the time-frequency plane. The vertical lines indicate the outer limits of the frequency intervals: I (0.4–2 Hz), II (0.15–0.4 Hz), III (0.05–0.15 Hz), IV (0.02–0.05 Hz), V (0.0095–0.02 Hz), and VI (0.005–0.0095 Hz).

Discussion In this study, the coherence between simultaneously measured ABP and Delta [HbO2] signals of healthy elderly and young subjects was assessed using wavelet-based coherence analysis. Our results show that for the elderly subjects, the Delta [HbO2] and ABP oscillations exhibited significant WCO in interval I (approximately 1 Hz) and significant WPCO in intervals I, II and IV. Remarkably, significant differences in WCO were found in intervals I and V of the elderly and the young subjects as well as in their WPCO in interval IV. WCO decomposes ABP and Delta [HbO2] signals into wavelet modes that are highly localized in frequency; this method also identifies the modes that are most linearly related (Rowley et al., 2007). A coherence that approaches unity in a specific frequency range suggests a linear relationship in this domain, whereas a coherence that approximates zero may indicate the absence of a relationship between signals (Bernjak et al., 2012). The presence of other modes in cerebral hemodynamics that are not due to systemic variables leads to low WCO (Rowley et al., 2007). In this study, ABP oscillations are reflected in oxyHb oscillations across a wide spectrum of oscillations (from intervals I to VI). This result is consistent with that of a previous study(Van Beek et al., 2012). Moreover, for the elderly subjects, WCO in interval I was

significantly higher than that in the young subjects, whereas that in interval V was significantly lower. For the elderly subjects, the significant WCO in interval I indicates the contribution of cardiac activity to the Delta [HbO2] and ABP oscillations. It is well known that the standard deviation of heart rate decreases significantly with age (Jensen-Urstad et al., 1997; Stein et al., 1997). Reduced variability of heart rate with aging might have contributed to greater coherence within the corresponding cardiac interval. CA is a high-pass filter that facilitates the transmission of BP changes to CBFV and filters gradual BP changes (Diehl et al., 1998; Zhang et al., 1998). The high coherence in interval I and low coherences in intervals II to VI further verify the high-pass filter function of CA in the healthy elderly people. The regulation of Delta [HbO2] is effective in the lowfrequency range of ABP fluctuations but not in the high-frequency range because of the time delay required to initiate cerebrovascular adaptations to the changes in perfusion pressure (Van Beek et al., 2008). Dynamic studies of CA quantify the rapid changes in CBF velocity (CBFV) in a major cerebral artery in relation to the rapid alterations in BP within the upper and lower limits (plateau phases) of sCA. Recent studies have shown that dynamic CA is impaired under several conditions, such as ischemic stroke (Eames et al., 2002) and carotid stenosis (White and Markus, 1997), which are highly prevalent in the elderly.

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R. Cui et al. / Microvascular Research 93 (2014) 14–20

a

a

0.9

Wavelet phase Coherence

Wavelet coherence

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.005 0.0095

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.005 0.0095

0.02

0.05

0.15

0.4

0.02

2

0.05

0.15

0.4

2

0.4

2

Frequency (Hz)

Frequency (Hz)

b 0.8

Wavelet coherence

0.7

0.9

Wavelet phase coherence

b

0.7 0.6 0.5 0.4 0.3

0.6 0.5 0.4 0.3 0.2 0.1

0.2 0 0.005 0.0095

0.1 0 0.005 0.0095

0.02

0.05

0.15

Frequency (Hz) 0.02

0.06

0.15

0.4

2

Frequency (Hz) Fig. 2. Wavelet coherence of arterial blood pressure (ABP) and Δ[HbO2] signals in the six frequency intervals in an elderly (a) and a young subject (b). The vertical lines indicate the outer limits of the frequency intervals: I (0.4–2 Hz), II (0.15–0.4 Hz), III (0.05–0.15 Hz), IV (0.02–0.05 Hz), V (0.0095–0.02 Hz), and VI (0.005–0.0095 Hz).

The cerebrovascular system is a part of the systemic circulation and is thus mediated by both central sympathetic activation and local myogenic or metabolic mechanisms (Priebe, 2000). The higher WCO in interval I indicated a stronger linear relationship between the cardiac activity of the Delta [HbO2] and ABP oscillations in elderly subjects than in young subjects. This result suggests that the time delay required to initiate cerebrovascular adaptations to the changes in perfusion pressure is shorter and thus the brain of elderly subjects is less sufficiently protected against the effects of rapid BP changes than those of young subjects. Although the functional and structural characteristics of blood vessels change with successive branching, a smooth single-celled layer of endothelial cells or of the endothelium that lines the inner surface of the vessels is generally found in the entire cardiovascular system

Fig. 3. Comparison of the wavelet coherence of the elderly and the young subjects in the six frequency intervals. Significant differences are marked with *p b 0.05 between the young and elderly subjects. Frequency intervals: I (0.4–2 Hz), II (0.15–0.4 Hz), III (0.05–0.15 Hz), IV (0.02–0.05 Hz), V (0.0095–0.02 Hz), VI (0.005–0.0095 Hz).

Fig. 4. Phase coherence of arterial blood pressure (ABP) and Δ[HbO2] signal in the six frequency intervals in an elderly (a) and a young subject (b). The dashed lines show the mean and two standard deviations above the mean for the coherence calculated from 100 surrogate signals per subject. The vertical lines indicate the outer limits of the frequency intervals: I (0.4–2 Hz), II (0.15–0.4 Hz), III (0.05–0.15 Hz), IV (0.02–0.05 Hz), V (0.0095–0.02 Hz), and VI (0.005–0.0095 Hz).

(Shiogai et al., 2010). Metabolic regulation involves control of according to the concentrations of metabolites (Shiogai et al., 2010). Such metabolic regulation is important role because it adjusts the blood flow to satisfy the oxygen requirement of cells (Humeau et al., 2004). The cerebral blood vessels have an inherent ability to keep the CBF fluctuation around certain value through myogenic, neurogenic, or metabolic mechanisms (Van Beek et al., 2008; Zhang et al., 2000). The low coherence in interval V suggests a reduced inherent ability to maintain a stable CBF during CA in elderly subjects. In this study, the wavelet transform with logarithmic frequency resolution was used to extract phase information from signals. WPCO was then used to identify oscillations with consistent phase differences. The WPCO indicates the consistency of the phase delay between two signals. In this study, WPCO allowed the identification of significant coherence even at low common power; this capability particularly

Fig. 5. Comparison of the phase coherence of the elderly and young subjects in the six frequency intervals. Frequency intervals: I (0.4–2 Hz), II (0.15–0.4 Hz), III (0.05–0.15 Hz), IV (0.02–0.05 Hz), V (0.0095–0.02 Hz), and VI (0.005–0.0095 Hz).

R. Cui et al. / Microvascular Research 93 (2014) 14–20

important when where low-frequency components significantly contribute cardiovascular signals (Bernjak et al., 2012). The ABP and Delta [HbO2] oscillations exhibited significant WPCO in intervals I, II and IV for the elderly subjects but not for the young subjects. Intervals I and II reflect the effects of cardiac and respiratory activities, respectively. The cerebrovascular system is part of the systemic circulation. Thus, significant WPCO in these intervals clearly indicates the existence of temporally constant interference between the ABP and Delta [HbO2] oscillations. Interestingly, the WPCO in interval IV was significantly higher level in the elderly subjects than in the young subjects. In generally, CA is caused by the cooperative action of both sympathetically mediated and local myogenic or metabolic mechanisms (Priebe, 2000). In the present study, the ABP–Delta [HbO2] coupling relationship in interval IV was weaker in the elderly subjects than in the young subjects at rest. This result suggests an altered CA status with aging. When using the WPCO measure to detect a causal relationship between signals, the null hypothesis that the coherence value is due to a chance relationship preserved over a limited number of correlated measurements must be considered (Sheppard et al., 2012). In finitelength signals, low-frequency components are represented by fewer periods than high-frequency components. Consequently, less variation in the phase difference occurs at low-frequencies and result in artificially increased phase coherence. Significant WPCO was tested during the evaluation of the coherence of two oscillatory time series that may have variable amplitude and frequency. The test was performed by generating AAFT surrogate signals via shuffling of the phases of the original time series to create a new time series with the same means, variances, and autocorrelation functions (and therefore the same power spectra) as the original sequences but without any phase relations. When the coherence value is equal to the standard deviations above the mean surrogate coherence, a causal relationship possibly exists between the signals regardless of their spectral similarities or differences (Berrnjak et al., 2012). The raw coherence values are not higher. Particularly, the phase coherence of cardiac component did not exhibit significance as indicated by the test of AAFT surrogate signals. This may be attributed to the big variability in the system variables. The coupling of systemic variables (e.g. ABP) to cerebral hemodynamic variables (e.g. HbO2) is due to the cooperative action of both sympathetically mediated and local myogenic mechanisms (Rowley et al., 2007). The inherent problem is that both systems exhibit considerable variability and this might result in low coherence values. In addition, we mainly report the significant differences in coherences between the two groups. Methodological considerations NIR light must first pass through the superficial tissue layers (scalp and skull) before reaching the cortex. Therefore, these superficial layers may provide noise as well as nonspecific hemodynamic variations and this would contaminate the measured signal. The interferences from superficial layers are often referred to as “global interference” (Medvedev et al., 2008; Zhang et al., 2007). As several authors have pointed out, depth-resolved measurements can be effectively achieved using detectors at short (~ 1 cm) and long (N3 cm) distances from the source (Medvedev et al., 2008; Strangman., 2003; Tachtsidis et al., 2008). In the present study, we used one light source and two detectors placed at 30 and 40 mm from the source to separate extracerebral (scalp and skull) and brain hemodynamic signals. For such configurations, the differences in the optical density (OD) as detected by the two detectors were mainly attributed to the tissue (cortex) absorption. In addition, as spontaneous oscillations are posture-dependent (Tachtsidis et al., 2004), NIRS and ABP measurements were collected in their comfortable sitting posture. A limitation of current study was the recordings period. The recordings lasted 900 s and oscillations with frequency below 0.0095 Hz

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would be represented with fewer than 5 cycles with frequency of 0.005 Hz. This may result in an unreliable detection of both the power and the amplitude within the interval. Recordings are usually recommended to last ten times the period of the lower frequency boundary of the investigated component (Bracic et al., 2000). Summary The coherence between simultaneously measured Delta [HbO2] and ABP signals in elderly and young subjects was assessed using waveletbased coherence analysis. Our results show that for the elderly subjects, the Delta [HbO2] and ABP oscillations exhibited significant WCO in interval I (approximately 1 Hz) and significant WPCO in intervals I, II and IV. The WCO in intervals I and V, and the WPCO in interval IV showed significant differences between groups (elderly and young subjects). The differences in WCO and WPCO between the elderly and the young subjects indicate an aging-related change in CA. The conclusions in the low frequency intervals — lower than 0.1 Hz need to be verified using longer recordings. This study provides new insight into the dynamics of Delta [HbO2] and ABP oscillations and may be useful in identifying risk for dynamic CA. The time delay effect can be obtained by calculating the phase shift between the two signals (Kvandal et al., 2013). Further study will focus on the time delay effect in young and elderly subjects. Acknowledgment This project was supported by the National Natural Science Foundation of China (Grant Nos. 31371002, 11272273, 81071223). References Bandrivskyy, A., Bernjak, A., Mcclintock, P., Stefanovska, A., 2004. Wavelet phase coherence analysis: application to skin temperature and blood flow cardiovascular engineering. Int. J. 4 (1), 89–93. Bernjak, A., Stefanovska, A., McClintock, P.V.E., Owen-Lynch, P.J., Clarkson, P.B.M., 2012. Coherence between fluctuations in blood flow and oxygen saturation fluct. Noise Lett. 11 (1) (1240013–12). Bracic, L.M., Stefanovska, A., Stajer, D., Urbancic-Rovan, V., 2000. Spectral components of heart rate variability determined by wavelet analysis. Physiol. Meas. 21, 441–457. Cheng, R., Shang, Y., Hayes Jr., D., Saha, S.P., Yu, G., 2012. Noninvasive optical evaluation of spontaneous low frequency oscillations in cerebral hemodynamics. NeuroImage 62, 1445–1454. Diehl, R.R., Linden, D., Lucke, D., Berlit, P., 1998. Spontaneous blood pressure oscillations and cerebral autoregulation. Clin. Auton. Res. 8, 7–12. Eames, P.J., Blake, M.J., Dawson, S.L., Panerai, R.B., Potter, J.F., 2002. Dynamic cerebral autoregulation and beat to beat blood pressure control are impaired in acute ischaemic stroke. J. Neurol. Neurosurg. Psychiatry 72, 467–472. Humeau, A., Koïtka, A., Abraham, P., Saumet, J.L., L'Huillier, J.P., 2004. Time-frequency analysis of laser Doppler flowmetry signals recorded in response to a progressive pressure applied locally on anaesthetized healthy rats. Phys. Med. Biol. 49 (5), 843–857. Jensen-Urstad, K., Storck, N., Bouvier, F., Ericson, M., Lindblad, L.E., Jensen-Urstad, M., 1997. Heart rate variability in healthy subjects is related to age and gender. Acta Physiol. Scand. 160 (3), 235–241. Jones, W.J., Williams, L.S., Bruno, A., Biller, J., 2003. Hypertension and cerebrovascular disease. Sem. Cerebrovasc. Dis. Stroke 3 (3), 144–154. Kvandal, P., Landsverk, S.A., Bernjak, A., Stefanovska, A., Kvernmo, H.D., Kirkebøen, K.A., 2006. Low frequency oscillations of the laser Doppler perfusion signal in human skin. Microvasc. Res. 72 (3), 120–127. Kvandal, P., Sheppard, L., Landsverk, S.A., Stefanovska, A., Kirkeboen, K.A., 2013. Impaired cerebrovascular reactivity after acute traumatic brain injury can be detected by wavelet phase coherence analysis of the intracranial and arterial blood pressure signals. J. Clin. Monit. Comput. 27 (4), 375–383. Li, Z.Y., Wang, Y.H., Li, Y., Wang, Y., Li, J.P., Zhang, L.L., 2010. Wavelet analysis of cerebral oxygenation signal measured by near-infrared spectroscopy in subjects with cerebral infarction. Microvasc. Res. 80, 142–147. Li, Z.Y., Zhang, M., Xin, Q., Chen, G.Q., Liu, F.F., Li, J.P., 2012. Spectral analysis of nearinfrared spectroscopy signals measured from prefrontal lobe in subjects at risk for stroke. Med. Phys. 39 (4) (2179–7). Li, Z.Y., Zhang, M., Xin, Q., Luo, S., Cui, R., Lu, L., 2013. Age-related changes in spontaneous oscillations assessed by wavelet transform of cerebral oxygenation and arterial blood pressure signals. J. Cereb. Blood Flow Metab. 33 (5), 692–699. Matteis, M., Troisi, E., Monaldo, B.C., Caltagirone, C., Silvestrini, M., 1998. Age and sex differences in cerebral hemodynamics: a transcranial Doppler study. Stroke 29, 963–967.

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