A novel approach for extracting pulse rate,respiratory rate and heart rate from photoplethysmogram

WANG Huimin，YANG Lu，LIANG Xingyu

(1. School of Information and Communication Engineering，North University of China，Taiyuan 030051，China； 2. Science and Technology on Electronic Test & Measurement Laboratory，North University of China，Taiyuan 030051，China)

Abstract：Photoplethysmogram (PPG)is a noninvasive method for detecting human cardiovascular pulse wave using optical technology.The PPG containing a lot of physiological information is from the MIMIC database.This paper proposes a combinatorial method of ensemble empirical mode decomposition (EEMD),cepstrum,fast Fourier transform (FFT)and zero-crossing detection to improve the robustness of the estimation of pulse rate (PR),heart rate (HR)and respiratory rate (RR)from the PPG.First,the PPG signal was decomposed into finite intrinsic mode functions (IMF)by EEMD.Because of its adaptive filtering property,the different signals were reconstructed using different IMFs when estimating different physiological parameters.Second,the PR was obtained by zero-crossing detection after rejecting low frequency IMFs containing artifacts.Third,IMFs with frequency between 1.00 Hz to 1.67 Hz (60 beats/min to 100 beats/min)were selected for estimating HR.Then,the frequency band that reflects the heart activity was analyzed by the cepstrum method.Finally,the respiratory signal can be extracted from PPG signal by IMFs with frequency between 0.05 Hz to 0.75 Hz (3 breahts/min to 45 breaths/min).Then the spectrum of signal was obtained by FFT analysis and the RR was estimated by detecting the maximum frequency peak.The algorithm has been tested on MIMIC database obtained from 53 adults.The experiment results show that the physiological parameters extracted by this integrated signal processing method are consistent with the real physiological parameters．And the computation load of this method is small and the precision is high (not larger than 1.17% in error).

Key words：photoplethysmogram (PPG);pulse rate (PR);respiratory rate (RR);heart rate (HR);cepstrum

0 Introduction

The theory of traditional Chinese medicine proves that the shape,magnitude and rhythm of pulse wave can reflect the physiological and pathological conditions of human body.Photoplethysmograph (PPG)is a widely used and fundamental sensor because it is cheap and easy to use.And it can help to extract many health-care parameters of interest[1].PPG signal consists of two components:baseline component and pulsation component.The baseline component varies slowly due to respiration and pulsation component usually has fundamental frequency,typically around 1 Hz,depending on heart rate (HR)[2].In order to obtain PPG in different tissue conditions,the blood volume of the tissue is usually used as the correction parameter.The schematic diagram of PPG measurement is shown in Fig.1.

Fig.1 Schematic diagram of PPG measurement

The alternating current (AC)is used to correct the sensitivity of the circuit system,and direct current (DC)is used to correct tissue blood content.Pulse information has been widely used in clinical detection,so the importance of extracting physiological parameters from PPG signals is self-evident.

The recorded PPG signals inherently contain respiratory information because the blood flow to the various body extremities may get affected by the movement of thoracic cavity during breathing[3].The existing methods of respiratory rate (RR)signal processing are as follows.The amplitude,intensity and frequency of PPG signals were described in Ref.[4] and used to estimate the RR values.Since noise can easily destroy the amplitude of PPG signal,the results obtained by this method are easily disturbed by noise.Similarly,Lazaro et al.[5]proposed a method based on the pulse width variability (PWV),and RR was measured by detecting the pulse apex,base,start and end points.However,this method is highly affected by artifacts.To reduce the effect of noises and motion artifacts,several time-frequency based approaches have been proposed.The short-time fourier transform was proposed in Ref.[6],and the time-varying correntropy spectral density function (SCD)was proposed in Ref.[7].However,the performance of the algorithm degrades as the epoch length decreases.The wavelet-based embedded algorithm was proposed in Ref.[8],but it is influenced by the selection of mother wavelet,the level of decomposition and performance reliability.Moreover,Ref.[9] used empirical mode decomposition (EMD)to extract respiratory signal from PPG signal.Aiming at the mode mixing problem caused by intermittency signal in the sifting process of EMD,ensemble empirical mode decomposition (EEMD)is presented.In this paper,EEMD is chosen to estimate physiological parameters.

Recently,EEMD is widely used for decomposing non-linear and non-stationary signal into finite intrinsic mode functions (IMF)[10].EMD acts essentially as a dyadic filter bank resembling those involved in wavelet decompositions[11].The EEMD denoising method outperforms the wavelet thresholding in term of efficiency[12].Therefore,we can purposefully and partially reconstruct the signal using the IMFs that correspond to the most important structures of the signal[13].Respiratory signal was obtained by reconstructing signal using low frequency IMFs.And when calculating pulse rate (PR)of PPG,the low frequency IMFs containing motion artifacts were removed.Then the instantaneous PR was obtained by zero-crossing detection.

Besides PR and RR,HR is another significant bio-marker that can be estimated from PPG for prognosis and diagnosis purposes[10].As for the estimation of HR from the PPG,the existing signal processing methods are the power spectrum[14]and wavelet transform (WT)[15].However,the cepstrum analysis method has higher spectral resolution[16].So,in this paper,IMFs with frequency between 1.00 Hz to 1.67 Hz were selected for reconstructing heart signal,then the cepstrum analysis method was proposed to estimate the HR.We explore the feasibility of using cepstrum to estimate HR for the first time.

In addition,EEMD is robust against motion artifacts and noises[17],therefore the proposed method can effectively and reliably extract PR,HR and RR from PPG signal.These parameters will contribute to the monitoring of chronic diseases and postoperative rehabilitation in the home and clinical settings.

1 BIDMC dataset

The BIDMC dataset containing signal and numerics was extracted from the much larger MIMIC II matched waveform database.The original data was acquired from critically-ill patients during hospital care at the Beth Israel Deaconess Medical Centre.PPG recordings were sampled atfs=125 Hz,from 53 adult patients with the age from 64 to 81.The length of PPG is 8 min.16 384(214)sampling points were selected to process.The PPG signal has two main characteristic points:the top of the principal wave and the top of the dicrotic wave.Fig.2(a)shows the original PPG signal.And partial enlargement drawing is shown in Fig.2(b).

Fig.2 Original PPG signal

2 Algorithm description

The analysis of PPG consists of three parts:the estimation of PR,HR and RR.Firstly,EEMD was performed on the PPG signal.The signal was reconstructed using different IMFs to analyze the characteristics of PR,RR and HR.Secondly,The IMFs containing artifacts were removed and the instantaneous PR signal was obtained by detecting the zero-crossings time of the PPG upstroke.Thirdly,IMFs with frequency between 1.0 Hz to 1.67 Hz (60 beats/min to 100 beats/min)were selected for estimating HR.Then,the frequency band that reflects the heart activity was analyzed by the cepstrum method.Finally,the respiratory signal can be extracted from PPG signal by using IMFs with frequency between 0.05 Hz to 0.75 Hz (3 breaths/min to 45 breaths/min).Then RR was obtained by detecting the maximum frequency peak within the respiratory frequency band.The PPG signal analysis flow chart is shown in Fig.3.

Fig.3 PPG signal analysis flow chart

2.1 EEMD analysis

The EMD has been proposed as an adaptive time-frequency data analysis method,which is mainly suitable for non-linear and non-stationary signal processing.To remove the mode mixing dilemma,an updated noise assisted version of EMD algorithm called ensemble EMD (EEMD)was proposed in Ref.[18].EEMD algorithm adds white noise of zero mean and unit variance to the signal and analyzes signal by using the average of ensembles trials of the EMD algorithm.The decomposition process of EEMD algorithm for any signalx(n)is as follows.

1)The normally distributed white noisew(n)is added to the original signalx0(n),which can be expressed as

x(n)=x0(n)+w(n).

(1)

2)The signal with white noisex(n)is taken as a whole,and then IMF components are obtained by using EMD algorithm.x(n)can be expressed as

(2)

wherenis the number of decomposed IMFs;di(n)is the IMF components;rn(n)is the residual term obtained from the decomposition.

3)Repeat steps 1)and 2)again and again.Each time a different normal distributed white noise series is added.

4)The final result is the integrated average of each acquired IMFs.

Flandrin et al.[19]proposed a method to construct filter banks based on the filtering characteristics of EEMD.Ignoring the residual term,the expression of the low-pass filter is

(3)

The expression of the high-pass filter is

(4)

The expression of the band-pass filter is

(5)

In this case,EEMD algorithm has fine filtering function.The pulse signal,heart information and respiratory signal are reconstructed by using different IMFs.

2.2 Estimation of PR

After PPG signal was decomposed by EEMD,the high-pass filter was selected as shown in Section 2.1.IMFs caused by artifacts and cardiac activity can be discarded.The zero-crossing method is required to obtain the PR from the PPG signal.Because the original signal is a sampled signal,there are almost no points with zero value.The method for extracting the signal frequency from the sampled data was proposed in Ref.[20].Based on that,this paper proposes a more accurate zero-crossing detection algorithm.

Let the original signal bex(n).If there are two points that satisfy

x(n)·x(n+1)≤0,x(n)≤0,

(6)

there must be a zero between the two points,so if the product of the two points is 0,the value ofx(n+1)is 0.Otherwise,the intersection of theX-axis and the line determined by the points ofx(n)andx(n+1)is the exact zero-crossing point.The starting point of this line isx(n)and the ending point isx(n+1).This straight line was divided intomparts.The greater them,the higher the accuracy,but the slower the calculation speed.Themselected in this paper is 100.Then,two points are selected from thempoints according to Eq.(6).And the average of these two points is used as the zero-crossing point,which refers to the coordinate value with zero amplitude when the signal changes from negative value to positive value.If the coordinate of the first zero-crossing point isk1and the second zero-crossing point isk2,then the period is

T=Ts(k2-k1),

(7)

whereTs is the sampling interval.The reciprocal of the period is ther1.According to this method,r2,r3,…,rnare found point by point to form the PR array,and the PR was obtained.

2.3 Estimation of HR

The range of human’s heart rate is 60 beats/min-100 beats/min.So,the band-pass filter was selected as seen in Section 2.1.IMFs with frequency between 1.00 Hz to 1.67 Hz were selected for estimating HR.Then,the frequency band that reflects the heart activity was analyzed by the cepstrum method.

There are various definitions of cepstrum,the complex cepstrum,real cepstrum and correlation function cepstrum.Here we use real cepstrum,which is defined as

y(n)=real(ifft(log(abs(fft(x(n)))))),

(8)

wherex(n)is PPG signal;in MATLAB,fft and ifft are positive and inverse fast fourier transform (FFT)function;real is function to returne the real part of complex number.If the original signal cycle isτand the amplitude ratio isa,cepstrum function is

(9)

It can be known from Eq.(9),on the cepstrum of the function,a series of pulses will appear atn=iτ(i=1,2,3,…).Evidently,we can recognize the frequency component of the signal on its cepstrum easily and extract the HR.

Below is the analysis of the computation load of cepstrum and WT.Cepstrum consists of the positive and inverse FFT.The computation load of WT and cepstrum are shown in Table 1.

In summary,cepstrum has higher localization accuracy and smaller computation load.

Table 1 Comparison of computation load

2.4 Estimation of RR

Besides synchronized changes in the heart,the PPG signal also includes respiratory-induced intensity changes.Therefore,the PPG signal regulated by respiratory activity can be used to obtain respiratory signal and becomes an alternative or indirect method for recording respiratory information[3].The usual RR for adult ranges from 16 breaths/min to 20 breaths/min.The IMFs with frequency below 0.05 Hz are considered as artifacts and that with frequency above 0.75 Hz are cardiac information[10].So,the band-pass filter was selected as seen in Section 2.1.The respiratory signal can be extracted from PPG signal by using IMFs with frequency between 0.05 Hz to 0.75 Hz.Then the signal spectrum is obtained by FFT analysis.The peak of spectrum is the frequency of respiratory,which is symbolized byrmax.The respiratory rateRcan be obtained by

R=60rmax.

(10)

3 Experiments and results

3.1 Decomposition of PPG signal using EEMD

The algorithm has been tested on data obtained from 53 adults in the BIDMC dataset[21].To save some space,PPG signal processing of an adult was shown in below.

The PPG signal was decomposed into IMFs by EEMD.The right column of Fig.4 shows the IMF components and left column shows the frequency of IMFs.

The dominant frequency of the IMFs is selected using FFT to detect the artifacts,cardiac and respiratory activity.As seen in Fig.4,the first several (5-8)IMFs with frequencies between 1.00 Hz to 1.67 Hz (60 beats/min to 100 beats/min)are selected for estimating HR;the middle (8-12)IMFs with frequency between 0.05 Hz to 0.75 Hz (3 breaths/min to 45 breaths/min)are selected for estimating RR;and the last several (13-14)IMFs with frequency below 0.05 Hz are considered as low frequency artifacts.When estimating the PR,the artifacts should be discarded.

Fig.4 IMFs decomposed from PPG by EEMD

3.2 Analysis of PR

Because the low-frequency components that change slowly were removed,the waveform had good positive and negative symmetry.The instantaneous PR was obtained by detecting the zero-crossings time of the PPG upstroke.The principal wave points and starting points of PPG signal were found and marked,as shown in Fig.5(a).Partial enlargement is shown in Fig.5(b).

Fig.5 PPG signal

The obtained instantaneous PR waveform is shown in Fig.6.

Fig.6 Instantaneous pulse rate waveform

The average of estimated PR is 77.5 Hz,and the real PR is 76.6 Hz.As known from the calculation,the error between the estimated PR and the actual PR is 1.17%.

3.3 Analysis of HR

The IMFs with the frequency of 1.00 Hz-1.67 Hz were selected to reconstruct the signal for estimating HR.Then it was analyzed by the cepstrum method.PPG signal is composite signal with five different frequency components in the range of 0.007 Hz-3 Hz,which are related to thermoregulation,blood pressure,autonomous nervous system,respiration and heart synchronous pulse[3].After obtaining the cepstrum,the frequency band of heart was analyzed.Then the frequency was calculated to obtain the heart rates.Fig.7 shows the cepstrum analysis of PPG.Fig.8 shows the frequency band that reflects the activity of the heart.The point marked in the figure is the peak of the heart activity frequency band,and the HR is the reciprocal of the time.

Fig.7 Cepstrum analysis of PPG

Fig.8 Heart activity frequency band

In this experiment,the max value point is 0.784 s,so the HR is the reciprocal of it,that is 1.28 Hz,which corresponds to 76.5 beats/min.The real HR is 76.7 beats/min.As known from the calculation,the error between the estimated HR and the actual HR is 0.26%.

3.4 Analysis of RR

The IMFs with the frequency of 0.05 Hz-0.75 Hz were selected to reconstruct the respiratory signal,as shown in Fig.9.Then the signal spectrum was obtained by FFT analysis.The RR was estimated by detecting the maximum frequency peak within the respiratory frequency band,as shown in Fig.10.For the purpose of verifying the accuracy of the respiratory rate obtained from the PPG using this method,the real respiratory signals from the BIDMC dataset were analyzed.Both the real respiratory signal and the PPG signal were collected at the same time.The real respiratory signals are shown in Fig.11.Accordingly,Fig.12 shows the spectrum of the real respiratory signal.

Fig.9 Estimated respiratory signal

Fig.10 Spectrum of estimated respiratory signal

Fig.11 Real respiratory signal

Fig.12 Spectrum of real respiratory signal

In this experiment,the maximum frequency peak is 0.336 Hz (in Fig.10).The RR is 0.336 Hz and it corresponds to 20.14 breaths/min.As seen in Fig.12,the maximum frequency peak of real respiratory is also 0.336 Hz.The estimated RR is consistent with the real RR.

4 Conclusions

The main innovation of this paper is the combined method of EEMD,FFT,cepstrum analysis and zero-crossing detection for processing physiological signal.The estimation of PR,HR and RR from PPG are accurate and reliable.

Characteristics of the signal in a certain frequency range are highlighted by using different IMFs to reconstruct the signal.The pure pulse signal was obtained by removing the IMF containing artifacts.Instantaneous PR was obtained by zero-crossing detection.In this paper,the zero-crossing detection algorithm has high precision,and the instantaneous PR obtained by this algorithm is accurate.IMFs with frequency between 1.00 Hz to 1.67 Hz were selected for estimating HR.Then,the frequency band that reflects the heart activity was analyzed by the cepstrum method.And the cepstrum has small computation load.The respiratory signal can be extracted from PPG signal by using IMFs with frequency between 0.05 Hz to 0.75 Hz.RR was estimated by detecting the maximum frequency peak within the respiratory frequency band.The accuracy of the combinatorial method was extensively validated by experiments.The obtained physiological parameters are consistent with the real parameters (not larger than 1.17% in error).Accurate and reliable extraction of the PR,HR and RR from PPG will improve the low-cost mobile-based healthcare systems.