1.

Introduction

The study of skin microcirculation is receiving increasing interest as recent studies have suggested that it may mirror other systemic vascular conditions.¹ Two of the main technologies that can be used to study microcirculation are laser Doppler flowmetry (LDF) and photoplethysmography (PPG).² The frequency characteristics of these physiological signals can be investigated using standard Fourier-based joint time-frequency analysis methods. For the analysis of signals with dynamic and irregular changes, an approach based on wavelet analysis (WA)³ is more appropriate; this can provide a higher time resolution giving a smoother frequency spectrum (Fig. 1) and reducing artifacts.⁴ Furthermore, WA does not require the signals to be stationary and it is, therefore, more widely applicable.

Fig. 1

Comparison of the frequency spectrum as calculated using Fourier analysis and wavelet analysis (WA) for (a) PPG and (b) LDF signals. Notice that the spectrum produced by WA is much smoother than the one obtained with Fourier analysis. Key: a.u., arbitrary units; AFU, arbitrary flux units.

The use of WA has been investigated in various biomedical applications including for the analysis of the electrocardiogram.⁵ Other groups have also extensively applied WA to LDF signals, demonstrating that the study of LDF low-frequency oscillations in different frequency bands can provide valuable information relative to cardiac, respiratory, myogenic, neurogenic, and endothelial activities. For example, Rossi et al.⁶ demonstrated that LDF blood flow low-frequency oscillations were increased in patients with hypertension compared with normal controls and that this difference disappeared after the patients followed an average of 8-weeks hypertensive treatment. A study by Ažman-Juvan et al.⁷ showed a reduction of LDF blood flow oscillatory components in patients with acute myocardial infarction as compared with healthy controls. They also showed that this reduction was more apparent in patients without reperfusion. General anesthesia was shown to reduce the amplitude of the frequency bands representative of sympathetic, myogenic, and endothelial activities.⁸ The content of these frequency bands has also been demonstrated to change after physical exercise⁹ and, in particular, the amplitude of the endothelial activity band was found to be increased in athletes as compared with less trained individuals.¹⁰ Another recent study by Li et al.¹¹ has applied a similar method for studying prefrontal near-infrared spectroscopy signals. However, this approach has not been investigated in finger PPG signals yet.

Time-domain analysis of PPG signals has shown promising results in a variety of medical applications including detection of peripheral arterial disease,¹² the assessment of autonomic function in primary biliary cirrhosis¹³ and chronic fatigue syndrome,¹⁴ arterial aging,^15,16 and the assessment of cardiovascular functions in systemic sclerosis.¹⁷ Our group has also demonstrated the possibility to use WA to analyze PPG signals for the quantification of cardiovascular changes in response to a deep inspiratory gasp.¹⁸ PPG can be significantly less expensive than LDF and the technology is less sensitive to movement artifacts. Furthermore, PPG measurement systems can be miniaturized and made highly portable. Therefore, it is of interest to explore whether or not PPG low-frequency oscillations can provide useful clinical information similar to LDFs.

The aim of this study was to characterize the correlation between PPG and LDF signals in the five physiological low-frequency bands in a group of healthy adult subjects. The correlation was quantified using two different possible approaches: (1) wavelet correlation analysis, and (2) correlation analysis of the amplitude of the integral wavelet spectrum (IWS).

2.

Methods

2.3.

Measurement Procedure

We utilized one of our standard clinical microvascular measurement protocols. Measurements were made in a microvascular measurement facility at an ambient room temperature of 23.5 $(\pm 0.5)°\mathrm{C}$ with relative humidity between 30% and 50%. Subjects rested in a supine position and acclimatized in the measurement environment for at least 10 min prior to their data collection. The analog outputs of the PPG and LDF systems were connected to a multichannel analog-to-digital converter (ADC); this allowed for the PPG and LDF signals to be recorded at the same time. The ADC captured each channel to a computer at a sampling rate of 2 kHz for 20 min with the subject in the supine position. Examples of LDF and PPG recordings are shown in Fig. 2. The analog output from the PPG system was left in arbitrary units (a.u.). The output voltage of the LDF system was multiplied by 100 in order to convert the signals to arbitrary flux units (AFU), according to the instructions of the manufacturer.

Fig. 2

Example signals: (a) full length 20-min PPG recording, and (b) 10-s excerpt PPG recording; (c) full-length 20-min LDF recording, and (d) 10-s excerpt LDF recording. All four plots are from the same recording of the same subject. Key: a.u., arbitrary units; AFU, arbitrary flux units.

2.4.

Wavelet Analysis

The wavelet transform $W_x(\nu ,\tau )$ of a signal $x(t)$ is defined in terms of an appropriate mother wavelet $\psi (t)$ as given in Eq. (1):

Eq. (1)

$$W_x(\nu ,\tau )=\sqrt{\nu }{\int }_{-\infty }^{\infty }x(t)\psi *[\nu (t-\tau )]\mathrm{d}t,$$

where $t$ is the time; $\tau$ is the time shift of the wavelet which can take any real value; $\nu$ is the oscillation frequency which can be any positive real number; and the symbol * indicates the operator of complex conjugation. The mother wavelet utilized in this study was the complex Morlet wavelet²⁰ [Eq. (2)]:

Eq. (2)

$$\psi (t)=e^{2\pi it}{e}^{-t^2/2{\sigma }^2}.$$

The IWS was calculated by integrating the squared absolute value of the wavelet transform over a period $T$, as described by Eq. (3):

Eq. (3)

$$M(\nu )=\frac{1}{T}{\int }_0^T{|W_x(\nu ,\tau )|}^2\mathrm{d}\tau .$$

The correlation $C_{xy}(\nu )$ between two signals $x(t)$ and $y(t)$ was also defined in terms of their wavelet transforms using Eq. (4).²¹ This approach allowed the correlation between the two signals to be estimated separately for each frequency $\nu$:

Eq. (4)

$$C_{xy}(\nu )=\frac{{\int }_0^T{W}_x(\nu ,\tau )W_y^{*}(\nu ,\tau )\mathrm{d}\tau }{\sqrt{{\int }_0^T{|W_x(\nu ,\tau )|}^2\mathrm{d}\tau {\int }_0^T{|W_y(\nu ,\tau )|}^2\mathrm{d}\tau }}\mathrm{.}$$

The absolute value of $C_{xy}(\nu )$ is limited to the interval [0,1] and represents the strength of the correlation of the oscillations at frequency $\nu$. The decay parameter $\sigma$ plays an important role in the calculation of the wavelet correlation function (Fig. 3). Lower values of $\sigma$ make it possible to obtain a smoother waveform with a sensible quantification of the correlation at the different frequencies. When the value of $\sigma$ increases, the absolute value of $C_{xy}(\nu )$ becomes less and less smooth and rapid changes start to appear, which are more likely to be caused by computational artifacts rather than a real effect. In the limited case of $\sigma =\infty$, the wavelet correlation is equivalent to the function that would be obtained using Fourier analysis and the modulus of $C_{xy}(\nu )$ becomes a constant equal to 1 for any $\nu$, without providing any significant information. In this study, we set the parameter $\sigma$ to the value 1 for wavelet correlation analysis.

Fig. 3

Wavelet correlation $C_{xy}(\nu )$ between PPG and LDF signals. The results are shown for different values of the parameter $\sigma$ of the Morlet mother wavelet. The value $\sigma =1$ (used in our study) gave the smoothest correlation; the value $\sigma =\infty$ gives a constant correlation of 1, equating to the case when Fourier correlation is used.

2.4.1.

Definition of low-frequency physiological bands

The low-frequency part of the wavelet spectrum was divided into five bands attributed to different physiological aspects: band I (0.6 to 2 Hz) representing cardiac activity; band II (0.145 to 0.6 Hz) representing respiratory activity; band III (0.052 to 0.145 Hz) representing myogenic activity; band IV (0.021 to 0.052 Hz) representing neurogenic activity; and band V (0.0095 to 0.021 Hz) representing endothelial activity.⁷

2.4.2.

Wavelet correlation analysis

The wavelet correlation function [Eq. (4)] was utilized to quantify the similarity between right and left body sites separately for PPG and LDF signals and between PPG and LDF signals at the same body site separately (and also with right and left sides averaged) in the different frequency bands. Higher values of the wavelet correlation function indicate higher synchronicity between the two signals at a given frequency, independent from their possible difference in amplitude.

2.4.3.

Integral wavelet spectrum

The amplitude of the IWS [Eq. (3)] was quantified for both PPG and LDF signals as the median value in each physiological frequency band, separately for each body site and also for the right-left average.

3.

Results

3.1.

Wavelet Correlation Analysis

The median IWS across all 12 subjects is shown in Fig. 4. Figure 5 shows the modulus of the wavelet correlation function across the different low-frequency bands. The median wavelet correlation between PPG and LDF signals (when right and left hands were averaged) was 0.45 for the cardiac activity, 0.49 for the respiratory activity, 0.86 for the myogenic activity, 0.91 for the neurogenic activity, and 0.91 for the endothelial activity. Right-to-left correlation of the PPG and LDF signals and single-site PPG-LDF wavelet correlations are also given in Table 1.

Fig. 4

Median integral wavelet spectrum (IWS) across all 12 subjects for both PPG and LDF signals. The IWS for LDF signals has been divided by a factor ${10}^6$ in order to report it in a scale comparable with PPG. Subplot (a) is for the right hand; (b) is for the left hand; and (c) is for right and left hands averaged. Key: a.u., arbitrary units; AFU, arbitrary flux units.

Fig. 5

Box-whisker plot for the absolute value of wavelet correlation for (a) bilateral PPG, (b) bilateral LDF, (c) PPG-LDF at the right hand, and (d) PPG-LDF at the left hand. Each box represents the central 50% of the data; whiskers extend to the entire range of the data. The frequency ranges for the five physiological bands are also highlighted: endothelial (E), neurogenic (N), myogenic (M), respiratory (R), and cardiac (C).

Table 1

Values of wavelet correlation between pairs of photoplethysmography (PPG) and laser Doppler flowmetry (LDF) signals for the five physiological frequency bands. The results are reported as median (first quartile to third quartile) across the 12 subjects. PPGr is the PPG signal taken from the right hand; PPGl is the PPG signal taken from the left hand; LDFr is the LDF signal taken from the right hand; LDFl is the LDF signal taken from the left hand; PPGavg is the average PPG signal from the right and left hands; LDFavg is the average LDF signal from the right and left hands.

	Cardiac	Respiratory	Myogenic	Neurogenic	Endothelial
${\mathrm{PPG}}_{\mathrm{r}}\text{-}{\mathrm{PPG}}_{\mathrm{l}}$	0.98 (0.95 to 0.99)	0.80 (0.71 to 0.87)	0.87 (0.80 to 0.92)	0.94 (0.90 to 0.97)	0.95 (0.89 to 0.98)
${\mathrm{LDF}}_{\mathrm{r}}\text{-}{\mathrm{LDF}}_{\mathrm{l}}$	0.71 (0.37 to 0.85)	0.60 (0.38 to 0.74)	0.89 (0.82 to 0.93)	0.93 (0.89 to 0.96)	0.93 (0.89 to 0.97)
${\mathrm{PPG}}_{\mathrm{r}}\text{-}{\mathrm{LDF}}_{\mathrm{r}}$	0.45 (0.28 to 0.67)	0.47 (0.33 to 0.63)	0.85 (0.65 to 0.85)	0.86 (0.74 to 0.93)	0.93 (0.89 to 0.96)
${\mathrm{PPG}}_{\mathrm{l}}\text{-}{\mathrm{LDF}}_{\mathrm{l}}$	0.43 (0.24 to 0.68)	0.45 (0.27 to 0.61)	0.75 (0.84 to 0.70)	0.91 (0.87 to 0.94)	0.87 (0.74 to 0.94)
${\mathrm{PPG}}_{\mathrm{avg}}\text{-}{\mathrm{LDF}}_{\mathrm{avg}}$	0.45 (0.26 to 0.70)	0.49 (0.29 to 0.67)	0.86 (0.78 to 0.92)	0.91 (0.85 to 0.95)	0.91 (0.81 to 0.95)

4.

Discussion

In this pilot study, we have assessed the correlation between PPG and LDF signals in the low-frequency range using wavelet correlation analysis and Spearman correlation analysis of the IWS amplitude. Measurements were performed in a temperature- and humidity-controlled facility and following a rigorous preparation protocol, which standardized the measurement conditions across subjects. Correlations and IWS amplitudes were characterized in a group of healthy adult males and this has provided reference normative values for future studies. The low-frequency range 0.005 to 2 Hz was subdivided into five bands which are representative of different physiological activities, namely cardiac activity (band I, 0.6 to 2 Hz), respiratory activity (band II, 0.145 to 0.6 Hz), myogenic activity (band III, 0.052 to 0.145 Hz), neurogenic activity (band IV, 0.021 to 0.052 Hz), and endothelial activity (band V, 0.0095 to 0.021 Hz).⁷ Wavelet correlation [Eq. (4)] was utilized to investigate the correlation of entire waveforms in the various bands. Spearman correlation analysis was utilized to assess the correlation of the amplitude of the IWS in the different bands.

Previous studies showed the possible clinical value of the information contained in these five low-frequency bands using WA of LDF forearm signals.^6–10 Other studies utilized an approach based on traditional Fourier analysis²² and also showed promising results. The approach based on WA, however, is more widely applicable—as it does not require the signals to be stationary, it reduces the effect of possible computational artifacts, and it is, in general, less sensitive to noise. Therefore, in this work we preferred to utilize WA. Based on our previous work,¹⁸ we used the complex Morlet mother wavelet [Eq. (2)] to perform the wavelet transform. The parameter $\sigma$ was set to the value of 1 to perform wavelet correlation analysis. This setting allowed minimizing the effect of computational artifacts on the wavelet correlation function.

Wavelet correlation analysis demonstrated high correlation between right and left sites for PPG signals in all five frequency bands. For LDF signals, the right-left correlation was also high in band III (myogenic activity), band IV (neurogenic activity), and band V (endothelial activity). However, it was lower for the cardiac and respiratory activity bands (Table 1) and this may be attributed in part to a higher sensitivity to noise and movement artifacts of LDF at these frequencies. The wavelet correlation between PPG and LDF signals was high in bands III, IV, and V at both the right and left body sites (Table 1); however, this correlation decreased to below 0.5 in bands I and II and this again was possibly because of the higher sensitivity of LDF to noise in these bands.

Spearman correlation analysis for the right-left averaged spectral amplitudes showed a statistically significant correlation ($p<0.05$) between PPG and LDF in the cardiac ($\rho =0.64$) and endothelial ($\rho =0.62$) bands. The correlation in the myogenic and neurogenic bands was medium ($\rho =0.55$ and 0.50, respectively), but these did not reach statistical significance in this case. The correlation in the respiratory band was low ($\rho =0.26$).

The results overall showed good correlation between PPG and LDF low-frequency oscillations and IWS amplitudes, especially in the three lowest bands related to myogenic, neurogenic, and endothelial activities. Interestingly, these findings are consistent with other results in the literature regarding the wavelet correlation between skin temperature and LDF which also reported good correlation in the myogenic, neurogenic, and endothelial frequency bands, but poor correlation for the other two higher frequency bands.²³ In this study, we have also characterized the amplitude of the IWS of PPG signals in the five low-frequency physiological bands (Table 2) and this has provided reference normative values that future studies can use for comparison with different healthy populations or different disease groups. For example, a recent study by Li et al.¹¹ utilized wavelet coherence to study the right-left relationship of near-infrared spectroscopy signals acquired from the forehead. This study reported decreased right-left wavelet coherence in the band attributed to myogenic activity in a group of elderly subjects with hypertension as compared with an age-matched group of elderly normotensive subjects.

Our research group has a specific interest in endothelial function and its assessment, and it is encouraging that the frequency analysis for PPG and LDF gives similar information in the published spectral ranges, ultimately enabling lower-cost PPG to be exploited for this purpose.

5.

Conclusions

This pilot study has shown good correlation between the low-frequency oscillations of PPG and LDF signals at the finger, especially in the frequency bands corresponding to myogenic, neurogenic, and endothelial activities. The amplitude of the PPG spectrum in each low-frequency band has also been quantified in order to provide reference normative values.