1 Introduction

Heart rate variability (HRV) refers to the variation of beat-to-beat interval, and it provides a non-invasive assessment of the balance between the cardiac sympathetic nervous system and the parasympathetic nervous system. HRV metrics has become a popular tool for diagnosis and prevention of some cardiovascular diseases such as sudden cardiac death and arrhythmia [1]. RR intervals with varying amplitudes are presented to enable the estimation of the respiratory rate and the temporal pattern of respiration [2]. Hence, electrocardiogram (ECG)-derived respiration in the context of HRV studies has been described in the literature [3, 4]. HRV analysis and extraction of a respiratory signal from the ECG are important way to assess the heartbeat. In addition, the subtle change of vessel pulse periods is denoted as pulse rate variability (PRV). Photoplethysmography (PPG) technology has developed to include the use of small, wearable, pulse rate sensors. PPG is predominantly carried out with finger or ear lobe sensors, and occasionally from the toe or nose to noninvasively monitor the arterial oxygen saturation and pulse rates. Therefore, wearable PPG sensors have become a very popular way to measure heart rate (HR) in clinical medical practice and research proposals because of its convenience [5]. Because measuring PPG is more convenient than ECG, PPG is proposed as an alternative source, a surrogate of ECG for HRV analysis [6, 7] or respiratory rate monitoring [8].

Some researchers [9,10,11,12] have correlated PRV and HRV and confirmed PRV as a good surrogate of HRV, which has been debated for a decade because respiration could be a confounding factor in HRV evaluation. Respiratory sinus arrhythmia (RSA) is reflected in high-frequency HR oscillations (usually > 0.15 Hz in the power spectrum of R–R intervals) [13], which refers to cyclical fluctuations in HR that are coincident with the respiratory cycle, and RSA increases during inhalation and decreases during exhalation. Hence, RSA is known to have important regulatory functions, and it is the simplest and most obvious phenotype of HRV. Respiration should affect both HRV and PRV because the volume and rate of respiration could affect HR. Some studies [14,15,16,17] have focused on pulse wave research, which seeks to address whether or not the ECG-based method determining HRV can be replaced by a technique associated with pulse wave measurement. These studies suggested that respiration, a confounding factor for HRV evaluation, should be considered during consciously controlled breathing. However, little is known about the direct effect of respiration on HRV, and specifically on actual differences between PRV and HRV. In addition, there is not enough evidence to evaluate the coherence between the measurements.

Changes occur at R–R intervals, which may be affected by breathing, physical exercise, mental stress, hemodynamic alterations, or metabolic changes. Observing the change in HR during breathing manipulation (i.e. RSA) is the most direct way to present actual differences between PRV and HRV because respiration frequency and depth strongly determine fluctuation amplitude of RSA [18]. As described above, the variance of RSA is a way to understand the coherence between heart rate variability and respiration derived from ECG and PPG. Hence, a one-lead ECG signal and four channel PPG signals were used to measure RSA during controlled breathing in this study. For instance, the ECG signal was determined from Lead II, and four limbs were used to determine the PPG signals. All subjects enrolled in this study performed both breathing rate and tidal volume manipulation in order to examine the effects of breathing variations on the parameters derived from HR and PR, and HRV and PRV. Thus, the aims of this study were as follows: (1) to examine whether or not the PR and PRV of either limb can be a surrogate of the HR and HRV in healthy subjects, (2) to examine whether or not the impact of HRV is equivalent to PRV during controlled breathing, and (3) to investigate cardiopulmonary coupling and its relationship with HRV during the controlled breathing tasks.

The outline of the paper was organized as follows. The procedure of gathering the signals, analysis, and their parameters were described in Sect. 2. Although HRV analysis was divided into time domain methods, frequency domain methods, time–frequency domain methods, and nonlinear methods, the short-term (~ 5 min) frequency-domain methods were not suitable for different physiological or pathological states of cardiovascular system. Hence, the most common measurements in the time domain, such as the mean of RR interval for normal beats and the standard deviation of all normal RR interval (SDNN), were used to investigate the coherence between HRV and PRV in this paper. A recurrence-plot-based analysis [19] was also employed to effectively assess the cardiopulmonary coupling of ultra-short-term HRV signals (about 1 min) during different breathing control of the subjects. The results of the comparisons were given in Sect. 3 and some concluding remarks were presented in Sect. 4.

2 Materials and Methods

2.1 Subjects and Data Acquisition

To provide a comparison between HRV derived from ECG and PRV derived from PPG, 30 healthy subjects were enrolled in this study, including 10 seniors and 20 younger individuals. Subjects, who had major cardiopulmonary disease or who were receiving regular treatments for diabetes mellitus, hypertension, renal or liver disease, were excluded from the study. The age rang of the younger group was 20–37 years old (mean age = 24 years), and the senior group was 50–67 years old (mean age = 60 years). The ratio of male and female subjects was 1:1 in both groups. The study was approved by the Institutional Review Board of Chang Gung Memorial Hospital, Taiwan (101 – 4896B). Written informed consent was obtained from all subjects enrolled in this study.

Each subject sat in a position with a comfortable posture during the experiment. Simultaneous PPG, ECG and respiratory signals were recorded using a polysomnography system (Alice 6 LDx, Philips) with a sampling frequency of 1.25 kHz and an A/D converter (12-bit resolution). The ECG signal was determined from Lead II, the breath signal was detected via chest wall motion, and four limbs were used to determine the PPG signals, including the left index finger (LF), right index finger (RF), left big toe (LT) and right big toe (RT). Each signal was resampled to 250 Hz then to be analyzed by a personal computer. On account of a significant difference between HRV and PRV at higher ambient temperatures [20], all recordings were performed in a bright and quiet room with a constant temperature of 24–25 °C.

2.2 Experimental Protocol

In order to consider possible breathing circumstances, two different breathing circumstances were defined: spontaneous breathing and controlled breathing (Phase I and Phase II). The experimental protocol included five tasks designed to assess breathing, including Resting I, Phase I, Resting II, Phase II, and Resting III (Fig. 1a). Each breathing task had lasted for 5 min. Subjects breathed freely in each resting task, included Resting I, II, and III. In each controlled breathing task, such as Phase I and II, subjects followed the procedure based on the study designs.

Fig. 1
figure 1

a Schematic representation of experimental protocol of breathing. b Typical respiratory patterns of controlled breathing; Phase I (top) and Phase II (bottom)

According to previous studies [21, 22], breathing frequency was defined as faster breathers (> 15 breaths per minute) and slower breathers (< 15 breaths per minute). Each controlled breathing state was performed at 1 min interval. In the breathing control task (see Fig. 1b), we defined five types of controlled breathings, which were natural paced breathing (NPB), rapid and deep breathing (RDB), slow and deep breathing (SDB), rapid and shallow breathing (RSB), and slow and shallow breathing (SSB). In brief, subjects were asked to inhale and exhale during NPB at 15 breaths/min intervals, and inhale and exhale deeply or shallowly at 5 and 30 breaths/min intervals in the controlled breathing tasks. An example of the polysomnography signals of each measurement during slow and deep breathing are presented in Fig. 2a.

Fig. 2
figure 2

a A representative example of polysomnography signals using thoracoabdominal belts, PPG and ECG (from top to bottom) during deep and slow breathing. b Illustrative example of ECG and PPG waveforms. Peak detection from ECG and PPG waveform and definition of the R-R interval (RRI) and peak-to-peak interval (PPI). RRI was calculated as the time interval of two successive R peaks of the ECG signal. The PPI of the upper peaks was calculated as the time interval of two successive peak of the first derivative of the PPG signal

2.3 Parameters for HRV and PRV Analysis

HRV parameters are usually derived from R peak detection and generation of the R–R interval signals.

The R–R intervals (RRI) are derived from the R peak of ECG signals. The similar procedure can be applied to PPG signals and their second derivatives to obtain P–P intervals from their upper P peaks.

Representative features of ECG and PPG waves of a representative subject over a short-time interval used in HRV or PRV analysis are shown in Fig. 2b. The length of ECG signal was represented by L, and the positions of R peak were determined by R peak detection. It was found that PPG peaks were in relation to the R peaks. A R peak detection algorithm utilizes double different methods [23] as the following equation:

$${\text{d}}_{1} \left( {\text{i}} \right) = {\text{x}}_{\text{ecg}} \left( {\text{i}} \right) - {\text{x}}_{\text{ecg}} \left( {{\text{i}} - 1} \right) , {\text{i}} = 1,2, \ldots ,{\text{L}} - 1$$
$${\text{d}}_{2} \left( {\text{j}} \right) = \left[ {{\text{d}}_{1} \left( {\text{j}} \right) - {\text{d}}_{1} \left( {{\text{j}} - 1} \right)} \right]^{2} , {\text{j}} = 1,2, \ldots ,{\text{L}} - 2$$

where \({\text{x}}_{\text{ecg}} \left( {\text{n}} \right)\) is the input signal of ECG, \({\text{d}}_{1} \left( {\text{i}} \right)\) is the first difference, and \({\text{d}}_{2} \left( {\text{j}} \right)\) is the squared double difference of the ECG signal. Then the \({\text{d}}_{2} \left( {\text{j}} \right)\) signal is filtered by bandpass filter. The dynamic threshold was determined by 80% of the peak of \({\text{d}}_{2} \left( {\text{j}} \right)\) after being filtered. In the sequence \({\text{d}}_{2} \left( {\text{j}} \right)\), the peaks of wave greater than the threshold value were selected as the windows. In the sequence \({\text{x}}_{\text{ecg}} \left( {\text{n}} \right)\), the maxima peaks were selected within processed windows as the R-peaks. The peaks of PPG were determined by the positions between two R peaks on the ECG. RRI and PPI were defined as the follows:

$${\text{RRI}}\left( {\text{k}} \right) = {\text{R}}\left( {\text{k}} \right) - {\text{R}}\left( {{\text{k}} - 1} \right)$$
$${\text{PPI}}\left( {\text{k}} \right) = {\text{P}}\left( {\text{k}} \right) - {\text{P}}\left( {{\text{k}} - 1} \right) , {\text{k}} = 1,2, \ldots ,{\text{N}}$$

Where \({\text{R}}\left( {\text{i}} \right)\) is the R peak and \({\text{P}}\left( {\text{i}} \right)\) is the peak of PPG. To ensure the accuracy of the detection results, all data were double-checked visually to make sure that there were no missing waves or false detection. To identify differences between HRV and PRV based on the breathing frequency and volume, some of the important time domain HRV parameters were calculated. Weinschenk et al. (2016) demonstrated some parameters via a 5-min short-term HRV with moderation to good agreements between PPG and ECG derived measurements during 1-min deep breathing tasks [24]. Therefore, based on their recommendations, appropriate parameters were used for time-domain HRV parameters. In this study, standard deviation of normal-to-normal intervals (SDNN) and standard deviation of all peak-to-peak intervals (SDPP) were the parameters to be applied.

$${\text{SDNN}} = \sqrt {\frac{1}{\text{N}}\sum\nolimits_{{{\text{i}} = 1}}^{\text{N}} {{\text{RRI(i)}} - \overline{\text{RRI}} } }$$
$${\text{SDPP}} = \sqrt {\frac{1}{\text{N}}\sum\nolimits_{{{\text{i}} = 1}}^{\text{N}} {{\text{PPI(i)}} - \overline{\text{PPI}} } }$$

Comparisons of individual HRV and PRV were presented as the rectangular window with 5 min length.

After SDNN and SDPP were determined, the window would shift by 30 s. Each window would yield a SDNN derived from RRI and SDPP derived from PPI.

2.4 Coherence for Cardiopulmonary Coupling

ECG-based cardiopulmonary coupling (CPC) is a novel HRV measure for sleep quality [25, 26]. In order to find out the coherence between ECG-derived and PPG-derived parameters [27], a recurrence plot was used to calculate the percentage ratio between the number of recurrence points and the total number of them [28]. Figure 3 shows an example of the recurrence plot. When given two time series of x(i) and y(i), a recurrence plot is a representation of the normalized distance between the points (x(i), y(i)) and (x(j), y(j)), plotted in the time-to-time domain [19, 20].

Fig. 3
figure 3

Example of recurrence plot. Two continuous time series a, x(i) = sin(i) is sine wave and y(i) = sin(i + t) is sine wave with time delay. The normalized distance b was computed based on two continuous time series. Recurrence plot c was obtained by a threshold value setting form normalized distance map

The normalized distance D(i, j) was calculated as follows:

$$D_{(i,j)} = \sqrt {\frac{{\left[ {x\left( i \right) - x\left( j \right)} \right]^{2} }}{var(x)} + \frac{{\left[ {y\left( i \right) - y\left( j \right)} \right]^{2} }}{var(y)} }$$

Where the time series x(i) and y(i) indicate two bi-dimensional cases; var(∙) indicates the time series variance. If the two points are sufficiently close to one another, i.e. the distance D(i, j) is lower than a fixed cut-off value, a dot is plotted in (i, j). A recurrent point in (i, j) means that the interactions between the signals in the instant i is almost the same as in the instant j (i.e. the interaction is recurring). If D(i, j) is higher than the threshold [29], (i, j) is not a recurrent point. A recurrent point indicates an isolated recurrence of an amplitude relationship between the signals. Percentage recurrence was defined as the percentage ratio between the number of recurrent points and the total number of all possible points. It quantified the number of time instants characterized by a recurrence in the signal interactions; the more frequent the signal dynamics, the higher the value of percent recurrence. The self-recurrence plot was applied as the baseline. To quantify the agreement, we derived the ratio of percentage recurrence from recurrence quantification analysis (RQA) according to a previous study [30]. RatioRR was calculated as the ratio of the range of percentage recurrence occupied by self-recurrence. RatioRR indicated that wherever the calculated correlation is closer to 1, the higher the coupling of the two signals. The RatioRR is briefly described in Fig. 4. All signals, including RRI, PPI and breathings, were normalized and resampled to 4 Hz to be analyzed by a personal computer. The coherence between the ECG-derived and PPG-derived respiratory signals during breathing tasks from ten subjects was analyzed to evaluate their relationships with cardiopulmonary coupling in the time domain. Figure 4 shows the coherence analysis results for one subject in the condition of NPB. As seen in Fig. 4a, a self-recurrence plot based on respiratory signals is used as the baseline. A RatioRR value of < 1 (see Fig. 4b, c) indicates that coherence was greater in the ECG-derived respiratory values than the PPG-derived ones.

Fig. 4
figure 4

Detail of the coherence analysis results at NPB for one subject: All signals, including RRI, PPI and breathing (using thoracoabdominal belts), were normalized and resampled at 4 Hz. Illustrative example of 50 s sample was shown on left side. Recurrence rate was presented as the percentage of black on the recurrence plot (right side). a Self-recurrence plot based on breathing signal was employed as the baseline. We found a correlation in the RatioRR of these recurrence plots between b ECG-derived respiration and c PPG-derived respiration

2.5 Statistical Analysis

To compare ECG-derived parameters with PPG-derived ones, within-subject analysis during the breathing task was used. Within-subject analysis assessed the significant changes in serial results in an individual [31]. RRI and PPI were determined during spontaneous breathing and controlled breathing (Phase I). RRI and PPI among the LF, RF, LT, and RT measured from each subject are compared by a Student’s t test, as shown in Fig. 5a. To compare HRV and PRV, a window with duration of 5 min was used. SDNN series were determined by using a window with a shift of 30 s. Each subject had 40 SDNN and SDPP. HRV and PRV were compared by the Student’s t-test, as shown in Fig. 5b. Obvious coherence was defined as a p-value ≤ 0.05; insufficient coherence was indicated by a p-value greater than 0.05; Bland–Altman analysis was used to determine the 95% confidence intervals of these differences [23]. To compare HRV determined via PRV with controlled breathing, series of SDNN derived from RRI, and SDPP derived from PPI were assessed between the data from spontaneous breathing (resting baseline) and the ones during controlled breathing. Values of RatioRR between the two different measurements were calculated via RQA. A ratio similar to 1 was defined as coherence with respiration. Each parameter and statistical value were calculated by Mathworks MATLAB R2008a (Mathworks, Natica, MA, USA) (Table 1).

Fig. 5
figure 5

Tachograms of RRI and PPI from either limb were obtained via the peak detecting algorithm. Two tachograms with few subtle differences are presented. a The time length of the PPI and RRI series analyzed was 5 min. The data win consists of segments sampled from RRI of healthy volunteers. b Series of SDNN between PRV and HRV was also calculated using a window with a 30-second shift (illustrating win and st). Series of SDNN and SDPP were calculated using Student’s t-test. P < 0.05 was considered statistically significant, as an indicator of good coherence

Table 1 The controlled breathing task indices definitions

3 Results

3.1 Comparisons of HR, PR/HRV and PRV

HR and PR were compared in the breathing tasks, including spontaneous breathing and controlled breathing. For between-subjects analysis, Table 2 shows statistical comparison results of ECG-derived HR and PPG-derived PR from each limb. Good agreements and significant differences were observed between HR and PR in two types of tasks. For within-subjects analysis, Fig. 6a shows that the percentage of differences between HR and PR was almost less than 10%, which demonstrated that the differences were not significant in the breathing tasks. Obvious coherence was observed between PR and HR in both the resting and controlled breathing tasks.

Table 2 Comparison of measurement results between ECG-derived RRI and PPG-derived PPI from each limb
Fig. 6
figure 6

Comparison of RRI and PPI between the spontaneous breathing and controlled breathing techniques. Within-subject analysis of the results of a HR and b HRV. LF: Left finger, RF : Right finger, LT : Left toe, RT : Right toe. The red color bar indicates percentage difference between monitoring derived from ECG and PPG

HRV and PRV were compared in all the breathing tasks. For between-subjects analysis, Table 3 shows statistical comparison results of ECG-derived HRV and PPG-derived PRV from each limb. Obvious agreements were observed between HRV and PRV in resting tasks, but significant differences were observed between HRV and PRV in breathing tasks. For within-subjects analysis, Fig. 6b shows that the percentage of differences between HRV and PRV was almost higher than 80%, which demonstrated that the differences between HRV and PRV were significant in the breathing tasks. PRV and HRV indices were different significantly with breathing manipulation. Therefore, PR may be an acceptable surrogate for HR with breathing manipulation, but PRV is not an acceptable one for HRV with the manipulation.

Table 3 Comparison of measurement results between ECG-derived SDNN and PPG-derived SDPP from each limb

3.2 Impact of HRV on Breathing Manipulation

Data from lead II of ECG were analyzed during the breathing tasks. Figure 7 shows results from the analysis of HRV and PRV via SDNN and SDPP. The differences of impact on HRV and PRV on controlled breathings between the young group and senior one were not significant. The mean SDNN of HRV is similar to that of PRV in both groups, as shown in Fig. 7a–d. The mean SDNN of HRV at SDB was 1.2–1.6 times greater than that at resting breathing. The mean SDNN of HRV at RSB was 0.5–0.7 times greater than that at resting breathing. The mean value at SDB was greater than that at the other controlled breathing tasks. The mean value of SDNN at deep breathing was greater than that at shallow breathing during rapid and slow breathing tasks. The results from PRV were similar to those from HRV. Results from the breathing tasks showed that the frequency-dependent changes on HRV have more impact than volume-dependent changes in this study. We also noted that slower breathing frequency has more impact on HRV than the rapid frequency, and the deep volume has more impact on that than the shallow volume.

Fig. 7
figure 7

Variability in heart rate amplitude during each breathing task. Values are presented as the ratio of mean of SDNN of healthy subjects at spontaneous breathing and controlled breathing (Phase I). Results of a HRV and b PRV in the young group. Results of c HRV and d PRV in the senior group

3.3 Comparison of ECG and PPG by Cardiopulmonary Coupling

Breathing signal data were collected via chest wall motion sensor. Lead II of ECG and PPG of a left or right finger were analyzed simultaneously during the breathing tasks. The bar chart of RatioRR with all groups shows that the RatioRR of HRV is higher than that of PRV; thus, the coupling results from HRV are superior to PRV. As shown in Fig. 8a there is better breathing correspondence with ECG than PPG, particularly for the senior group (see Fig. 8b) with more differences than the young group (see Fig. 8c).

Fig. 8
figure 8

Results of RatioRR between ECG-derived and HRV-derived parameters during each breathing task. Values of RatioRR were presented as mean ± SD in a all groups, b the young group and c the senior group

4 Discussion

To date, this has been the only study to assess the coherence of heart period data derived from ECG and PPG based on breathing frequency and breathing volume of respiratory analysis by within-subject analysis.

This was achieved by comparing ECG- and PPG-derived parameters by the Student’s t-test, and the ratio of the PR range. In this study, ECG-derived HR and PPG-derived PR were compared in the breathing tasks, including spontaneous and controlled breathings. As expected, the results of PPG-derived PR were consistent with that of ECG-derived HR recoded in the breathing interval. We found that the PPG-derived PR from either limb was an acceptable surrogate of ECG-derived HR, as reported in the literature [10, 11, 24, 33]. However, no obvious coherence appeared in spontaneous breathings. This may be due to noise from the amplitude of heart rate oscillations without breathing manipulation.

The most obvious evidence was that the breath frequency (~ 0.2 Hz) was predominantly detected from HRV of normal subjects during resting. Furthermore, the shifts of breathing frequency in HRV during breathing manipulation in this study also demonstrated the impact of respiration on HRV. Hence, it is important to consider breathing state, including frequency and tidal volume, in HRV analysis and interpretation. Most studies that consider the impact of respiration on HRV only discuss either breathing frequency or tidal volume. In this study, breathing frequency and volume were discussed together. The results showed that the SDB pattern had the greatest impact on HRV and was able to change physiological parameters, such as blood pressure, which may be largely responsible for the differences [11]. When comparing our results with previous studies [10,11,12, 24, 32] on the impact of breathing manipulation on the normal variation of HRV, we can confirm that both SDNN and RatioRR in the time-domain parameters are more appropriate to analyze the impact of breathing frequency on HRV during breathing manipulation. Furthermore, an interesting finding of our study was the impact of the parameters on HRV, which was frequency > volume > mind, in sequence.

Breathing frequency should affect the results of HRV and PRV measures [33]. Schäfer et al. (2013) [11] investigated many studies that have explained why PPG-derived PRV is not equivalent to ECG-derived HRV. Wong et al. (2012) [10] compared PRV variables with HRV parameters on healthy subjects and showed that PRV exhibited highly significant coherence between all HRV measures and the corresponding PRV measures of both hands. However, differences between PRV and HRV have also had been demonstrated in other studies. For example, the conclusions of a previous study [34] clearly demonstrated that respiratory pulse rate does not reflect respiratory heart rate precisely in standing subjects, and patients with low HRV. These studies have proven that physical or mental state and even body posture during PRV measurement may affect the results [35]. Hence, we analyzed heart rate variability using ECG and PPG simultaneously to assess their coherence via within-subject analysis. HRV and PRV were compared in all the breathing tasks. In addition, the fact that the differences between HRV and PRV are significant may attributable to the sensitivity of PRV parameters to pulse transients and artifacts in the breathing interval [36]. Therefore, in view of this paper, the measurement results in PRV would not be replaced in HRV.

We also analyzed the coherence of cardiopulmonary coupling between PPG-derived and ECG-derived parameters to evaluate the impact of breathing manipulation. The results from all groups showed that RatioRR from HRV was higher than that of PRV. This indicated that the coupling result of respiratory analysis from ECG-derived HRV is superior to that of PPG-derived PRV. However, the actual physiologic meaning of HRV is not clear, particularly at very low frequency, which may suggest that the impact is associated with the surrounding soft tissue during pulse transfer. If PRV was used to replace HRV, the results of HRV will be affected by other factors to an unknown extent, as the impact of peripheral arteries on HRV remains unknown [37]. The differences in vessel status would lead to varying impact on the paths of pulse transmission. Therefore, many studies have suggested that HRV is somewhat overestimated by PRV [11]. The coherence between PRV and HRV would be impaired if subjects were undergoing physical activity or mental stress [35]; therefore, PPG-based devices are not acceptable alternatives for ECG in HRV analysis.

5 Conclusion

This study utilized the time-domain estimation method to investigate the coherence between HRV and respiration which parameters were both derived from ECG and PPG of healthy subjects under the circumstances of controlled breathing. Coherence analysis was used to assess the results. Respiratory fluctuations affected signals from pulse wave more than those from ECG. The velocity of the pulse wave could change because of cardiac output and varying aortic transmural pressure during mechanical breathing manipulation. Some studies have also demonstrated that respiratory pulse rate cannot precisely reflect respiratory heart rate in standing subjects and patients with low HRV. Therefore, we proposed that HR modulation should be considered, and ECG signals are more precise than PPG wave signals. Because of the opposing opinions, there is no conclusive consensus on whether or not the PRV of either hand can serve as a surrogate of HRV. The principal conclusion of this study is that PPG-based devices cannot be employed to detect HRV.