Heart rate extraction from PPG signals using variational mode decomposition

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Available online at www.sciencedirect.com

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Original Research Article

Heart rate extraction from PPG signals using variational mode decomposition

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Hemant Sharma * Department of Electronics & Communication Engineering, National Institute of Technology, Rourkela 769008, India

article info

abstract

Article history:

Monitoring of vital signs using the photoplethysmography (PPG) signal is desirable for the

Received 19 June 2018

development of home-based healthcare systems in the aspect of feasibility, mobility,

Received in revised form

comfort, and cost-effectiveness of the PPG device. In this paper, a new technique based

27 September 2018

on the variational mode decomposition (VMD) for estimating heart rate (HR) from the PPG

Accepted 3 November 2018

signal is proposed. The VMD decomposes an input PPG signal into a number of modes or sub-

Available online xxx

signals. Afterward, the modes which are dominantly influenced by the HR information are selected and further processed for extracting HR of the patient. The proposed scheme is

Keywords:

validated over a large number of recordings acquired from three independent databases,

PPG

namely the Capnobase, MIMIC, and University of Queens Vital Sign (UQVS). Experiments are

Heart rate

performed over different data length segments of the PPG recordings. Using the data length

VMD

of 30 s, the proposed technique outperformed the existing techniques by achieving the lower

PCA

median (1st quartile, 3rd quartile) values of root mean square error (RMSE) as 0.23 (0.19, 0.31)

STFT

beats per minute (bpm), 0.41 (0.31, 0.56) bpm and 1.1 (0.9, 1.22) bpm for the Capnobase, MIMIC, and UQVS datasets, respectively. Since the shorter data length is more suitable for the clinical applications, the proposed technique also provided satisfactory agreement between the derived and reference HR values for the shorter data length segments. Performance results over three independent datasets suggest that the proposed technique can provide accurate and reliable HR information using the PPG signal recorded from the patients suffering from dissimilar problems. © 2018 Nalecz Institute of Biocybernetics and Biomedical Engineering of the Polish Academy of Sciences. Published by Elsevier B.V. All rights reserved.

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1.

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Accurate and reliable monitoring of various critical physiological vitals such as heart rate (HR), respiratory rate (RR) and blood pressure (BP) using simple, less-expensive and feasible

Introduction

non-invasive device is needed to facilitate home-based health observation. The photoplethysmographic (PPG) signal acquired from pulse oximetry is one of the powerful candidates to encourage the physiological telemonitoring and pervasive healthcare. The PPG signals are primarily used to measure the

* Corresponding author at: Department of Electronics & Communication Engineering, National Institute of Technology, Rourkela 769008, India. E-mail address: [email protected] https://doi.org/10.1016/j.bbe.2018.11.001 0208-5216/© 2018 Nalecz Institute of Biocybernetics and Biomedical Engineering of the Polish Academy of Sciences. Published by Elsevier B.V. All rights reserved. Please cite this article in press as: Sharma H. Heart rate extraction from PPG signals using variational mode decomposition. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.11.001

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blood oxygen saturation (SpO2), but they can also be used for non-invasive measurement of various physiological parameters including HR, RR, BP, and cardiac output [1]. Monitoring of these physiological vital signs from this simple, less-expensive, and handy device is beneficial not only in routine health supervision but also to support in the clinical diagnosis of various cardiorespiratory problems such as pneumonia [2], sepsis [3], and pulmonary embolism [4]. Moreover, efficient monitoring of HR from the PPG signal is helpful in fitness to regulate training load in exercises [5]. The PPG signals are obtained from pulse oximeters that apply the Beer–Lambert law for estimating the hemoglobin oxygenation [6]. In pulse oximeters, two light emitting diodes (LEDs) are used that emitting red (660 nm) and infrared (940 nm) lights to illuminate the tissues. A photodiode receiver is employed to measure the reflected light from the tissues. The oxygenated blood transmits the red light but absorbs the infrared light, and the deoxygenated blood acts in the inverted fashion [6]. Further, the intensity of detected light varies with each heartbeat due to change in the blood volume in tissues. These variations in blood volume over time are displayed using a PPG signal which consists of a pulsatile (AC) component and a constant (DC) component [7]. The pulsatile component shows the periodicity of PPG signal resembling the cardiac rhythm, and therefore the HR can be computed precisely from the PPG signal. Several algorithms have been developed by the researchers to improve the efficiency of HR estimation from the PPG signal [1,8–17]. Initially, PPG-based HR and RR estimation using the band-pass filter was proposed in [8–10]. Johansson et al. investigated the PPG signals recorded more than 8 h continuously from newborn infants for estimating HR based on the adaptive filtering [11]. An adaptive high-pass filter (Bessel type of 16th order) was used for estimating HR [11]. Later, Olsson et al. applied a high pass filter with a cut-off frequency of 1.67 Hz to the PPG signal for determining HR of more than 100 bpm [12]. The use of the filtering techniques for monitoring of HR from the PPG signal possesses the limitations of optimum realization of filter order and selection of the frequency band to be used in filtering. Also, if the HR lies outside the predefined frequency band, then estimation of HR using the filtering techniques will be erroneous. Later, more sophisticate time-frequency approach based on smoothed pseudo-Wigner Ville distribution (SPWVD) is employed to get HR from the PPG signals recorded during different motions of the finger [13]. The SPWVD technique is employed to overcome the motion artifacts affecting the pulse oximetry for improved estimation of HR [13]. Using SPWVD, the mean absolute error was reduced to 6 bpm from 16 bpm for the weighted moving average and 11 bpm for the fast Fourier transform (FFT) techniques [13]. However, an error (in HR) of 6 bpm is not tolerable in the clinical practice. In [15], authors used the empirical mode decomposition (EMD) with parametric power spectral analysis (based on autoregressive modeling) for estimating HR from the intrinsic mode functions (IMFs) of the PPG signal. The EMD technique suffers from the problem of mode-mixing which generates severe aliasing in the timefrequency distribution making the physical significance of IMF imprecise [17]. An algorithm based on the time-varying correntropy spectral density (CSD) for deriving HR and RR is

presented in [16]. In [16], each PPG recording is investigated using two window sizes (60 s and 120 s), and the cardiac frequency peak is detected in the range of 30 to 180 bpm. The CSD based algorithm performed effectively than the existing approaches, but its performance degrades when segment length is shortened as mentioned by the authors in [16]. In clinical applications, the short data length is more appropriate for estimating the physiological parameters (or vital signs). Recently, Motin et al. applied the ensemble empirical mode decomposition (EEMD) technique to the PPG signals followed by IMF filtering and the principal component analysis (PCA) to estimate HR of the patient [17]. The authors in [17] validated their algorithm on two independent databases and showed comparatively better results for their method on the epochs of duration 30 s each. The EEMD technique, however, overcomes the problem of mode-mixing in the EMD but it introduced another one that accepts the residual noise in input signal reproduction [18]. The presence of artifacts and low perfusion variations in the PPG signal severely affects the accuracy of HR estimated using filtering of the PPG signals in the predefined frequency band [19]. Also, most of the techniques in the literature used PPG epochs of duration not less than the 30 s for validation purpose, but the short-term recordings are more suitable for clinical applications. Therefore, further research needs to be carried out for an accurate and reliable HR estimation from the short data length epochs of the PPG signal. Recently, the variational mode decomposition (VMD), which is a fully intrinsic and non-recursive method to process the non-stationary signals is proposed [20]. This decomposition method has been used in different types of applications such as speech signal detection [21], sleep apnea detection [22], and seismic time-frequency analysis [23]. Most of the decomposition methods in the literature are limited by their algorithmic ad-hoc nature missing mathematical theory (EMD), recursive shifting in most approaches that prevents for backward error correction, the failure to proper handle with noise, the hard band restrictions (the wavelet techniques), and the selection of predefined filter bank boundaries (the empirical wavelet transform) [20]. In this context, the VMD method computes the related bands adaptively, and simultaneously estimates the corresponding modes, and thus properly balancing the error between them. Specifically, the variational model can address the presence of noise in the input signal efficiently. In VMD, each mode is directly updated in the Fourier domain which makes the constraint optimization problem very simple and fast [20]. Hence, the VMD method has become a popular tool to investigate the nonstationary signals for various applications including biomedical signal processing and speech signal processing. The VMD decomposes a non-stationary signal into various sub-signals or modes, and these modes show specific sparsity properties while reproducing the input signal. In VMD, each mode is compact around a center frequency with limited bandwidth, and therefore it can be utilized for extracting the desired component in the composite signal precisely. In this paper, a novel technique based on the VMD for estimating HR from the PPG signal is proposed. In the proposed technique, the VMD is used to decompose the PPG signal into various modes where each mode consists of energy, center frequency, and bandwidth different than the other modes. The

Please cite this article in press as: Sharma H. Heart rate extraction from PPG signals using variational mode decomposition. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.11.001

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modes which are dominantly modulated by cardiac rhythm are selected and further processed using a data-driven technique known as the PCA. The principal components (PCs) are ordered in such a way that the first PC holds most of the variations in the selected modes. As the selected modes are dominantly influenced by the HR signal, it is expected that the HR information of the patient will appear in the first PC itself. Next, the first PC is investigated using the short-time Fourier transform (STFT) to estimate HR of the patient. The experiments are performed over three independent datasets to validate the proposed PPG derived HR scheme. The rest of the paper is organized as follows. Section 2 describes datasets used for the experiments, proposed methodology, and performance measures. Section 3 presents the results of the proposed technique. Section 4 discusses the performance of the proposed algorithms. Finally, Section 5 concludes the work.

2.

Material and methods

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The proposed PPG derived HR technique is applied to three different datasets acquired from different subjects with dissimilar problems. The performance of the proposed approach is assessed by comparing the derived HR with the reference HR value computed using the simultaneously recorded ECG signal. This section describes the datasets used in this work followed by the proposed methodology accompanied by its illustration with a block diagram. The parameters used to measure the performance of the proposed technique are also discussed.

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2.1.

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The proposed PPG derived HR approach is validated through experiments performed over the recordings of three publicly available independent databases, namely the Capnobase, MIMIC and the University of Queens Vital Sign (UQVS) databases. The recordings of these databases are acquired from different subjects enduring from dissimilar health problems. For the experimental use, three different sliding time windows of duration 10 s, 15 s, and 30 s (without overlap) are used to segment the PPG recordings into three different length epochs. As a result, three HR values are estimated corresponding to three different data length epochs. The detailed description of the datasets used in this study is provided below.

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2.1.1.

Data

Capnobase database

The Capnobase database, available at CapnoBase.org [24], consists of different physiological signals including ECG, PPG, and respiration which are simultaneously recorded. These physiological signals are obtained from 59 children (median age: 8.7, range 0.8–16.5 years) and 35 adults (median age: 52.4, range 26.2–75.6 years) during the surgery and routine anesthesia at the British Columbia Children's Hospital and St. Paul's Hospital, respectively [25]. All signal recordings are acquired at a rate of 300 Hz using S/5 Collect software (Datex– Ohmeda, Finland). The entire data is divided into the test set and the calibration set. In this study, the test set containing the

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recordings from 42 subjects (29 children and 13 adults) collected during spontaneous breathing for the duration of 8 min [25], is used for the experimental purpose. Further, these recordings are segmented into different length epochs which are visually inspected so that the extracted epochs are uncorrupted.

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2.1.2.

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MIMIC database

The MIMIC database, available at Physionet.org [26], contains 72 recordings of concurrently recorded ECG, PPG, respiration, BP signals collected in intensive care unit (ICU) from 90 patients. These vital signals are obtained at a sampling rate of 125 Hz. This study requires simultaneous recorded ECG and PPG signals for the performance evaluation of the proposed approach. In these recordings, some of the recordings do not have either ECG or PPG signal or both. Also, in the visual inspection of remaining data, some recordings are found severely corrupted by noise. Therefore, a total of 25 recordings are selected from which 1800 segments of duration 60 s each are extracted manually which are visually uncorrupted. These extracted 60 s data segments are further fragmented into different length epochs of duration 10 s, 15 s, and 30 s (without overlap) for experimental purpose.

The UQVS database comprises different vital signals such as ECG, PPG, respiration, BP, and HR which are simultaneously recorded during 32 surgical cases of patients at the Royal Adelaide Hospital [27]. These cases comprised of 25 general anesthetics, 3 spinal anesthetics, and 4 cases of sedation [27]. The number of records in each case varies from 2 to 30 (approximate duration of 10 min each) with differing quality of both the ECG and PPG signals. The data were collected at a sampling rate of 100 Hz. In the visual inspection of UQVS database, a majority of the signals are affected by noise and artifacts. For this study, a record from each case is selected in such a way that the selected recording is comparatively less corrupted by noise. These records are further segmented into different length epochs for experimental use.

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2.2.

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2.1.3.

University of Queens Vital Sign database

Proposed methodology

In this paper, the VMD technique is used to decompose the PPG signal into different modes. In the decomposition, some of the modes are dominantly modulated by the cardiac rhythm which can be separated by the FFT based analysis of modes. The PCA technique is utilized on the selected modes to get the component representing the maximum variation in the selected modes. The first PC is analyzed using the STFT algorithm for estimating the HR frequency. The steps involved in HR estimation from the PPG signal using the proposed VMD based technique are illustrated using a block diagram shown in Fig. 1.

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2.2.1.

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Variational mode decomposition

The VMD is a fully intrinsic and adaptive algorithm that decomposes a given signal into a number of modes of different center frequency, energy, and bandwidth. Each sub-signal has a center frequency with limited bandwidth and possesses the specific sparsity upon reconstructing the input signal. As a

Please cite this article in press as: Sharma H. Heart rate extraction from PPG signals using variational mode decomposition. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.11.001

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Fig. 1 – The proposed adaptive PPG derived HR scheme using the VMD technique.

Fig. 2 – An example of VMD based decomposition of PPG signal into five different modes. (a) PPG signal (Capnobase dataset); (b)–(f) represent different modes; and (g)–(k) show the spectrums obtained using FFT of mode1 to Mode5, respectively.

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result, the VMD method can be utilized for extracting the desired component in the composite signal precisely. The VMD approach includes mainly three steps [20]: (i) computation of one-sided frequency spectrum pertaining to the analytical representation of the input signal by means of the Hilbert transform, (ii) each mode is multiplied with an exponential function in order to shift its frequency spectrum to the baseband where the frequency of exponential function (e
jvkt, where vk denotes the center frequency corresponds to kth mode) is fixed according to the center frequency of the mode, and (iii) bandwidth of the mode is estimated using the Gaussian smoothness applied to the demodulated signal [20]. In VMD method, initialization of the parameters including the total number of modes (K), quadratic penalty factor (a), mode center frequency (vk), time-step of the dual ascent (tau), the tolerance defined for convergence (tol), and DC part imposed (dc) is needed before decomposing the input signal. The initialization of these parameters depends on the application. A larger value of a in the VMD technique is not appropriate for catching the center frequencies of modes accurately. Contrarily, a smaller value of a will lead to trade-off for the robustness of extracted modes against noise [20]. Clearly, selection of an appropriate value of a can be advantageous in terms of achieving the best performance of the VMD-based approach. In the current study, the value of a is selected empirically as 300. The center frequencies (vk) of modes are uniformly initialized. The PPG signal is decomposed

into 5 mode or sub-signals (i.e., K = 5). The values of other parameters, namely tau, tol, and dc are chosen as 0, 10
7, and 2, respectively. Fig. 2 depicts different mode signals obtained from the PPG decomposition using the VMD and their frequency spectrums. It can be analyzed from the different frequency spectrums shown in Fig. 2 that some of the modes have a dominant peak in the HR frequency range. Therefore, these modes can be further processed to get the HR information.

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2.2.2.

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Mode selection using FFT

Upon decomposing the PPG signal using the VMD method, Mode1 represents the low-frequency information associated with the respiratory-induced modulation and noise as shown in Fig. 2(b). Therefore, in this work, Mode1 is not considered for further processing of HR estimation. The higher order modes are corresponding to the high-frequency components in the PPG signal. Some of these higher order modes are dominantly modulated by cardiac rhythm. These HR dominated modes can be used to obtain the HR information of the patient. To select such modes, the FFT algorithm is applied to each mode to obtain the frequency at which the maximum power is obtained. After computing the dominant frequency for each mode, those modes having the dominant frequency in the range of 0.6–5 Hz are selected and further processed for HR estimation. In the example shown in Fig. 2, Mode2 to Mode3 have a dominant frequency in the above defined range.

Please cite this article in press as: Sharma H. Heart rate extraction from PPG signals using variational mode decomposition. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.11.001

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Fig. 3 – The first PC (left) of the selected modes and its spectrum (right). Here, the first PC is computed from the selected modes of the example shown in Fig. 2 [the frequency axis in spectrum is mentioned to 20 Hz for better illustration of HR frequency peak].

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2.2.3.

The accuracy of estimated HR is determined by comparing it with the reference HR value (HRR) computed from the ECG signal. In ECG, first the R-peak locations are detected using the Pan–Tompkins's algorithm described in [30]. Next, the reference HR frequency is computed by taking reciprocal of the average value of time-intervals computed between successive R peaks. Finally, HRR is obtained by multiplying the reference HR frequency with 60.

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2.3.

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Principal component analysis

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The selected modes are further processed using the PCA technique. The PCA technique applied over the correlated modes results in different uncorrelated signals which are referred to as the principal components (PCs). The PCs are ordered in such a way that the first PC corresponds to the maximum variation in the selected modes. As the selected modes are dominantly influenced by the HR signal, the HR information of the patient will appear in the first PC itself. Therefore, the first PC is used to estimate HR of the subject. Fig. 3 depicts the first PC obtained using the PCA technique applied to the selected modes from the example shown in Fig. 2. In the frequency spectrum of the first PC as presented in Fig. 3, the frequency peak in the range of 0.6–5 Hz exhibit HR frequency of the patient.

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2.2.4.

HR computation

The first PC of the selected modes contains the cardiac rhythm information. The STFT algorithm is employed for estimating HR from the first PC assuming that HR remains constant for a shorter duration. The following steps are used here for HR computation.  The STFT of the first PC is obtained by computing 2048-point FFT on the sliding time-window of duration 5 s with 50% overlap. Hence, a new FFT is computed every 2.5 s.  Let L be the total number of time-windows for which the FFTs are computed. For ith time-window, the frequency ( fi) corresponds to the dominant peak in the HR range is computed.  A vector V is constructed containing L frequency values corresponding to L different time-windows (i.e., V = {f1, f2, . . ., fL}).  Next, the mean value of elements in the vector V is computed. This mean value itself is denoted as the mean HR frequency ( f HR) for a given PPG epoch. To obtain HR in bpm, the HR frequency fHR is multiplied with 60. Hence, HRD = fHR  60 (bpm), where HRD denotes the estimated HR value.

Performance measures

The estimated value of HR is compared with the reference value in order to assess the performance of the PPG derived HR technique. In this study, the performance of the proposed approach is evaluated based on mainly three parameters including the mean absolute error (MAE), average percentage error (PE), and root mean square error (RMSE). These three parameters are defined as [17,31]

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N 1X MAE ¼ jHRD ðnÞ
HRR ðnÞj; N n¼1

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PE ¼

N 1X jHRD ðnÞ
HRR ðnÞj

N n¼1

HRR ðnÞ

100%;

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vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X ½HRD ðnÞ
HRR ðnÞ2 ; RMSE ¼ t N n¼1

369 (3)

where HRD(n) and HRR(n) are the derived HR and reference HR values, respectively, for nth epoch, and N denotes the total

Please cite this article in press as: Sharma H. Heart rate extraction from PPG signals using variational mode decomposition. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.11.001

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Fig. 4 – Box-whiskers plots of derived and reference HR values for different datasets. (a, d, g) Correspond to EL = 10 s, (b, e, h) correspond to EL = 15 s, and (c, f, i) correspond to EL = 30 s [HRD and HRR denote the derived and reference HR, respectively, and EL = epoch length].

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number of epochs in a PPG recording. In addition to these parameters, the Pearson's correlation coefficient (PCC) is also computed to assess the agreement between the derived HR and reference HR values.

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3.

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For performance evaluation of the proposed technique, the experiments are performed over three different data length epochs of durations 10 s, 15 s and 30 s extracted from the recordings of three independent databases, namely the Capnobase, MIMIC, and UQVS databases. The estimated HR values are compared with the reference values calculated from ECG epochs of the same duration as of the PPG epochs. The performance measures are computed from the epochs of each recording. Therefore, the performance parameters which are presented in the successive paragraphs are mentioned in terms of the median value and interquartile range (1st quartile, 3rd quartile).

Results

Table 2 – The RMSE values computed for the Capnobase, MIMIC, and UQVS datasets. The parameter are shown as median value (1st quartile, 3rd quartile). Database

Capnobase MIMIC UQVS

RMSE (bpm) EL = 10 s

EL = 15 s

EL = 30 s

0.55 (0.41, 0.72) 0.68 (0.63, 1.01) 1.9 (1.7, 2.5)

0.37 (0.32, 0.45) 0.55 (0.51, 0.9) 1.5 (1.24, 1.9)

0.23 (0.19, 0.31) 0.41 (0.31, 0.56) 1.1 (0.9, 1.22)

Box-whiskers plot of HRD and HRR computed from different length epochs of the PPG and reference (ECG) signals for all three datasets are illustrated in Fig. 4 (Fig. 4(a)–(c) for Capnobase dataset, Fig. 4(d)–(f) for MIMIC dataset, and Fig. 4 (g)–(i) for UQVS dataset). In Fig. 4, the median value and interquartile range of HRD and HRR values are precisely identical for different length epochs of the Capnobase and MIMIC datasets, and are approximately matching in the case of UQVS dataset. The plots in Fig. 4 show that the derived HR ( HRD) is analogous to the reference HR (HRR) values.

Table 1 – The MAE and PE values computed for different data length epochs extracted from the Capnobase, MIMIC, UQVS datasets. The MAE and PE values are presented as median (1st quartile, 3rd quartile). MAE (bpm)

Dataset a

Capnobase MIMIC UQVS a

PE (%)

EL = 10 s

EL = 15 s

EL = 30 s

EL = 10 s

EL = 15 s

EL = 30 s

0.41 (0.33, 0.50) 0.54 (0.51, 0.75) 1.2 (0.96, 1.61)

0.29 (0.26, 0.34) 0.45 (0.41, 0.65) 1.19 (0.93, 1.37)

0.19 (0.15, 0.25) 0.33 (0.26, 0.39) 0.91 (0.81, 1.19)

0.48 (0.41, 0.68) 0.70 (0.58, 0.95) 1.87 (1.41, 2.20)

0.36 (0.30, 0.41) 0.63 (0.48, 0.73) 1.64 (1.4, 1.95)

0.24 (0.19, 0.30) 0.39 (031, 0.50) 1.38 (1.11, 1.78)

EL = epoch length.

Please cite this article in press as: Sharma H. Heart rate extraction from PPG signals using variational mode decomposition. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.11.001

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Fig. 5 – Comparison between the derived and reference HR values computed for different EL extracted from the Capnobase, MIMIC, and UQVS datasets. (a–c) Correspond to EL as 10 s, (d–f) correspond to EL as 15 s, and (g–i) correspond to EL as 30 s. The dotted line represents the case when HRD = HRR.

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The MAE and PE values are computed to assess the error between the derived and reference HR values. Table 1 shows the MAE and PE values computed for different data length epochs acquired from the three datasets. The median values of MAE and PE for the Capnobase and MIMIC datasets are found to be less than 1 bmp per subject in all three cases of epoch length (EL) as 10 s, 15 s, and 30 s. Also, in most of the cases of the Capnobase and MIMIC datasets, the MAE and PE values are even less than 0.5 bpm which shows a good agreement among the HRD and HRR values. In the case of UQVS dataset, the MAE and PE values, however, are comparatively larger specifically for the EL as 10 s and 15 s. Nevertheless, the proposed technique provided a satisfactory performance for the UQVS dataset also. Another quantitative assessment of the difference between HRD and HRR is carried out using the RMSE as shown in Table 2. In the experiments, the median values of RMSE for the Capnobase and MIMIC datasets are obtained significantly lower and even less than 0.5 bpm per subject in some cases. The RMSE value is obtained comparatively larger in the case of EL as 10 s and 15 s of the UQVS dataset, but the proposed algorithm provided effective results with EL as 30 s. It may also be highlighted here that the error between the derived and reference HR values decreases as the EL increases. Further, accuracy and reliability of the proposed PPG derived HR algorithm can be assessed by plotting the estimated HR values corresponding to their reference values as shown in Fig. 5. A dotted line mentioned in Fig. 5(a)–(i) signifies the best agreement between derived HR and reference HR. The PCC is also mentioned in each of the subplot of Fig. 5 that shows the correlation between derived and reference HR values. If the

PCC reaches to 1 that means HRD and HRR values are optimally correlated to each other and error tends to zero. It can be observed from Fig. 5 that, in most of the cases of EL for all three datasets, the PPC value is always greater than 0.95 and even approximately unity in some cases. These results demonstrate that the derived HR values are almost similar to the reference HR values even in the case of shorter data length epochs.

4.

Discussion

This study is focused on the development of an algorithm for estimating accurate and reliable HR using the PPG signals recorded from the patients suffering from unalike problems. For this purpose, a novel approach based on the VMD for estimating HR from the PPG signal is proposed. The VMD applied to the PPG signal produces different modes where each mode has a center frequency, bandwidth, and energy different than that of the other modes. In the proposed technique, the modes, which are dominantly modulated by the cardiac rhythm, are selected and further processed for estimating the HR value. Some of the selected modes in VMD appear due to amplitude noise lies in the HR frequency range. Consequently, estimation of HR from the signal obtained by only reconstructing the selected modes may be erroneous and this, in turn, will lead to degrading the preciseness of HR estimation. Therefore, in the proposed approach, the PCA is applied to the selected modes to separate the HR information. The PCA technique provides different uncorrelated components referred to as the PCs. In PCA, the PCs are a linear transformation of the selected mode signals with transforma-

Please cite this article in press as: Sharma H. Heart rate extraction from PPG signals using variational mode decomposition. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.11.001

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Table 3 – The median (1st quartile, 3rd quartile) values of RMSE computed for the Capnobase, MIMIC, and UQVS datasets using FFT applied over the first. Database

Capnobase MIMIC UQVS

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RMSE (bpm) EL = 10 s

EL = 15 s

EL = 30 s

0.72 (0.63, 0.84) 0.81 (0.72, 1.01) 2.96 (1.91, 4.9)

0.67 (0.58, 0.97) 0.77 (0.71, 1.1) 1.9 (1.52, 5.5)

0.65 (0.51, 0.96) 0.73 (0.69, 0.97) 1.39 (1.24, 2.8)

tion coefficients given by the eigenvectors of the covariance matrix. The PCs are ordered in such a way that the first PC corresponds to the maximum variation in the selected modes. Because the cardiac rhythm-related variation in the selected mode signals is significant, most of the variability is expressed by the first PCs. This allows computation of HR from the first PC itself. The higher order PCs describe subtle variation not described by the first PC. Additionally, in the proposed algorithm, Mode1 is not considered for further processing of HR estimation as it contains the information of other lowfrequency components including noise, respiratory movements, and artifacts. This further reduces the possibility of appearing substantial low-frequency movement artifacts and noise in the first PC. Subsequently, only those modes are processed using the PCA which are dominantly influenced by the cardiac rhythm; as a result, the first PC will contain the information of heart rate of the patient. Due to the non-stationary nature of the HR signal, estimation of HR using the FFT may provide imprecise results. Therefore, in this study, the STFT algorithm is applied to the first PC for determining the HR value assuming that the HR is constant for a small time window. For comparison purpose, the experiments are also performed with computing HR using the FFT algorithm applied to the first PC. Table 3 presents the median values of RMSE per

subject for different data length epochs extracted from three datasets used here. In Table 3, HRD is computed from the first PC using the FFT algorithm. Upon comparing the results shown in Tables 2 and 3, computation of HR using the STFTbased approach provided better agreement between the estimated and reference HR values than the case of the FFT algorithm. The performance of the PPG derived HR techniques also depends on the data length of the PPG signal to be used for estimating HR. It may be highlighted here that the data length to be analyzed is very important in various diagnosis processes including sleep apnea detection, sleep quality measurement and other respiratory related disorders [17]. Also, the shorter data length is more appropriate for the clinical practice. Previously, some studies in the literature [16,17] mentioned that the accuracy of their algorithm decreases as the data length decreases. As a result, most of the techniques in the literature are assessed over the epochs of minimum 30 s duration [15–17]. In the current study, the proposed VMDbased approach is tested over different length epochs of the PPG signal. Despite the increase in the error with decreasing the data length, the proposed approach shown efficacious performance in the case of shorter data length segments (e.g., EL = 10 s) as shown in Tables 1 and 2.

485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508

4.1.

509

HR estimation for very short data length

The performance of the proposed algorithm is evaluated over very short data length of 5 s also. For this purpose, the PPG signal is segmented into epochs of duration 5 s, and the HR value is estimated for each of the epoch. Now, for the computation of HR, the STFT of the first PC is obtained by computing FFT on the sliding time-window of duration 2 s with 50% overlap. Hence, a new FFT is computed for every 1 s. The median values of RMSE computed between the reference and estimated HR values are obtained as 0.92 (069, 2.49) bpm,

Fig. 6 – The VMD-based decomposition of noisy PPG signal (SNR = S5 dB). Here, two sine functions are added to generate artificial motion artifact noise and their frequencies are chosen arbitrarily as 0.5 Hz and 0.2 Hz. Please cite this article in press as: Sharma H. Heart rate extraction from PPG signals using variational mode decomposition. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.11.001

510 511 512 513 514 515 516 517 518

612 615 614 613 610 609 608 607 606 605 604 603 602 601 600 599 598 611

BBE 317 1–12

1.5 (1.2, 1.9) 1.9 (1.6, 3.8) 2.1 (1.7, 3.8) 1.8 (1.4, 2.2) 2.8 (2.3, 4.6) 3.2 (2.8, 4.7) 2.4 (1.9, 3.1) 3.5 (2.8, 5.8) 4.2 (2.9, 8.6) 1.5 (1.1, 2.2) 2.5 (1.6, 4.6) 2.5 (1.9, 3.7) 1.8 (1.4, 2.3) 3.1 (2.4, 5.9) 3.7 (2.7, 4.5) 1.9 (1.6, 2.7) 4.5 (2.8, 6.4) 5.1 (2.8, 7.9) 1.1 (0.9, 1.4) 1.7 (1.4, 3.1) 1.9 (1.4, 2.9) 1.3 (1.0, 1.6) 2.2 (1.8, 3.4) 2.6 (1.9, 3.1) EEMD-PCA PSD EMD UQVS

1.4 (1.1, 1.9) 3.0 (2.3, 4.6) 3.2 (1.9, 5.9)

0.9 (0.8, 1.3) 1.3 (1.2, 2.7) 1.5 (1.2, 3.0) 1.1 (1.0, 1.4) 1.45 (1.2, 2.5) 1.9 (1.4, 3.1) 1.1 (1.0, 1.2) 1.5 (1.2, 2.7) 2.1 (1.1, 3.3) 1.0 (0.9, 1.1) 1.4 (1.2, 1.7) 1.4 (1.0, 2.6) 1.2 (0.9, 1.2) 1.5 (1.0, 2.5) 1.6 (1.1, 3.2) 1.2 (0.9, 1.4) 1.6 (1.2, 2.2) 1.8 (1.2, 4.0) 0.93 (0.8, 1.0) 1.1 (1.0, 1.4) 1.2 (1.0, 2.0) 0.98 (0.8, 1.1) 1.2 (1.0, 1.8) 1.5 (1.1, 2.3) EEMD-PCA PSD EMD MIMIC

1.05 (0.9, 1.1) 1.2 (1.1, 1.7) 1.6 (1.2, 2.8)

0.74 (0.6, 1.1) 1.0 (0.9, 1.8) 1.1 (0.8, 2.0) 0.90 (0.8, 1.1) 1.0 (0.9, 1.8) 1.2 (1.0, 1.9) 0.97 (0.9, 1.3) 1.1 (1.0, 1.8) 1.6 (1.1, 2.5) 0.90 (0.6, 1.3) 1.1 (0.7, 2.0) 1.1 (0.7, 2.5) 0.92 (0.7, 1.3) 1.1 (0.8, 2.0) 1.2 (0.8, 2.1) 1.0 (0.8, 1.4) 1.2 (0.8, 2.1) 1.4 (0.8, 2.3) 0.65 (0.5, 0.9) 0.85 (0.7, 1.2) 0.89 (0.7, 1.8) 0.73 (0.6, 1.0) 0.87 (0.7, 1.3) 0.96 (0.8, 1.8) EEMD-PCA PSD EMD Capnobase

0.82 (0.7, 1.3) 0.94 (0.8, 1.3) 1.1 (0.8, 1.9)

EL = 15 s EL = 10 s

EL = 15 s

EL = 30 s

EL = 10 s

EL = 15 s

EL = 30 s

EL = 10 s

RMSE (bpm)

The proposed PPG-derived HR approach is also applied over the noisy PPG signals to track its performance in the case of noise. For this purpose, a simulated noise signal (including motion artifacts and white Gaussian noise) is added to the real PPG signals. The resultant signals (noisy PPG signals) are used for HR estimation using the proposed algorithm. To construct a noise signal, the motion artifacts are modeled using the lowfrequency sine functions [32] because the finger and hand motions in daily activity correspond to low-frequency components in the PPG. This analysis is carried out by selecting frequencies of the sine functions less than the cardiac range. The artificial motion artifact signal and white Gaussian noise are added to the real PPG signals to obtain the noisy PPG signals. The motion artifact noise added in the PPG signal is a lowfrequency signal, and it appears in the lower order modes of the VMD as it can be seen in Fig. 6. Here, Fig. 6 illustrates the VMD-based decomposition of PPG added with noise (signalto-noise ratio (SNR) =
5 dB). In the mode selection process using FFT, these low-frequency mode signals are left out, and the selected modes (Mode2 and Mode3) are processed using the PCA technique for determining the cardiac information. Therefore, the VMD itself does the job of extracting these lowfrequency motion artifacts in the lower order modes. From the experimental analysis, it is observed that the performance of the proposed approach does not degrade significantly in most of the subject recordings due to low-frequency motion artifacts added in the PPG signal for SNR =
5 dB. Further, the error between the derived and estimated HR values increases as the value of SNR decreases. However, the algorithm fails to estimate the HR accurately when the frequency spectrum of the motion artifact noise lies in the cardiac rhythm range. In that case, the spectrum of both the motion artifact noise and HR signal overlaps with each other. Subsequently, the first PC does not always reflect the HR information accurately due to the substantial magnitude of motion artifact present in the selected modes. Further, it must also be highlighted here from the experimental analysis that if the motion artifact signal is composed of many sine functions and the recorded PPG signal already contains the low-frequency motion artifact noise, sometimes the decomposition of PPG signal into five modes may not be sufficient as many of the modes may be corresponding to the artifact components. In this situation, none of the modes may be selected in the mode selection step for further processing required for HR computation. This problem can be resolved by appropriately selecting the

PE (%)

530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576

Performance in noisy conditions

MAE (bpm)

4.2.

Method

529

Dataset

0.84 (0.68, 2.24), and 3.11 (1.81, 6.29) for the Capnobase, MIMIC, and UQVS datasets, respectively. The median value of RMSE for the data length of 5 s has increased significantly as compared to that for the data length of 10 s. These results further support the observation of previous works that the error computed between the reference and derived HR values increases as the data length of PPG decreases. However, the short data length segments are more suitable in the clinical processing, but the large error in HR is not accepted for the diagnosis purpose.

Table 4 – Performance measures computed for different existing techniques. The parameters are shown as median value (1st quartile, 3rd quartile).

519 520 521 522 523 524 525 526 527 528

EL = 30 s

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Please cite this article in press as: Sharma H. Heart rate extraction from PPG signals using variational mode decomposition. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.11.001

9 577 578 577 579 578 577 580 579 578 577 581 580 579 578 577 582 581 580 579 578 577 583 582 581 580 579 578 577 584 583 582 581 580 579 578 577 585 584 583 582 581 580 579 578 577 586 585 584 583 582 581 580 579 578 577 587 586 585 584 583 582 581 580 579 578 577 588 587 586 585 584 583 582 581 580 579 578 577 589 588 587 586 585 584 583 582 581 580 579 578 577 590 589 588 587 586 585 584 583 582 581 580 579 578 577 591 590 589 588 587 586 585 584 583 582 581 580 579 578 577 592 591 590 589 588 587 586 585 584 583 582 581 580 579 578 577 593 592 591 590 589 588 587 586 585 584 583 582 581 580 579 578 577 594 593 592 591 590 589 588 587 586 585 584 583 582 581 580 579 578 577 595 594 593 592 591 590 589 588 587 586 585 584 583 582 581 580 579 578 595 594 593 592 591 590 589 588 587 586 585 584 583 582 581 580 579 578 596 595 594 593 592 591 590 589 588 587 586 585 584 583 582 581 580 579 596 595 594 593 592 591 590 589 588 587 586 585 584 583 582 581 580 579 597 596 595 594 593 592 591 590 589 588 587 586 585 584 583 582 581 580 597 596 595 594 593 592 591 590 589 588 587 586 585 584 583 582 581 580 598 597 596 595 594 593 592 591 590 589 588 587 586 585 584 583 582 581 598 597 596 595 594 593 592 591 590 589 588 587 586 585 584 583 582 581 599 598 597 596 595 594 593 592 591 590 589 588 587 586 585 584 583 582 599 598 597 596 595 594 593 592 591 590 589 588 587 586 585 584 583 582 600 599 598 597 596 595 594 593 592 591 590 589 588 587 586 585 584 583 600 599 598 597 596 595 594 593 592 591 590 589 588 587 586 585 584 583 601 600 599 598 597 596 595 594 593 592 591 590 589 588 587 586 585 584 601 600 599 598 597 596 595 594 593 592 591 590 589 588 587 586 585 584 602 601 600 599 598 597 596 595 594 593 592 591 590 589 588 587 586 585 602 601 600 599 598 597 596 595 594 593 592 591 590 589 588 587 586 585 603 602 601 600 599 598 597 596 595 594 593 592 591 590 589 588 587 586 603 602 601 600 599 598 597 596 595 594 593 592 591 590 589 588 587 586 604 603 602 601 600 599 598 597 596 595 594 593 592 591 590 589 588 587 604 603 602 601 600 599 598 597 596 595 594 593 592 591 590 589 588 587 605 604 603 602 601 600 599 598 597 596 595 594 593 592 591 590 589 588 605 604 603 602 601 600 599 598 597 596 595 594 593 592 591 590 589 588 606 605 604 603 602 601 600 599 598 597 596 595 594 593 592 591 590 589 606 605 604 603 602 601 600 599 598 597 596 595 594 593 592 591 590 589 590 607 606 605 604 603 602 601 600 599 598 597 596 595 594 593 592 591 607 606 605 604 603 602 601 600 599 598 597 596 595 594 593 592 591 590 608 607 606 605 604 603 602 601 600 599 598 597 596 595 594 593 592 591 608 607 606 605 604 603 602 601 600 599 598 597 596 595 594 593 592 591 609 608 607 606 605 604 603 602 601 600 599 598 597 596 595 594 593 592 609 608 607 606 605 604 603 602 601 600 599 598 597 596 595 594 593 592 610 609 608 607 606 605 604 603 602 601 600 599 598 597 596 595 594 593 610 609 608 607 606 605 604 603 602 601 600 599 598 597 596 595 594 593 610 609 608 607 606 605 604 603 602 601 600 599 598 597 596 595 594 611 610 609 608 607 606 605 604 603 602 601 600 599 598 597 596 595 594 611 610 609 608 607 606 605 604 603 602 601 600 599 598 597 596 595 612 611 610 609 608 607 606 605 604 603 602 601 600 599 598 597 596 595 612 611 610 609 608 607 606 605 604 603 602 601 600 599 598 597 596 613 612 611 610 609 608 607 606 605 604 603 602 601 600 599 598 597 596 613 612 611 610 609 608 607 606 605 604 603 602 601 600 599 598 597 614 613 612 611 610 609 608 607 606 605 604 603 602 601 600 599 598 597 614 613 612 611 610 609 608 607 606 605 604 603 602 601 600 599 598 615 614 613 612 611 610 609 608 607 606 605 604 603 602 601 600 599 598 615 614 613 612 611

BBE 317 1–12

10 610 609 608 607 606 605 604 603 602 601 600 599 616 615 614 613 612 611 674 617 675 617 676 618 677 618 678 619 679 620 680 621 681 622 682 623 683 624 684 625 685 626 686 627 687 628 688 629 689 690 630 691 631 692 632 693 633 694 634 695 635 696 636 697 637 698 638 699 639 700 640 701 641 702 642 703 643 702 704 644 703 645 704 646 705 703 647 704 648 705 649 706 650 707 651 708 652 709 653 710 654 711 655 712 656 713 657 714 658 715 659 716 660 717 661 718 662 719 663 720 664 721 665 722 666 723 667 724 668 725 669 726 670 725 727 671 726 672 727 726 673

biocybernetics and biomedical engineering xxx (2018) xxx–xxx

number of decomposition levels (K) or/and quadratic penalty factor (a) value in the VMD method.

4.3.

Comparison with existing techniques

The performance of the proposed technique is compared with the existing methods based on CSD [16], PSD [16], EMD [15], and EEMD-PCA [17]. The performance measures for the existing approaches are computed for different data length epochs of the three datasets. The median values of MAE, PE, and RMSE are presented in Table 4 for the different existing approaches. Upon comparing the performance results of different techniques, it can be observed that the proposed technique outperformed the PSD, EMD, and EEMD-PCA based methods for all three datasets. Also, the authors in [16] mentioned the limitation of the CSD-based algorithm that a minimum window length of 60 s is required to obtain reliable estimations of HR. It was also found by the experimental analysis that the CSD-based method performs very poorly when the data length is lesser than 60 s, and thus the results for the CSD-based approach are not presented in Table 4. If the performance results of the proposed technique are compared with that of the CSD as presented in [16], the VMD-based approach produces the smaller value of RMSE error even though the epoch length used for the validation in CDS-based technique was comparatively much larger than that of used in this study. Moreover, many other algorithms have also been developed for extracting HR information from the PPG signal [5,33–42]. In [5,33–40], the authors computed the HR value using the PPG signal recorded from wrist sensors during high-intensity exercise. In such conditions, the motion artifacts noise in PPG lies in the HR frequency range, thus making the estimation of HR from PPG difficult. The proposed PPG-derived HR algorithm is validated on the PPG signal recorded from the finger of resting subjects suffering from different problems. Therefore, the performance results of the proposed method cannot be compared with that presented in [5,33–40]. Also, the limitation of the proposed technique in the case of motion artifact noise present in the PPG has been discussed previously. In [41], the authors used their personal database for extracting HR information from the PPG of patients. The authors in work [42] used the facial PPG to determine the HR value during dynamic illuminance changes where the facial PPG is obtained by a camera. This study is limited to the PPG signal recorded from the finger of subjects at resting state and the VMD-based investigations on PPG signals recorded during exercise or intense physical activity for HR estimating will be addressed in the future work. Most of the PPG derived HR algorithms in the literature were validated using the recordings of either Capnobase dataset [15–17,25] or MIMIC dataset [17] or their personal dataset acquired from the healthy subjects [10,13]. The performance of any PPG derived HR approach can be analyzed effectively when the experiments are performed over a large number of recordings obtained from the patients with dissimilar problems. For this purpose, the performance of the proposed algorithm is assessed over three independent datasets. Based on the experimental results shown in Tables 1, 2 and 4, the proposed technique is seen to be performed efficiently in the multiple datasets. In the case of UQVS dataset, the proposed approach obtained relatively large errors than the case of

674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703

Capnobase and MIMIC datasets. A possible reason for this large error is that the recordings of UQVS database were highly corrupted due to noise and artifacts. However, for the experiment purpose, the selected recordings of UQVS database are visually verified for the noise and artifacts, but due to the quality for the signals in UQVS database, even the selected recordings were carrying significantly noise. Despite the quality of the recordings in UQVS database, the proposed technique provided satisfactory results. The VMD-based decomposition of an input signal requires prior selection of the input parameters in VMD as discussed in Section 2.2. Unlike to the EMD which is a data-driven technique, the VMD method requires an appropriate selection of the input parameters. Selection of these parameters also influence the performance of the proposed PPG derived HR technique. In this study, these parameters are selected empirically to obtain the best performance of the proposed technique over the multiple datasets. It may be discussed here that, in the PPG decomposition using VMD, some of the modes consist of low-frequency information of the input. An example of VMD-based PPG decomposition is shown in Fig. 2 where Mode1 corresponds to the low-frequency component of the input signal. As the respiratory signal is a low-frequency signal [43], the lower order modes of VMD applied over the PPG signal may provide the respiratory-related information of the subject. Estimation of the respiratory rate from the PPG signal based on the VMD method can be considered for future investigations.

5.

Conclusion 704

This paper proposes a novel algorithm based on the VMD for extracting HR from the PPG signal of the patient. In the proposed scheme, the PPG signal is decomposed into different modes using the VMD method. These modes are further processed using the PCA and STFT algorithms for estimating HR of the patient. The proposed approach is applied successfully over three independent datasets namely Capnobase, MIMIC, and UQVS. Experiments are performed over different data length segments (including 10 s, 15 s, and 30 s) of the PPG signals. The derived HR using the proposed technique is found to be analogous with the reference HR by achieving the lower values of MAE, PE, and RMSE, and the higher values of correlation computed between the derived and reference HR values. Despite the increase in the error with decreasing the data length, the proposed algorithm is provided effective performance in the case of shorter data length segments also. The performance results suggest that the proposed technique is more suitable than the existing algorithms (used for comparison purpose) for continuous and ambulatory monitoring of HR from the PPG signal recorded from the different subjects suffering from unalike problems.

Uncited references [28,29].

Please cite this article in press as: Sharma H. Heart rate extraction from PPG signals using variational mode decomposition. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.11.001

Q2

705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727

BBE 317 1–12 biocybernetics and biomedical engineering xxx (2018) xxx–xxx

727

references

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793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861

BBE 317 1–12

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Please cite this article in press as: Sharma H. Heart rate extraction from PPG signals using variational mode decomposition. Biocybern Biomed Eng (2018), https://doi.org/10.1016/j.bbe.2018.11.001